Parametric vibrations of viscoelastic orthotropic cylindrical panels of variable thickness

Abstract

In modern engineering and construction, thin-walled plates and shells of variable thickness, subjected to various static and dynamic loads, are widely used as structural elements. Advances in the technology of manufacturing thin-walled structural elements of any shape made it possible to produce structures with predetermined patterns of thickness variation. Calculations of strength, vibration and stability of such structures play an important role in design of modern apparatuses, machines and structures. The paper considers nonlinear vibrations of viscoelastic orthotropic cylindrical panels of variable thickness under periodic loads. The equation of motion for cylindrical panels is based on the Kirchhoff-Love hypothesis in a geometrically nonlinear statement. Using the Bubnov-Galerkin method, based on a polynomial approximation of deflections, the problem is reduced to the study of a system of ordinary integro-differential partial differential equations, where time is an independent variable. The solution to the resulting system is found by a numerical method based on the feature elimination in the Koltunov-Rzhanitsyn kernel used in the calculations. The behavior of a cylindrical panel with a wide range of changes in physico-mechanical and geometrical parameters is investigated.

Calculation methods for plate and beam elements of box-type structure of building

“…. By virtue of this expression and taking into account (24), we obtain the general solution of the problem for bending plate elements in the following form [8][9][10]:…”

“…In [19]- [24], the dynamic characteristics and vibrations of various axisymmetric and plane structures are considered, taking into account various geometries, spatial factors and inelastic properties of materials. The solution to the problem is performed by the finite element method and by expanding the solution in terms of natural vibration modes.…”

Dynamic analysis of an orthotropic viscoelastic cylindrical panel of variable thickness

“…Similar to [2], introducing the stress function  into equation [20], we obtain the equation of motion of an orthotropic viscoelastic cylindrical panel relative to the deflection w and the stress function .…”