Dynamic stability of a non-conservative viscoelastic rectangular plate

Based on the thin-plate theory and the two-dimensional (2D) viscoelastic differential constitutive relation, the differential equation of motion of the viscoelastic rectangular plate subjected to uniformly distributed tangential follower force in Laplace domain is deduced, the equation is suitable for various viscoelastic models of differential type. The differential equation of motion of the viscoelastic plate constituted by the Kelvin–Voigt model under the action of uniformly distributed tangential follower force in time domain is also derived. The generalized eigenequations of non-conservative viscoelastic rectangular plate, with four edges simply supported, two opposite edges simply supported and other two edges clamped are established by the differential quadrature method, and the curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies vs. uniformly distributed tangential follower force are obtained, the factors influencing the dynamic stability of the visoelastic rectangular plate are discussed.