Icase on Damping Mechanisms in Beams

Modal analysis is a worldwide used methodology that allows fast and reliable identification of system dynamics in complex structures. In the last decades several methods have been developed in quest to improve accuracy of modal models extracted from test data and to enlarge the applicability of modal analysis in industrial context. Damping in composite materials is an important parameter affecting the dynamic behavior of structures, controlling the resonant and near-resonant vibration levels.

Journal of Sound and Vibration, 2002

This paper deals with the characterization of damping in dynamical structural systems. In particular, the problem of how the modal damping ratios change with di!erent boundary conditions is addressed. It is shown that only Rayleigh-type damping is actually independent of boundary conditions and modal damping ratios can be easily converted from one boundary condition to another. This condition applies independently to continuous, discrete and discretized systems.

The paper deals with distributed-parameter modeling of oscillations with fliud-structure interaction of an elastic cantilever with ferromagnetic mass at its free end which Ues in field of a permanent magnet. The FEA is used to solve this class of problems.

2002

Damping properties are of significant importance in determining the dynamic response of structures, and accurate prediction of them at the design stage, especially in the case of light-weight, wind-sensitive buildings, is very desirable. Unfortunately, damping parameters can not be deduced deterministically from other structural properties and recourse is generally made to data from experiments conducted on completed structures of similar characteristics. Such data is scarce but valuable, both for direct use in design and for furthering research into the phenomenon and modelling of damping.

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.

Composite Structures, 1999

An improved dynamical model for vibration damping in composite structures is introduced to investigate the stacking sequence and the degree of anisotropy as a function of the vibration modes. Extensive investigation has been carried out from the ®tting of modal measurements with lowest residual errors to establish quasi-uniform mass damping models in terms of normal coordinates system. The analysis of the obtained results proves not only the eciency of the proposed model but also its applicability in any wide range of frequency spectrum of composites.

Journal of Vibration and Acoustics, 2015

Measurements are presented from a two-beam structure with several bolted interfaces in order to characterize the nonlinear damping introduced by the joints. The measurements (all at force levels below macroslip) reveal that each underlying mode of the structure is well approximated by a single degree-of-freedom (SDOF) system with a nonlinear mechanical joint. At low enough force levels, the measurements show dissipation that scales as the second power of the applied force, agreeing with theory for a linear viscously damped system. This is attributed to linear viscous behavior of the material and/or damping provided by the support structure. At larger force levels, the damping is observed to behave nonlinearly, suggesting that damping from the mechanical joints is dominant. A model is presented that captures these effects, consisting of a spring and viscous damping element in parallel with a four-parameter Iwan model. The parameters of this model are identified for each mode of the s...

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016

The inclusion of damping in the equations of motion of FEM-based structural models yields a complex (quadratic) eigenvalue problem. In this paper is presented a variant of a general method [4], [5] for real-space modal transformation of damped multi-degree-offreedom-systems (MDOFS) with non-modal (non-proportional) symmetric damping matrix. The method is based on the conjugated complex right eigenvectors of the system, normalized relative to the general mass matrix. After state-space formulation of the equations of motion a real modal transformation matrix is built by a combination of two complex transformations, which is the main advantage of the presented method. Analytically expressions for the modal transformation basis are developed be the aid of computer algebra software (MATLAB). Applying the suggested method to the special case of proportionally damped system, an analytical expression for the constant phase lag of the free vibration modes has been derived. The conversion of the developed general real transformation matrix into the modal matrix of the undamped problem is analytically proved by taking into account the synchronous free oscillations in this special case. The derived formulas for the modal transformation basis contain the real and the imaginary parts of the eigenvectors and the associated eigenvalues. A numerical examplevibration of a rotor blade of a wind turbine-demonstrates the performance of the presented modal decomposition method for the general case of nonproportional damped system. The damping matrix of this example contains structural and aerodynamic damping. The initial computation of the complex eigensolution of the FEM beam model in the presented example and all subsequent computations are done by the aid of the Symbolic Math Toolbox of MATLAB. The suggested procedure can be applied in structural systems containing different damping and energy-loss mechanism in various parts of the structure and also in structure-environment interaction problems, where a non-modal damping matrix is occurring.

The Oberst Beam Method (OBM) is widely used for the measurement of damping level of materials. This method is a classical method based on a multilayer cantilever beam which consists of a base beam and one or two layers of other materials. The base beam is almost always made of a lightly damped material such as steel and aluminum. If the Oberst Beam Method is to be used, it is essential to establish a very accurate measurement methodology.OBM is referenced in some standards and widely used in scientific studies, detailed information in the literature on how to perform a successful Oberst Beam experiment is very limited. This is the main subject that the paper aims to address. The analysis is based on a frequency response function measured between the imposed velocity at the center and an arbitrary point on the beam. Structural damping coefficient of the material under test can be deduced using classical formulations of the ASTM E756 standard for typical materials or using a finite element model for more complex cases. Keywords: Damping Coefficient, Frequency Response Function (FRF), Oberst Beam Method, Loss Factor.

This dissertation reports a systematic study on analysis and identification of multiple parameter damped mechanical systems. The attention is focused on viscously and non-viscously damped multiple degree-offreedom linear vibrating systems. The non-viscous damping model is such that the damping forces depend on the past history of motion via convolution integrals over some kernel functions. The familiar viscous damping model is a special case of this general linear damping model when the kernel functions have no memory.