Regular and Chaotic Dynamics of Flexible Plates

Abstract

Nonlinear dynamics of flexible rectangular plates subjected to the action of longitudinal and time periodic load distributed on the plate perimeter is investigated. Applying both the classical Fourier and wavelet analysis we illustrate three different Feigenbaum type scenarios of transition from a regular to chaotic dynamics. We show that the system vibrations change with respect not only to the change of control parameters, but also to all fixed parameters (system dynamics changes when the independent variable, time, increases). In addition, we show that chaotic dynamics may appear also after the second Hopf bifurcation. Curves of equal deflections (isoclines) lose their previous symmetry while transiting into chaotic vibrations.

Contact Interaction of Plates and Beams Under the Influence of White Noise

“…It is proved that when taking into account several forms of oscillations, the reaction of a nonlinear model differs greatly from that of the calculation model with one degree of freedom. The article [19] shows that by taking into account the number of degrees of freedom we can significantly affect reliability of the results. The work [20] presents calculations of vibrations and radiation of sound of reinforced plates covered with a damping layer under harmonic load and load of the white noise type.…”