The asymptotic solution of the first dynamic boundary value problem of the theory of elasticity for two-layered orthotropic plate
Journal Title: Հայաստանի գիտությունների ազգային ակադեմիայի տեղեկագիր․ Մեխանիկա - Year 2011, Vol 64, Issue 2
Abstract
The first dynamic boundary problem of the theory of elasticity for two-layered orthotropic plate is considered. The solution of the problem is presented in the form of product of two types of functions. The first of them depends on three-dimensional coordinates and the second is the exponential function of the frequency of external influence and the time. By transition to dimensionless coordinates and displacements the singularly perturbed system of differential equations is obtained.This system is solved by the asymptotic method. The general asymptotic solution of the internal problem is found, which is completely defined as a result of satisfying of boundary conditions on the face of the plate. If the function which is present in the boundary conditions is a polynomial, the iterated process breaks and the mathematically exact solution of internal problem is obtained. The exact solutions for special cases of loadings are given.
Authors and Affiliations
Lenser Aghalovyan, Tatevik Zakaryan
Keywords
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