Abstract:
The main methods for modeling dissipative characteristics of layered composites are considered: the principle of elastic-viscoelastic correspondence and 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. It is noted that the energy method for modeling energy dissipation at vibrations of layered composite structures is a special case of the method, based on the principle of elasticviscoelastic correspondence. Shown, that in addition to the classical formulation of the energy method, in which the terms energy balance equations are approximately found by their own forms and vibration frequencies of a conservative mechanical system, there is one more an 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 shortcomings - the need to be limited to the use of classical theories of thinwalled structures (Bernoulli-Euler, Kirchhoff-Love) for descriptions of deformation of composite structures. It has been found that the use the classical formulation of the energy method allows with a high accurately predict the values of mechanical loss coefficients up to $\eta_\mathrm{max} = 0,02$. Further increase in damping levels construction is accompanied by a decrease in the accuracy of the forecast.
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