Abstract

The relevance of the topic is determined by the search for the transcendental frequency equations that are reduced to algebraic and the influence of both boundary conditions at the edges of a rectangular plate and geometric and mechanical characters on the inherent oscillatory frequencies of rectangular flat elements is considered and the previous results for a rectangular plate whose material satisfies a viscoelastic model of Maxwell is generalized. When studying oscillatory processes in a solid deformable body, it is advisable to take the kernel of viscoelastic operators regularly, since only such operators describe the instantaneous elasticity and then the viscous flow, which is characteristic of deformable solids. Integro-differential equations with regular kernels are known to be equivalent to partial differential equations.

中文翻译：

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各向同性均质弹性板振动过程的求解

摘要

通过搜索简化为代数的先验频率方程来确定主题的相关性，并考虑矩形板边缘的两个边界条件以及几何和机械特性对矩形平面元件固有振动频率的影响对材料满足麦克斯韦粘弹性模型的矩形板的先前结果进行了推广。在研究固体可变形体中的振动过程时，建议定期采用粘弹性算子的核，因为只有这样的算子先描述瞬时弹性，然后描述粘性流体，这是可变形固体的特征。具有正则核的积分微分方程等效于偏微分方程。