Vibrations of Cylindrical Shell Structures Filled With Layered Viscoelastic Material

Ismoil Safarov,Abdurakhim Marasulov,Tokhir Jurayev,Мuhsin Теshaev,Bahodir Raxmonov,D Bazarov

doi:10.1051/e3sconf/202126401027

Abstract

A thin-walled shell and a thick-walled mass (cylinder) in contact with it, made of a different material, are structural elements of many machines, apparatus, and structures. The paper considers forced steady-state vibrations of cylindrical shell structures filled with a layered viscoelastic material. The study aims to determine the damping properties of vibrations of a structurally inhomogeneous cylindrical mechanical system under the influence of harmonic loads. The dynamic stress-strain state of a three-layer cylindrical shell filled with a viscoelastic material under the action of internal time-harmonic pressure is investigated. The oscillatory processes of the filler and the bonded shell satisfy the Lamé equations. At the contact between the shell and the filler, the rigid contact conditions are satisfied. Dependences between stresses and strains for a linear viscoelastic material are presented in the form of the Boltzmann-Voltaire integral. The method of separation of variables, the method of the theory of potential functions (special functions), and the Gauss method are used to solve this problem. Based on the analysis of the numerical results, it was found that the dependence of the resonant amplitude of the shell displacements on the viscous properties of the filler is 12-15%. Analysis of the results obtained shows that the study of vibrations of shells containing fillers according to the rod theory will lead to rather large erroneous results (up to 20%).

Highlights

Acceleration of scientific and technological progress, intensive development of the national economy will lead to the need to create new systems and technologies that should work in wide ranges of speeds, temperatures, pressures, and loads
The works [7, 8, 9] are devoted to calculating the stress-strain state of the dynamic processes of thin-walled shells and the elastic or viscoelastic filler contained in them
The material of the multilayer cylinder is a typical highly filled polymer, the physical and mechanical characteristics of which are determined by the nature of the binder, the adhesion of the binder to the multilayer filler

Summary

Introduction

Acceleration of scientific and technological progress, intensive development of the national economy will lead to the need to create new systems and technologies that should work in wide ranges of speeds, temperatures, pressures, and loads. They must be convenient for operation, comfortable for humans, environmentally friendly, silent, etc The works [7, 8, 9] are devoted to calculating the stress-strain state of the dynamic processes of thin-walled shells and the elastic or viscoelastic filler contained in them. These issues affect the literature on solid fuel engines to one degree or another. The quasi-static linear theory of viscoelasticity was usually used

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