Nonlinear oscillations of a viscoelastic cylindrical panel with concentrated masses

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.

Analytical evaluation of the fundamental frequency of natural vibrations of the spatial coverage

“…The pavement is a rectangular structure with a size 2 2 na na  (Figs. 1,2). The truss rests on the sides on rigid vertical posts [21].…”

“…The problems of natural vibration frequencies of structures are usually solved numerically [1][2][3][4][5][6][7]. These solutions are basic for many problems of the dynamics of structures, including the analysis of the seismic resistance of structures [2,8].…”

The lower limit of the first frequency of natural vibrations externally statically indeterminate truss: analytical solution

“…The first (fundamental) frequency in the natural frequency spectrum is the most important. Finding the entire spectrum requires the use of numerical methods [1,2]. There are two approximate estimates for determining the first frequency.…”

Dynamics of a Viscoelastic Plate Carrying Concentrated Mass With Account of Physical Nonlinearity of Material. Part 1. Mathematical Model, Solution Method and Computational Algorithm

“…В работах [36,37] данный метод решения был усовершенствован и распространен для решения нераспадающихся ИДУ. На основе этого метода было получено множество численных результатов [38][39][40][41][42].…”