Energy dissipation during vibrations of non-uniform composite structures. 2. Method of solution

Abstract

This paper describes the method of numerical solution to decaying vibration equations for heterogeneous composite structures. The system of algebraic equations is generated through Ritz method using Legendre polynomials as coordinate functions. First, real solutions are found. To find complex natural frequencies of the system, the obtained real natural frequencies are taken as initial values, and then, by means of the third-order iteration method, complex natural frequencies are calculated. The paper discusses the convergence of numerical solution of the differential equations describing the motion of layered heterogeneous structures, obtained for unsupported rectangular two-layered plate. Bearing layer of the plate is made of unidirectional CRP, its elastic and dissipation properties within the investigated band of frequencies and temperatures are independent on vibration frequency. The bearing layer has one of its outer surfaces covered with a layer of “stiff” isotropic viscoelastic polymer characterized by temperature-frequency relationship for the real part of complex Young’s modulus and mechanical loss factor. Validation of the mathematical model and of the numerical solution method performed through comparison of calculation results for natural frequencies and loss factor versus test data (for two composition variants of two-layered unsupported beam) has shown their good correlation.