Dynamic stability of a viscoelastic plate

Abstract

The paper considers the problem of stability of a viscoelastic plate subjected to intermittent load. A differential equation was designed, which describes the dynamic stability of the plate stressed by permanent and alternating loads across the plate’s plane. A solution in the form of a series with separated variables has been examined. Linear differential equations of the third order were obtained for the time function. A critical frequency equation was obtained as well. The major domains of dynamic instability were investigated. Another analysis was dedicated to the way the position of the prime instability domain is affected by relaxation time as well as correlation between long-term and instantaneous moduli of elasticity.