In this paper the results of a study of the dynamic characteristics of thin-walled composite curved viscoelastic pipes under the influence of internal pulsating pressures is presented. The relationship between stress and strain is described by the Aviary equations. Based on the principle of calculus of variations, the equations of the dynamics of curvilinear shells are obtained. The obtained integral and integro-differential equations are solved using the finite element method, the Mueller and Gauss methods. The results of calculations of the natural frequencies of the shell and the curved rod are compared. As a result of the calculation, it was found that, shell vibrations occur at higher frequencies than rod vibrations (manifestation of a boundary effect). With this difference, the natural frequency, which has no analogue in the rod model decreases. This is due to the fact that, in this case the transverse vibrations of the section itself become significant, the rod. Some mechanical effects were discovered when taking into account the rheological properties of the pipe material.
Detailed review of the problem of wave removal of energy through the border of finite area of a foundation is given in the paper. Variation statement, methods and algorithms of solution of different dynamic problems for viscous-elastic system with account of non-reflective conditions on the border of finite foundation are given. The possibility to use non-reflective conditions is shown in tests problems.Dynamic behavior of heterogeneous viscous-elastic system "dam -foundation" is studied under short-time intensive load subjected to the foundation. Weak dependence of energy dissipation in a system with hereditary viscous-elastic properties of material on the frequency of natural oscillations, as well as dependence of wave removal of energy on principal natural frequencies of system oscillations are revealed.
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