Nonlinear oscillations of a viscoelastic cylindrical panel with concentrated masses

Dadakhan Khodzhaev D.A,Rustamkhan Abdikarimov,Nikolay Vatin,A Borodinecs,V Sergeev,N Vatin

doi:10.1051/matecconf/201824501001

Abstract

The problems of oscillations of a viscoelastic cylindrical panel with concentrated masses are investigated, based on the Kirchhoff-Love hypothesis in the geometrically nonlinear statement. The effect of the action of concentrated masses is introduced into the equation of motion of the cylindrical panel using the δ function. To solve integro-differential equations of nonlinear problems of the dynamics of viscoelastic systems, a numerical method is suggested. With the Bubnov–Galerkin method, based on a polynomial approximation of the deflection, in combination with the suggested numerical method, the problems of nonlinear oscillation of a viscoelastic cylindrical panel with concentrated masses were solved. Bubnov–Galerkin’s convergence was studied in all problems. The influence of the viscoelastic properties of the material and concentrated masses on the process of oscillations of a cylindrical panel is shown.

Highlights

With intensive progress in modern industry one of the most important problems in machine-building and engineering is the decrease in specific consumption of materials of the structures and machines
The thinner the element the more flexible it is, and the more pronounced is its tendency to the buckling and the loss in stability. The latter is accompanied by the catastrophic growth of deformation and, as the rule, by the failure of structures. From this point of view, when manufacturing a light, strength and reliable structures, the most acceptable are the composite materials, which allow to improve considerably an operational characteristics of these structures and, sometimes, to manufacture the structures, which could not be realized with traditional materials
The procedure of the design and projecting of structures made of composite materials is rather complicated; it requires the account of their real properties

Summary

Introduction

With intensive progress in modern industry one of the most important problems in machine-building and engineering is the decrease in specific consumption of materials of the structures and machines. Similar problems of oscillation and dynamic stability of an elastic and viscoelastic plates, cylindrical panels and shells in different state without concentrated masses were considered in [6,7,8,9,10,11,12] It is well known, that the majority of composite materials possess pronounced viscoelastic properties [13,14,15]. On the basis of this method, a great number of numeric results [20,21,22,23] were obtained, agreeing well with theoretical and experimental data [24] The aim of this works is to study nonlinear problems of oscillation of viscoelastic cylindrical panel with concentrated masses

Methods

Results and Discussion

Conclusions