Dynamic stability of heated geometrically irregular plates on the basis of the Reisner model

Abstract

On the basis of the continuum model of geometrically irregular plate the problem of dynamic stability has been solved. The Reissner type model is considered. The heated plate with ribs is subjected to periodic temporary coordinate of the tangential forces. For the tangential forces a nonhomogeneous boundary problem of membrane thermoelasticity in displacements is solved. The system of singular equations of dynamic stability recorded through the function of the deflection and additional functions. The additional functions characterize the law of change of stresses in vertical planes dependent variables x and y. The solution is reduced to the Mathieu equation. The characteristics of the Mathieu equation represented by terms in classical theory of plates and contain corrections of temperature, transverse shear and ribs. Three areas of dynamic stability of the thermoelastic system are determined. Quantitative analysis has been carried out. Dependence of the configuration of the areas of dynamic stability on temperature, shear deformation in vertical planes and relative height of ribs is presented.

Keywords

• thermal stability
• dynamics
• irregularity
• singularity
• instability areas
• reissner model
• mathieu equation