Mode Shapes

The object of research is the development of a novel approach for the free vibration analysis of 3D curved cellular bridges using the Panel Element Method (PEM). The free vibration analysis of 3D curved cellular bridges was performed by the proposed Panel Element Method (PEM). The objective of this research is to examine the relationship between natural frequencies, mode shapes, and computational efficiency and the geometric configuration of curved bridge decks. Method. The PEM simulates curved cellular decks as assemblies of planar and non-planar panel modules based on a wide column analogy where two rigid arms joined by a flexible member mimic coupling between bending and torsion. Intrinsic dynamic properties are determined analytically using strain energy minimum principles, implemented in MATLAB for parametric analysis. Comparison with the Finite Element Method (FEM) assesses mode of vibration discrepancies and computational cost. Validation is done externally by solving the equations of equilibrium for bridge geometries with different curvature radius, support types, and cell shapes. Results. The PEM is verified against FEM by a variety of case studies for various bridge profiles and supports. It is found that the natural frequencies and mode shapes could be predicted accurately by the PEM with variation of less than 7% in fundamental modes compared to FEM. A high degree of computational efficiency by PEM is proved with over 90% savings in computational efforts without any accuracy loss. The paper concludes that the PEM is a good method for free vibration analysis that can achieve a compromise between accuracy and computational efficiency and is a possible substitute for the analysis of the dynamic behavior of curved bridge decks with various configurations.

In a framed-tube tall building, shear wall systems are the most efficient structural systems for increasing the lateral load resistance. A novel and simple mathematical model is developed herein which calculates the natural frequencies of such tall buildings. The analyses are based on a continuous model, in which a tall building structure is replaced by an idealized cantilever beam that embodies all relevant structural characteristics. Governing equations and the corresponding eigenproblem are derived based on the energy method and Hamilton's principle. Solutions are obtained for three examples; using the separation of variables technique implemented in MATLAB. The results are compared to SAP2000 full model analysis; and they indicate reasonable accuracy. The computed natural frequencies for structures 50, 60 and 70 storey buildings were overestimate 7, 11 and 14 percent respectively. The computed errors indicate that the proposed method has acceptable accuracy; and can be used during the initial stages of designing of tall buildings; it is fast and low cost computational process.

An analytical investigation has been conducted to examine the dynamic characteristics of a dual rotor system of an electromagnetic retarder. It focuses on the effects of mass imbalance in rotors and the system's inclination, which are essential for ensuring stability and optimal performance. The governing equations that describe the nonlinear dynamic response of the system under varying levels of unbalance were derived using the Lagrange method along with finite element modeling, which incorporates lumped mass and Euler beam models. The system's critical speeds and mode shapes are determined by solving an eigenvalue problem. The forced response analysis indicated that the rotational amplitude surpasses the transverse amplitude due to the overhung rotor configuration, which amplifies the centrifugal force as speed increases, influenced by different degrees of unbalanced mass. The amplitude of vibration is lower within the operational range; however, the system's tilt is critical and should be considered during the retarder design.

Nowadays, more extensive use of wood in buildings is of sustainable interest. Key point for environmentally friendly timber structures, appropriate to urban ways of living, is the development of high-rise timber buildings. Serviceability issues are nowadays the main limitation to the complete development of tall timber buildings. Among them, excessive vibrations due to human activities (such as walking or dancing) or external excitation (such as wind, or road traffic) induce annoyance and other discomforts. Amplitude and duration have been recognized as the two most governing parameters when it comes to human sensitivity to vibration [1]. Damping has therefore a large beneficial influence since it decreases both the amplitude of steady-state oscillations as well as the duration of transient oscillations. Despite its substantial effects, damping is however rarely prescribed in design codes or standards, and is at best included under the form of a constant whose origins remain unclear...

The torsional mode of the atomic force microscope (AFM) cantilevers has been widely used in various measurements where the high sensitivity of the AFM [1,2,3]. The approximated frequency and mode shape of the overhang-shaped cantilevers are usually used and give rises to several inconsistency between the calculated values and the experimental results. In this talk, we present the calculation of the frequency and mode shape of the width-varying cantilevers so that the frequency and modeshape of any higherorder mode could be obtained. This gives fruitful method for the experimentalist to choose the suitable geometric parameters for the cantilever targeting a specific frequency.

References:
[1] Le Tri Dat, Chi Cuong Nguyen, Nguyen Duy Vy and Amir F. Payam, Tuning the flexural frequency of overhang-/T-shaped microcantilevers for high harmonics, Japanese Journal of Applied Physics 62(10) 107002 (2024).
[2] Nguyen Duy Vy, Alessio Morelli, Vinh N.T. Pham, Dewar Finlay, Amir Farokh Payam, Dynamics analysis of width-varying microcantilevers: Interplay between eigenfrequencies, contact stiffness and interaction forces, International Journal of Solids and Structures 259, 112027 (2022).
[3] Le Tri Dat, Vinh N. T. Pham, Nguyen Duy Vy, Amir F. Payam, Frequency equation and semi-empirical mechanical coupling strength of microcantilevers in an array, Microscopy Research & Technique 85(9)
3237-3244 (2022).

This study investigates the dynamics of planar open-loop robotic systems with n-link elastic arms connected via revolute joints, focusing on multiple collision phenomena. The equations of motion are derived using the recursive Gibbs-Appell algorithm, and collisioncontact dynamics are modeled with a regulated approach. Transverse vibrations of the links are modeled using the Timoshenko beam theory, incorporating structural damping and air resistance for improved accuracy. The joints are assumed to be frictionless and backlash-free, while friction forces are considered at ground contact points. The system operates in two phases: flight and collision. During collisions, viscoelastic forces introduce stiff differential equations, requiring special handling due to the short collision duration. Accurate detection of collision onset and termination is achieved using a novel computational algorithm. To validate the model, the dynamic behavior of a three-link robotic system is simulated. Four distinct mode shapes are used to analyze their effects on the elastic deformation of the links. A comparative analysis highlights the influence of mode shapes on system behavior, demonstrating the framework's precision and efficiency in modeling and simulation.

This paper is concerned with wave propagation in a curved elastic layer with rectangular cross section. By applying the classical Lamé formulation of displacements, the exact solutions of equations of elastodynamics for such a layer in the plane and antiplane formulations are compared with their counterparts for a straight layer. Simultaneously, the classical Bernoulli-Euler theory for a curved beam is also used in the comparison and the static limit case of the Lamé decomposition is also investigated.

Since composite materials such as laminated composite plates have high specific strength and high structural efficiency, they have been used in many structural applications. It is therefore very important to make clear the vibration characteristics of the laminated plates for the design and the structural analysis. Especially, the vibration characteristics of the laminated plates with attached mass are essential. However, we cannot find the theoretical or experimental approaches for the free vibration of laminated plates with attached mass. In the present study, the experimental and numerical approaches are applied to the free vibration of cantilevered symmetrically laminated plates with attached mass. First, by applying the experimental modal analysis technique to the cantilevered symmetrically laminated plates with attached mass, the natural frequencies and mode shapes of the plates are obtained. Next, the natural frequencies and mode shapes of the cantilevered symmetrically laminated plates with attached mass are calculated by Finite Element Method (FEM). Finally, from the experimental and numerical results, the effect of the moment of inertia of the attached mass to the natural frequencies and mode shapes of the cantilevered symmetrically laminated plates are clarified.

This paper intends to study, investigate and optimize the effect of aspect ratio such as width and height on the dynamic behavior of a plate in terms of frequency and mode shapes.The research involves simulating and building plate models using ANSYS software. Modal analysis is adopted to predict the dynamic behavior of the plate. MATLAB code is developed to estimate the natural frequency values mathematically. Numerical results are compared with mathematically calculated frequency values. A total of 25 ANSYS models are built. The study has investigated up to eight dynamic modes shapes. The effects of the aspect ratios are presented in this article. Increasing the width can slightly increase the natural frequency values however increasing the thickness can significantly increase the values of the natural frequency. The range of the width values was from 40, 45, 50, 55, and 60 mm. The range of thickness values was from 10, 15, 20, 25, and 30 mm. This effect was seen to take place more in flexural (bending) modes. Flexural, Lateral, torsional, and buckling mode types were observed during the modal analysis. The rank of these modes for each model was dependent on the width and height of the plate.

This paper provides a comprehensive analysis, using nonlocal stress-driven integral theory, of the static behavior of a nanoscale beam of bidirectionally graded materials. After a brief explanation of the mathematical formulation of BDFGMs, the work done and strain energy expressions derived from the displacement field are discussed. Variational formulations and Hamilton's principle are used to develop the equilibrium equation. An analytical development of the nonlocal kernel for stress-driven integral theory and formulated governing equation which was nondimensionalized later. Explicit equations for displacement and moment are obtained by solving this equation using the Laplace transformation. Three different boundary conditions are examined, and differences in the maximum displacement with respect to the nonlocal parameter and the two material FGM parameters are displayed both visually and in table form. The results exhibit excellent agreement and provide a standard for further research when they are closely compared to the existing numerical data. This work contributes to the knowledge of BDFGMs under nonlocal effects generated by stress-driven integral theory and offers solutions that have been confirmed for further investigation.

The natural frequencies and mode shapes of bone are widely used in the diagnosis of bone fracture healing, bone remodeling, osteoporosis diagnosis, and implant-bone interaction. These characteristics can be estimated using numerical analysis and finite element modeling and measured and validated by modal testing of laboratory samples. Bone heterogeneity in finite element models affects its natural frequency. In this research, the effect of bone heterogeneity and density-elasticity relationships on the natural frequency of bone and the accuracy of their estimation have been investigated. A cow tibia bone was prepared and subjected to modal test. The experimental results of the modal test were compared with the results of the 3D finite element model created from the bone CT scan images. Inhomogeneity based on the proposed density-elasticity relationships was applied element by element (continuous) and regionally based on a tolerance (discrete) in the model. Comparing the results of heterogeneous models with experimental results shows that there is very little difference between the natural frequencies of discrete and continuous heterogeneous models. So, for the first five frequencies, a discrete heterogeneous model with 20 regions can predict the natural frequencies with an error of less than 2% with less cost and shorter time.

Based on the classical laminated plate theory, a variational approach for the study of the statical and dynamical behaviour of arbitrary quadrilateral anisotropic plates with various boundary conditions is developed. The analytical formulation uses the Ritz method in conjunction with natural coordinates to express the geometry of general plates in a simple form. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram-Schmidt procedure. The algorithm developed is quite general and can be used to study fibre reinforced composite laminates with symmetric lay-ups, which may have general anisotropy and any combinations of clamped, simply supported and free edge support conditions. Various numerical applications are presented and some results are compared with existing values in the literature to demonstrate the accuracy and flexibility of the present method. New results were also determined for plates with different geometrical shapes, combinations of boundary conditions, several stacking sequences and various angles of fibre orientation.

Resumo. A presente comunicação tem como objectivo apresentar o Reforço da Ponte sobre o Rio Soure, no Ramal de Alfarelos. O reforço desta ponte foi dividido em duas empreitadas. Numa primeira fase foi realizado o reforço e reabilitação estrutural da estrutura metálica do tabuleiro e foram introduzidos os montantes e desviadores do sistema de pré-esforço exterior que faz parte integrante da intervenção na ponte. Numa segunda fase foi realizado o reforço de fundações e a introdução de um sistema de pré-esforço exterior no tabuleiro.

This paper deals with the dynamic response of pump-turbine impellers. A pump-turbine impeller is a complex structure attached to a rotor and rotating inside a casing full of water with very small clearances between the rotating and the stationary parts. The dynamic response of this type of structures is very complex and it is very much affected by the connection to the rotor as well as by the added mass and boundary conditions. As a consequence its calculation presents several uncertainties. First, the dynamic response of pump-turbine impellers is introduced. Second an experimental investigation in a real impeller attached to the rotor and inside the machine was carried out. For this investigation, the impeller of an existing pump-turbine unit with an installed power of 110 MW and a diameter of 2.87 m was studied. For a better analysis of the experimental results a numerical model using FEM was also built-up. Frequencies and mode-shapes were identified numerically and experimentally and the characteristics of the structural response analyzed. To determine the influence of the rotor and supporting structures on the impeller response the results were compared with the ones obtained with the same impeller but suspended (non-connected to the rotor). Experimental and numerical simulation were also used for this case. The changes in the dynamic response due to the rotor connection were determined. Finally the results obtained are compared with the results from other pump-turbine impellers of different designs and general conclusions about the dynamics of this type of structures are given.

Designing and fabricating space frame chassis structure requires a certain set of knowledge especially in design, material selection and metal joining and fabrication which will result in rigid, sturdy and competitive chassis design. The outcome of the design will reflect the success of chassis especially if the chassis design is used for racing competition. This study focuses on the analysing the initial chassis design using mode shape analysis and the mode shape frequencies and characteristic produced from the analysis are studied. The modelling and the finite element model of the chassis structure are carried out using coordinate system in ANSYS Design Modeller and ANSYS APDL Version 13 respectively. The main objective of this analysis is to establish the natural frequency and mode shape characteristic corresponds to the natural frequency from the chassis structure to ensure that the ride comfort is beyond the unhealthy frequency range. Result from the study can be used to study the dynamic behaviour and to improvise the overall dynamic response of the chassis structure.

Because violins are traditionally hand-crafted using wood, each one is unique. This makes the design of repeatable experiments studying some aspects of its dynamic behavior unfeasible. To tackle this problem, an adjustable finite element (FE) model of a violin soundbox using the geometry and behavior of the “Titian” Stradivari was developed in this paper. The model is parametric, so its design and material properties can be varied for before/after comparisons in both the frequency and time domains. Systematic simulations revealed that f-holes set lower in the top, as seen in some Stradivari violins (e.g., Hellier, Cremonese), raise the frequency of the Hill (a feature in the bridge mobility); conversely, the higher set f-holes seen in some Guarneri violins (e.g., Principe Doria) reduces such frequency. This agrees with the widespread belief that the high-frequency response of Stradivari violins is stronger than Guarneri violins. Changes in the response of the system were quantified ...

Scour is the main cause of bridge failure in the United States and around the world. It involves the loss of soil from around bridge foundations due to fast flowing water. Monitoring bridge scour is challenging as it occurs underwater. A scour monitoring technique that uses accelerometers on the bridge piers and deck to provide real-time measurements of ambient vibration, from which scour-induced changes in the natural frequencies of the bridge may be monitored, has recently emerged. However, field validation of this method is difficult as scour is hard to predict-a monitoring system would need to be installed on a candidate bridge with no guarantee that natural scouring would occur within the trial monitoring period. Previous research on vibration-based scour monitoring has therefore been limited to laboratory-based experiments and numerical simulations. This paper presents a field study in which a bridge with preexisting scour was monitored throughout a repair program, which involved the controlled raising of the riverbed level (i.e. scour in reverse). Ambient vibration due to vehicle traffic over the bridge was monitored before, during and after the repair, using eight high-sensitivity accelerometers and a remote data acquisition system. The riverbed profile was measured with sonar scanning before and after the repair. Numerical modeling predicted a 3-5% change in the first two natural frequencies of the bridge due to the scour repair. However, the actual frequencies measured on site, derived using operational modal analysis (in this case, Frequency Domain Decomposition), showed a high degree of variation. Alternative structural response parameters (mean power spectral density at the modal peaks and the modal amplitude) were found to capture the change in behavior resulting from scour. The opportunities for using these alternative parameters as a measure of scour, and the challenges involved in using operational modal analysis for scour monitoring on a real bridge, are discussed in detail.

Failure in structure and machine component subjected to vibration generally takes place at natural frequencies at which amplitude of vibration becomes quite high. For failure analysis it is therefore important to understand the behaviour of component at natural frequencies. In this paper study of out-of-plane vibrations in square plate and tweeder by digital speckle pattern interferometry (DSPI) is studied and presented. For analysis of the DSPI fringes, speckle noise has to be removed. Removal of speckle noise in the speckle interferograms depends mainly upon texture and number of speckles present in the speckle interferograms. Our recent investigations show that a filtering scheme based on combination of average and Symlet wavelet filter and combination of Wiener and Symlet wavelet filter is effective in removing the speckle noise present in the speckle interferograms of vibrating square plate made of aluminum and tweeder surface made of diffused foil respectively. Experimental results are presented.

The effect of using an image fiber on the speckle fringe visibility in an endoscopic DSPI is analyzed here. An endoscope system was designed and developed, using image fiber as the speckle pattern image conduit, to work in the out-of-plane speckle interferometric configuration and experiments were carried out using a curved phantom tissue specimen as the test target. Experimental results obtained using the developed system are compared with that obtained using conventional DSPI system. To obtain a relative and quantitative comparison of the quality of the fringes obtained employing the two methods, an evaluation method that can give a quantified 'score' is proposed here.

According to increase of population in cities, tall buildings have been become interesting and fascinating for urban managers and engineers. Tubular frame structure is one of the most efficient systems in tall buildings under lateral load. The analysis of these structures usually involves considerable time and effort due to large number of members and joints. Several methods for evaluating shear lag and estimating stress of frame elements are presented recently. According to one of these methods, tube frame is assumed as a web and flange panel and then by considering deformation functions for web and flange frames and writing their stress relations as well as use of minimum energy basis, functions are presented for lateral and vertical displacement of the structure. Two relation groups suggested in this paper are capable of considering shear lag both in flange and web frames in the base of frame. The simplicity and accuracy of the proposed method is demonstrated through the numerica...

This paper intends to study, investigate and optimize the effect of aspect ratio such as width and height on the dynamic behavior of a plate in terms of frequency and mode shapes.The research involves simulating and building plate models using ANSYS software. Modal analysis is adopted to predict the dynamic behavior of the plate. MATLAB code is developed to estimate the natural frequency values mathematically. Numerical results are compared with mathematically calculated frequency values. A total of 25 ANSYS models are built. The study has investigated up to eight dynamic modes shapes. The effects of the aspect ratios are presented in this article. Increasing the width can slightly increase the natural frequency values however increasing the thickness can significantly increase the values of the natural frequency. The range of the width values was from 40, 45, 50, 55, and 60 mm. The range of thickness values was from 10, 15, 20, 25, and 30 mm. This effect was seen to take place more in flexural (bending) modes. Flexural, Lateral, torsional, and buckling mode types were observed during the modal analysis. The rank of these modes for each model was dependent on the width and height of the plate.

The main goal of this work was to study the dynamic behaviour of an existing bridge, the railway bridge of Canelas, under the action of high speed rail and two three-dimensionally modelled trains, the Alfa Pendular and the Double-TGV. The bridge is located on the railroad that connects Lisbon and Porto, near Aveiro, and consists on two tracks in two independent decks. This is a composite filler beam type bridge, with six 12 m simply supported spans. The short span railway bridges for high speed traffic are particularly interesting, because of their resonance issues, which cause high vibration levels. This kind of structure led to the development of new requirements for the verification of structural safety, track stability and passenger comfort, as well as the investigation of newer and more accurate methodologies of analysis. These methods lead to results that are closer to reality, since the regulations result too conservative in many structural design situations. Initially, this study consisted on a research of other papers on short span bridges, as a way to understand its singularities, and a detailed analysis of the regulation on the dimensioning of high speed railway bridges (Standards EN1991-2 and EN1990-AnnexA2). The approach considered the leading dynamic analysis methodologies, with an emphasis on moving loads numerical methodologies and vehicle-structure dynamic interaction, since those are applied in the case in study, describing the implementation of both in the combination of two software applications, ANSYS and Matlab. The setup of the calibrated model of the bridge, as well as the experimental tests that allowed that calibration, were described. A flexible body three-dimensional model of an Alfa-Pendular car, used in the vehicle-structure interaction analysis was presented. A stiff body three-dimensional numeric model, formed by rigid beam elements articulated with springs and dampers that simulate the suspensions, with concentrated loads in correspondence with the real vehicle masses in ANSYS, based on the geometrical and mechanical data from ERRI D214/RP9 was developed. Finally, dynamic analysis were performed, using the moving loads and interaction methods, for the circulation of Alfa-Pendular and Double-TVG, in terms of displacements and vertical accelerations. These were measured in different locations of both bridge and trains, and compared with the European standards verifications. It was also possible to compare the results obtained with both methodologies, and comment on the differences of the dynamic behaviour of the bridge and both trains, especially for resonant speeds.

Resumo. Nesta comunicação, apresenta-se o projecto de execução de um viaduto (viaduto principal mais viadutos de acesso) integrado no programa de exploração de uma mina de propriedade da empresa mineradora VALE S.A., para ser executado no Brasil. Estruturalmente, o viaduto principal é composto por uma superestrutura contínua de quatro vãos de grandes dimensões (97,50 m + 170,00 m + 170,00 m + 97,50 m) e será construído pelo método dos avanços sucessivos. O acesso das viaturas ao viaduto é feito lateralmente por dois viadutos mistos aço-betão simplesmente apoiados com 40,5 e 29,0 m de vão, sendo que um deles é de curvatura acentuada-R=40,0 m.

The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government 17 COSATI CODES FIELD GROUP SUBGROUP 18 SUBJECT TERMS (continue on reverse if necessary and identify by block number) Flexible Appendage, Finite Element Analysis, Mode Shapes, Equations of Motion 19 ABSTRACT (continue on reverse if necessary and identify by block number) This thesis details the design of the Naval Postgraduate School's Flexible Spacecraft Simulator and the first attempts at simulation and control of the model. The effect of flexible structures on the attitude control of spacecraft has been a topic of research for many years. Only recently has the technology to actually test models and theory on the ground been available. At the Naval Postgraduate School, an experimental testbed for research into this area has been constructed. This facility has a model of a satellite with a flexible arm floating on air pads to eliminate the effects of friction. A mathematical model of the system has been constructed and simulations of various maneuvers have been run, utilizing proportional-derivative (PD) control as well as a Linear-Quadratic-Gaussian (LQG) compensator. Results show that both PD and LQG work well for station keeping, but that the LQG compensator is better for slewing the arm.

One of the modal parameters that indicate damage in a structure are mode shapes. They can be used both for detection and localization of damage, since their shape is locally disturbed by the potential damage. Their another advantage, comparing with natural frequencies or damping factors, is fact that they are less sensitive to environmental factors like ambient temperature changes. The problem is that for small damages the changes in shape of mode are difficult to be detected. To improve this detectability authors decided to subtract the mode shapes of the damage structure from analogous mode shape of the structure in reference state. Additionally to even more improve the sensitivity of the method and allow for some automation of damage detection, the wavelet analysis was introduced.

In this paper, an analytical approach for free vibration analysis of four edges simply supported rectangular Kirchhoff plates is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for plate with simply supported boundary condition are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of a simply supported rectangular Kirchhoff plate. Subsequently, the eigenvalue problem for free vibration of plates is formulated and the equation of plate natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

A parametric formulation for preliminary design of tubed-system tall buildings is presented in which some optimality criteria and practical constraints are considered. Here, a minimum compliance optimization formulation, developed by other researchers, is applied to a framed-tube structure. The tube behavior is modeled as a cantilevered box beam. Independent variable in this problem is thickness of the box, and a formulation for its optimal value is proposed. The challenge in this research was treatment of the lower bound constraint on thickness in an analytical manner. To deal with this constraint, a critical height parameter is introduced, and the design domain is divided into two zones of constant thickness and constant curvature. This definition allows for computation of optimal thickness distribution along the structure through an analytic dimensionless equation. Most of the previously published papers in the field of tall structures are suitable for abstract analyses but not for design. In addition, most of them are computer-based. Considering these limitations, the current research presents a hand-calculation method for preliminary design, suitable for sensitivity analyses and parametric studies. As the presented formulations are dimensionless, they are applicable in any dimensional system. Different static loading patterns are considered; including the concentrated, uniform, triangular and quadratic forms. A numerical example is presented to demonstrate the ease of the proposed method in application, and the analysis results are presented by charts to validate the efficiency of it.

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The present paper emphasizes on the estimation of natural frequencies and mode shapes of a shaft supported by more than three bearings. In advent of this, a counter shaft of already developed experimental setup has been considered. The natural frequencies and mode shapes of counter shaft are deteremined analytically by adopting Holzer's method and the results obtained are then compared with the results of software based approach. By adopting the same method , Stresses in the shaft and amplitudes of rotors are also estimated. Based on the obtained data the generallised mathematical models have been formulated for the prediction of stresses in shaft and amplitudes of rotors. Significant independent variables which influence the phenomenon i.e development of stresses and amplitudes of rotor have been accounted in terms of a group of pie terms. These group of pie terms are accomplished with the help of dimensional analysis technique and they are used to formulate the mathematical models. In this paper the qualitative and quantitative analyses of the established mathematical models are also carried out.

Resumo. Nesta comunicação, apresenta-se o projecto de execução de um viaduto (viaduto principal mais viadutos de acesso) integrado no programa de exploração de uma mina de propriedade da empresa mineradora VALE S.A., para ser executado no Brasil. Estruturalmente, o viaduto principal é composto por uma superestrutura contínua de quatro vãos de grandes dimensões (97,50 m + 170,00 m + 170,00 m + 97,50 m) e será construído pelo método dos avanços sucessivos. O acesso das viaturas ao viaduto é feito lateralmente por dois viadutos mistos aço-betão simplesmente apoiados com 40,5 e 29,0 m de vão, sendo que um deles é de curvatura acentuada-R=40,0 m.

This paper discusses an analytical model developed to study the linear and nonlinear dynamic response of a four-story steel miniature building subjected to low-level and high-level shake table tests inducing nominally elastic and inelastic response, respectively. The analytical model was calibrated and validated against the results of the experimental program. A comparison of measured and calculated responses is made in the paper. Of particular interest, absolute floor accelerations were found more sensitive to high-frequency content than other response parameters such as base shear force and overturning base moment. The seismic performance of gravity-dominated beams is also examined in this paper. It was found that the cumulative nature of rotation demands in this type of beams should be considered in seismic design. The model is also used to observe differences in dynamic response of buildings when subjected to shake table tests with low fidelity in the reproduction of earthquake records.

The new cable-stayed bridge built for the North-South axis road of Bari in order to overpass the railway of RFI and Ferrotramviaria s.p.a. has been recently built and opened to the traffic. The bridge is 626 m long and the central cable-stayed bays have a total length of 225 m. They are supported by cables connected to a central upside down Y-shaped pylon. The peculiarity is that this column is about 60° rotated with respect to the axis of the bridge deck. A dynamic load tests was developed previously to open the bridge to conventional traffic. 26 piezoelectric accelerometers have been utilized in different positions of the cables-stayed bays to record the accelerations produced by environmental forces and by the impact produced by a loaded truck passing over a bump. Operational Modal Analysis has been applied by mean of Artemis software to determine the first fundamental frequencies and the mode shapes. The main frequency of this non-symmetric pylon is the main frequency of all the stayed bridge.

In this article, dynamic parameters (natural frequencies and mode shapes) of tall buildings that consist of framed tube and shear walls are obtained using a simple approximate method. The three-dimensional structure is replaced by an equivalent cantilever beam, considering both bending and shear deformations. On the basis of dynamic equilibrium, the governing differential equation of motion is obtained and converted to its corresponding weak form. B-spline functions are then utilized to approximate the weak form and to obtain the final matrix form of the problem. Finally, by applying essential boundary conditions, the natural frequencies and corresponding mode shapes are calculated. To demonstrate the accuracy of the proposed method, numerical examples are solved, and the results are compared with those obtained from SAP2000 computer analysis. The results show that the proposed method is efficient and accurate enough to be used in preliminary design.

Resumo. Apresenta-se uma metodologia de análise estocástica dos efeitos dinâmicos da passagem de grupos de peões sobre pontes pedonais, assumindo uma distribuição Gaussiana da frequência da passada, com valor médio em correspondência com frequências naturais da estrutura. As ferramentas computacionais desenvolvidas com base nesta metodologia foram aplicadas ao estudo do comportamento dinâmico de uma ponte catenária existente no Campus da FEUP, tendo os resultados obtidos por via numérica sido confrontados com valores previamente alcançados por via experimental, por forma a validar a formulação numérica desenvolvida.

In the current investigation numerical and radial basis function neural network (RBFNN) are adopted for diagnosis of fault in a cantilever composite beam structure present in form of transverse cracks. The presence of cracks a severe threat to the performance of structures and it affects the vibration signatures (Natural frequencies and mode shapes). The material used in this analysis is graphite fiber reinforced polyimide composite. The Numerical analysis is carried out by using commercially available software package ANSYS to find the relation between the change in natural frequencies and mode shapes for the cracked and un-cracked composite beam. Which subsequently used to the design of smart system based on RBFNN for forecast of crack depths and locations following inverse technique. The RBFNN controller is developed with relative natural frequencies and relative mode shapes difference as input parameters to calculate the deviation in the vibration parameters for the cracked dynamic structure. The output from the RBFNN controller is relative crack depth and relative crack location. Results from numerical analysis are comparing with experimental results having good agreement to the results predicted by the RBFNN controller.

This article presents an analysis of forced vibrations of a homogeneous cantilever beam using a vision method. Based on measurements, displacements of defined beam points have been determined as a function of time in directions perpendicular to and along the beam axis together with the trajectory of these points in the plane of the beam transverse vibrations. A model describing the displacement of the beam with a moving holder (kinematic excitation) is presented along with formulas defining motion of points in the plane of the beam transverse vibrations, which have been verified experimentally by recording beam vibrations using a specialised vision system.

A 64-story, performance-based design building with reinforced concrete core shear walls and unique dynamic response modification features (tuned liquid sloshing dampers and buckling-restrained braces) has been instrumented with a monitoring array of 72 channels of accelerometers. The responses of the building to ambient motions from ground or wind were recorded and analyzed to identify modes and associated frequencies and damping. Not unexpectedly, the low-amplitude dynamic characteristics are considerably different than those computed from design analyses. Nonetheless, these computed values serve as a baseline against which to compare future strong shaking responses. Such studies help to improve our understanding of the effectiveness of the response modification features at various levels of shaking, to evaluate the predictive capabilities of the design analysis tools and to improve similar designs in the future.

With the development of technology, human beings, who can easily cover long distances, have not been able to give up bicycles, although they are advancing in the field of transportation every day. The bike is still attractive as it does not require long and costly maintenance, is light and handy. The human-powered bicycle is a nature and environment friendly vehicle in addition to motorized transportation vehicles. In this study, in general a bicycle frame design suitable for daily and mountain roads, ergonomically designed according to human body size was designed and the stresses and elongations that occur in the analysis programs were examined.

The Proper Orthogonal Decomposition (POD) method is applied to the vibrations analysis of a metal plate. The data obtained from the metal plate under vibrations were measured with a laser vibrometer. The metal plate was subject to vibrations with an electrodynamical shaker in a range of frequencies from 100 to 5000 Hz. The deformation measurements were taken on a quarter of the plate in a rectangular grid of 7 x 8 points. The plate deformation measurements were used to calculate the eigenfunctions and the eigenvalues. It was found that a large fraction of the total energy of the deformation is contained within the first six POD modes. The essential features of the deformation are thus described by only the six first eigenfunctions. A reduced order model for the dynamical behavior is then constructed using Galerkin projection of the equation of motion for the vertical displacement of a plate.

Boundary characteristic orthogonal polynomials in two variables (BCOPs) have been built up over an elliptical domain occupied by a thin elastic plate. Half of the plate boundary, y ≤ 0, is taken simply supported while the other half is kept free. The orthogonal polynomial sequence (OPS) is generated from a set of linearly independent functions satisfying the essential boundary conditions of the problem and tabulated in advance, once and for all, for various values of the aspect ratio r = b/a of the plate with the desired precision. Free flexural vibrations of the plate have been examined by using these polynomials in the Rayleigh-Ritz method. Successive approximations have been worked out to ensure convergence. Comparisons have been made with known results in literature. Three-dimensional mode shapes and the associated contour lines have been plotted in some selected cases.

Rayleigh-Ritz method has been employed to obtain approximations to frequencies and mode shapes of circular plates with variable thickness. The boundary is either clamped, simply supported or completely free. The main distinguishing feature of the present investigations is that the thickness approximation is done by measuring thickness at a suitable set of sample points and then using interpolation to get the approximating polynomial. Thus, unlike other methods already available in literature where either linear or quadratic variation of thickness has been examined, here one can have a polynomial of arbitrary degree depending upon the number and locations of the sample points. The results have been tabulated in a large number of cases and three-dimensional mode shapes have been plotted for some selected cases. Comparison has been made with available results. A short tables are also given to depict the rate of convergence with the order of approximation.

Fibre-reinforced polymer composite has many uses in structural components that required high strength, stiffness, and damping capacity. Cross and quasi-laminated epoxy composites with and without nano Al2O3 were used in this investigation to determine flexural modulus, natural frequency, damping ratio, and mode shapes by using analytical, experimental, and numerical (ANSYS) methods. It was demonstrated that adding 2 % nano Al2O3 improved the flexural modulus and the damping ratio while decreased the natural frequency. Cross number 2 and quasi number 2 had the highest natural frequency for cross and quasi laminate groups which are equal to 23.5 Hz and 20.25 Hz experimentally, respectively. On the other hand, the higher damping ratio was achieved for cross number 1 with nano Al2O3 and quasi number 2 with nano Al2O3 for both cross and quasi laminates, which are equal to 0.707 % and 0.693 %, respectively. The flexural modulus and damping ratio are inversely related to each other. Howeve...

Fibre-reinforced polymer composite has many uses in structural components that required high strength, stiffness, and damping capacity. Cross and quasi-laminated epoxy composites with and without nano Al2O3 were used in this investigation to determine flexural modulus, natural frequency, damping ratio, and mode shapes by using analytical, experimental, and numerical (ANSYS) methods. It was demonstrated that adding 2 % nano Al2O3 improved the flexural modulus and the damping ratio while decreased the natural frequency. Cross number 2 and quasi number 2 had the highest natural frequency for cross and quasi laminate groups which are equal to 23.5 Hz and 20.25 Hz experimentally, respectively. On the other hand, the higher damping ratio was achieved for cross number 1 with nano Al2O3 and quasi number 2 with nano Al2O3 for both cross and quasi laminates, which are equal to 0.707 % and 0.693 %, respectively. The flexural modulus and damping ratio are inversely related to each other. Howeve...

Resumo. Apresenta-se uma metodologia de análise estocástica dos efeitos dinâmicos da passagem de grupos de peões sobre pontes pedonais, assumindo uma distribuição Gaussiana da frequência da passada, com valor médio em correspondência com frequências naturais da estrutura. As ferramentas computacionais desenvolvidas com base nesta metodologia foram aplicadas ao estudo do comportamento dinâmico de uma ponte catenária existente no Campus da FEUP, tendo os resultados obtidos por via numérica sido confrontados com valores previamente alcançados por via experimental, por forma a validar a formulação numérica desenvolvida.

Fibre-reinforced polymer composite has many uses in structural components that required high strength, stiffness, and damping capacity. Cross and quasi-laminated epoxy composites with and without nano Al2O3 were used in this investigation to determine flexural modulus, natural frequency, damping ratio, and mode shapes by using analytical, experimental, and numerical (ANSYS) methods. It was demonstrated that adding 2 % nano Al2O3 improved the flexural modulus and the damping ratio while decreased the natural frequency. Cross number 2 and quasi number 2 had the highest natural frequency for cross and quasi laminate groups which are equal to 23.5 Hz and 20.25 Hz experimentally, respectively. On the other hand, the higher damping ratio was achieved for cross number 1 with nano Al2O3 and quasi number 2 with nano Al2O3 for both cross and quasi laminates, which are equal to 0.707 % and 0.693 %, respectively. The flexural modulus and damping ratio are inversely related to each other. Howeve...

Resumo. Apresenta-se uma metodologia de análise estocástica dos efeitos dinâmicos da passagem de grupos de peões sobre pontes pedonais, assumindo uma distribuição Gaussiana da frequência da passada, com valor médio em correspondência com frequências naturais da estrutura. As ferramentas computacionais desenvolvidas com base nesta metodologia foram aplicadas ao estudo do comportamento dinâmico de uma ponte catenária existente no Campus da FEUP, tendo os resultados obtidos por via numérica sido confrontados com valores previamente alcançados por via experimental, por forma a validar a formulação numérica desenvolvida.

Most real-world phenomena exhibit nonlinear behavior. The behavior of steel leaf spring is nonlinear. It is having relatively high weight, and change in solid axle angle due to weight transfer specially during cornering of vehicle. That will lead to oversteer and directional instability under such situation it is very difficult for driver to control vehicle. These are some defect of metallic leaf spring so considering automobile development and importance of relative aspect such as fuel consumption, weight, ride quality, and handling development of new material is necessary in the automobile industry. In practice, engineering structures display a certain degree of nonlinearity, often due to a combination of nonlinear material properties, geometric effects, structural joints and nonlinear boundary conditions. Normally these effects are neglected by linearization in the intended working range. However, it becomes increasingly more important to take the nonlinear effects into account. ...