Transverse vibration of viscoelastic rectangular plate with linearly varying thickness and multiple cracks

Based on the thin-plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equations of motion of the viscoelastic plate with linearly varying thickness and an arbitrary number of all-over part-through cracks are established, and the expressions of the additional rotation angle induced by the cracks are deduced. We assume that it is elastic in dilatation, but postulate the Kelvin–Voigt laws for distortion, the complex eigenvalue equations of the viscoelastic plate with linearly varying thickness and multiple cracks are derived by the differential quadrature method. The general eigenvalue equations of the viscoelastic plate with multiple cracks under different boundary conditions are calculated. The effects of various geometric parameters, dimensionless delay time and dimensionless crack parameters on the transverse vibration characteristics of a viscoelastic plate containing multiple all-over part-through cracks are analyzed.