Диссипативные свойства трехслойных композитных структур. 2. Метод решения

Abstract

Object and purpose of research. This paper discusses a three-layered plate made up by two rigid anisotropic layers and soft isotropic medium layer of viscoelastic polymer. Each of the two rigid layers is an anisotropic structure formed by a finite number of arbitrarily oriented orthotropic viscoelastic composite layers. The purpose of this work is to develop a numerical solution method for decaying vibration equations of three-layered unsupported rectangular plates. Materials and methods. The system of algebraic equations is constructed as per Ritz method using Legendre polyno-mials as coordinate functions. The first step is to find real solutions. To find complex natural frequencies of the system, their initial values are taken as real natural frequencies thus found, with subsequent calculation of complex frequencies as per the method of third-order iterations. Main results. This paper discusses the results of convergence analysis for a numerical solution of differential motion equations with respect to an unsupported rectangular three-layered plate with transversally isotropic rigid layers. The material for these rigid lay-ers is unidirectional carbon-reinforced plastic (CRP) with elastic dissipation properties, within the investigated range of frequencies and temperatures, independent on its vibration frequency. For the soft isotropic medium layer of viscoelastic polymer, temperature-frequency curve governing the real part of complex elasticity modulus and mechanical loss coefficient is taken into account. Validation of the mathematical model and the numerical solution method, the comparison of calculated and experimental natural frequencies and mechanical loss coefficients for the two variants of three-layered unsupported plate has demonstrated their good correlation. Conclusion. This paper suggests and validates the numerical solution method for decaying vibration equations of three-layered unsupported rectangular plate made up by two rigid monoclinic layers and soft isotropic medium layer of viscoelastic polymer.