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.
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