The regions of dynamic instability of a plate, the material of which obeys the hereditary low of viscoelasticity, at the second resonance

Abstract

Abstract The problem of determining the side regions of dynamic instability of a rectangular plate, the material of which obeys the hereditary law of deformation, is considered. The solution of the integro-differential equation of vibrations of a plate loaded in its plane with constant and variable loads is considered. The solution used is a series with separated variables. An equation is obtained to determine the critical frequencies of even regions of instability. The influence of the parameters of the nucleus on the position of the second region of dynamic instability is investigated.