Chaotic analysis of Kelvin-Voigt viscoelastic plates under combined transverse periodic and white noise excitation: an analytic approach

摘要

Due to the use of materials with high structural damping in new applications and the role of plates as one of the basic elements of many engineering and interdisciplinary structures, the study of the stability of viscoelastic plates is very important in real conditions. In this article, the border curves of instability for a nonlinear Kelvin-Voigt viscoelastic plate under combined lateral periodic and white noise excitation are obtained analytically. Firstly, the governing equation of the plate is derived and then transformed into a nonlinear stochastic ordinary differential equation using Galerkin's method. Secondly, Melnikov's equation and its modified version in a stochastic sense are evaluated. At last, the border curves of instability for many types of plates and different variations of plate parameters and external excitations are obtained and drawn. The results show how and when the chaotic behavior changes by varying the plate parameters or fluctuating the intensities, magnitudes or frequencies of the external loads. It is shown that in the presence of white noise excitation the chaotic area become larger and this effect is larger at the frequencies far from the natural frequency of the corresponding linear system. It is also shown that under a combination of periodic and white noise excitations the chaotic behavior at low damping values might be completely different from the case there is only a periodic force.