We study unsteady elastic-diffusion vibrations of a rectangular isotropic Kirchhoff plate. The coupled elastic-diffusion multicomponent continuum model is used to formulate the problem. We are using the d’Alembert variational principle to obtain from the model the equations of longitudinal and transverse vibrations of a rectangular isotropic elastodiffusive Kirchhoff plate. The problem solution is sought in integral form. The kernels of integral representations are the Green’s functions. For their determination, the Laplace transform and expansion in double Fourier series are used. As an example, we consider the bending of a simply supported plate. The effect of bending on the diffusion processes in the plate is investigated.

我们研究矩形各向同性Kirchhoff板的非定常弹性扩散振动。用耦合的弹性扩散多组分连续体模型来表达该问题。我们使用d'Alembert变分原理从模型中获得矩形各向同性弹性扩散Kirchhoff板的纵向和横向振动方程。以整体形式寻求问题解决方案。整体表示的核心是格林的功能。为了确定它们，使用了双重傅里叶级数的Laplace变换和展开。例如，我们考虑一个简单支撑的板的弯曲。研究了弯曲对板中扩散过程的影响。