Dynamic Stability of Cracked Viscoelastic Rectangular Plate Subjected to Tangential Follower Force

Based on the thin plate theory and the two-dimensional viscoelastic differential type constitutive relation, the differential equation of motion of a viscoelastic plate containing an all-over part-through crack and subjected to uniformly distributed tangential follower force is established in Laplace domain. Then, by performing the Laplace inverse transformation, the differential equation of motion of the plate in the time domain is obtained. The expression of the additional rotation induced by the crack is given. The complex eigenvalue equations of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force are obtained by the differential quadrature method, and the $δ$ method is adopted at the crack continuity conditions. The general eigenvalue equations of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force under the different boundary conditions are calculated. The transverse vibration characteristics, type of instability, and corresponding critical loads of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force are analyzed.