黏弹性环形板的临界载荷及动力稳定性

利用线性黏弹性力学的Boltzmann叠加原理，在考察位移单值性条件的基础上，给出黏弹性环形板非线性动力学分析的初边值问题。通过Galerkin方法和引进新的状态变量，将其化归为四维非线性非自治常微分方程组，从而得到黏弹性环形板的四种临界载荷，同时考察了几何缺陷对黏弹性薄板临界载荷的影响。根据Floquet理论，得出黏弹性形板在周期激励下的线性动力稳定性判据。综合使用非线性动力学中的数值分析方法，研究了参数对黏弹性环形板非线性动力稳定性的影响。

CRITICAL LOADS AND THE DYNAMICAL STABILITY OF VISCOELASTIC ANNULAR PLATES

The initial-boundary-value problem for dynamical analyses of viscoelastic annular plates is given by means of the Boltzmann's superposition principle in the linear viscoelasticity on the basis of single valuedness demand on the displacement. It may be reduced to a four-dimensional nonlinear non-autonomous ordinary differential equations formulating the dynamical behaviors of an annular plate by using Galerkin method and introducing two new state components. Four types of critical loads of viscoelastic annular plates are obtained, and the influence of geometric imperfections on the critical loads of viscoelastic thin plates is considered. Stability criteria of viscoelastic annular plates subjected to periodic forces are achieved according to the Floquet theory. The numerical methods in nonlinear dynamics are applied to investigate the influence of parameters on the nonlinear dynamical stability of viscoelastic annular plates.