Many engineering structural elements are subjected during manufacture process or service to step ... more Many engineering structural elements are subjected during manufacture process or service to step excitation field. Vibration analysis of structural systems to step perturbation field has then become a vital requirement for modern structural engineering. The objective in this paper is to demonstrate that the hardening or softening nonlinearity affects some properties of viscoelastic dynamical systems under step loading field. The accuracy and reliability of the predicted performance is verified by comparison with numerical results. Phase diagrams are simulated to also verify the linear stability analysis according to the Lyapunov theory. Analytical and numerical results are found to be in satisfactory agreement. It is again found that the steady state forced response follows a power function of excitation rather than the linear law predicted by the viscously damped linear harmonic oscillator. So, it is shown that the stiffening or softening nonlinearity affects not only the transient...
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