Abstract
Mathematical model of the problem of vibration of thin-walled structural elements has been constructed based on Kirchhoff-Love theory. The problem is reduced, using the Bubnov-Galerkin method, to the solution of a set of nonlinear integro-differential Volterra type equations with weakly-singular kernels of relaxation. A numerical method based on the use of quadrature formulae being used for their solution. The influence of rheological parameters of the material on the values of critical velocity and amplitude-frequency characteristics of viscoelastic thin-walled structural elements is analyzed. It is shown that tacking account viscoelastic properties of the material of thin-walled structures lead to a decrease in the critical rate of gas flow.
Highlights
The theory of viscoelasticity is attracting more and more interest from researchers due to the widespread use of new materials in technology and traditional materials in specific conditions
Much attention has been paid to studying the dynamics of essentially nonlinear viscoelastic mechanical systems [6-12], [26, 27]
The upper exact limit of the velocity set {V} is chosen as a criterion for determining the critical rate of gas flow; it ensures the convergence of the Bubnov-Galerkin expansion (2) for all t=0 (Fig. 1), i.e. the following condition is satisfied
Summary
The theory of viscoelasticity is attracting more and more interest from researchers due to the widespread use of new materials in technology and traditional materials in specific conditions. Evidence of this is the publication of several articles [1-5]. Much attention has been paid to studying the dynamics of essentially nonlinear viscoelastic mechanical systems [6-12], [26, 27]. The basic research trend consisted of preliminary reduction of problems using variational methods of a continuous structure to a system with one-or-two degrees of freedom, which was analyzed either numerically or using analytical methods of nonlinear mechanics. The main attention was paid to determining the qualitative effects caused by the impact of nonlinear forces.
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