TRANSACTIONS OF THE KRYLOV STATE RESEARCH CENTRE

Science journal

 
ISSN (print) 2542-2324 /(online) 2618-8244


Articles of The Transactions of KSRC








Dissipative properties of three-layered composite structures. 2. Solution method



Full text article ( in russian)

Year

 
2022

Issue

 
399

Volume

 
1

Pages

 
55-64

Caption

 
Dissipative properties of three-layered composite structures. 2. Solution method

Authors

 
Yartsev B., Ryabov V., Parshina L.

Keywords

 
solution method, Legendre polynomials, linear algebraic equations, damping, numerical solution convergence, validation, natural frequency, mechanical loss coefficient

DOI

 
10.24937/2542-2324-2022-1-399-55-64

Summary

 
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.
Subject matter 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 uni-directional 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.

Rubrics

 
Naval architecture

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ISSN (print) 2542-2324 / ISSN (online) 2618-8244

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