TY - JOUR

T1 - Methods for Modeling the Dissipative Characteristics of Layered Composites

AU - Рябов, Виктор Михайлович

AU - Ярцев, Борис Александрович

PY - 2024/9/1

Y1 - 2024/9/1

N2 - Abstract: The main methods for modeling the dissipative characteristics of layered composites are considered: the principle of elastic–viscoelastic correspondence and the energy method. Mathematical models of damped oscillations are given for layered anisotropic plates. A numerical procedure for solving the problem of damped oscillations of a three-layer monoclinic plate containing a two-stage method for solving a complex eigenvalue problem is described. It is noted that the energy method for modeling energy dissipation in the case of vibrations of layered composite structures is a special case of the method, based on the principle of elastic–viscoelastic correspondence. It is shown, that in addition to the classical formulation of the energy method, in which the terms of the energy-balance equation are approximately found according to their eigenforms and the vibrational frequencies of a conservative mechanical system, there is one more approximate method for calculating the dissipative characteristics of orthotropic composite structures. The advantages of this method are the possibility of using existing commercial software systems (Ansys et al.), which numerically implement the finite-element method, and the shortcomings are the need to be limited to the use of classical theories of thin-walled structures (Bernoulli–Euler, Kirchhoff–Love) to describe the deformation of composite structures. It is found that using the classical formulation of the energy method allows with high accuracy to predict the values of loss factors up to ηmax = 0.02. A further increase in the damping levels of the structure is accompanied by a decrease in the accuracy of the prediction.

AB - Abstract: The main methods for modeling the dissipative characteristics of layered composites are considered: the principle of elastic–viscoelastic correspondence and the energy method. Mathematical models of damped oscillations are given for layered anisotropic plates. A numerical procedure for solving the problem of damped oscillations of a three-layer monoclinic plate containing a two-stage method for solving a complex eigenvalue problem is described. It is noted that the energy method for modeling energy dissipation in the case of vibrations of layered composite structures is a special case of the method, based on the principle of elastic–viscoelastic correspondence. It is shown, that in addition to the classical formulation of the energy method, in which the terms of the energy-balance equation are approximately found according to their eigenforms and the vibrational frequencies of a conservative mechanical system, there is one more approximate method for calculating the dissipative characteristics of orthotropic composite structures. The advantages of this method are the possibility of using existing commercial software systems (Ansys et al.), which numerically implement the finite-element method, and the shortcomings are the need to be limited to the use of classical theories of thin-walled structures (Bernoulli–Euler, Kirchhoff–Love) to describe the deformation of composite structures. It is found that using the classical formulation of the energy method allows with high accuracy to predict the values of loss factors up to ηmax = 0.02. A further increase in the damping levels of the structure is accompanied by a decrease in the accuracy of the prediction.

KW - composite

KW - dissipative characteristics

KW - energy method

KW - modeling

KW - natural frequency

KW - oscillations

KW - principle of elastic–viscoelastic correspondence

UR - https://www.mendeley.com/catalogue/0e20fac1-f031-3924-bc1b-03759cc70bb0/

U2 - 10.1134/s1063454124700250

DO - 10.1134/s1063454124700250

M3 - Article

VL - 57

SP - 392

EP - 400

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -