Dynamic thermal stability of a geometrically irregular shallow shell of constant torsion under the action of a load periodic by~its~time coordinate

G. N. Belostochny ; S. A. Grigoriev ; L. Yu. Kossovich ; O. A. Myltcina

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 22 (2022) no. 4, pp. 468-478

Résumé

In the framework of a Love type model, a geometrically irregular isotropic shallow constant torsion shell is considered. It is based on a strict continuum-shell-rib model. It is assumed that the geometrically irregular shell is heated to a constant temperature $\theta_0$, two opposite edges are exposed to a tangential load periodic by its time coordinate, the amplitude and frequency of which are known ($p(t)=p_0 \cos \vartheta t$). The problem of determining the regions of dynamic instability of a thermoelastic system is reduced to considering a singular system of three differential equations of dynamic thermal stability of a geometrically irregular shell in displacements containing a term with tangential forces in the Brian form. These forces arising in the shell during its heating are preliminarily determined on the basis of closed solutions of the singular system of differential equations of the momentless thermoelasticity of the geometrically irregular shell. The specific initialized system of equations is transformed into the Mathieu equations, which are written in terms of the classical athermal theory of smooth plates containing corrections for geometric parameters  — curvature, the relative height of the reinforcing elements, their number, and temperature. The first three regions of dynamic instability of a geometrically irregular shell are determined. A quantitative analysis of the influence of the geometric parameters of the elastic system and temperature on the configuration of the regions of dynamic instability is carried out.