Analytical study on dynamic response of multi-layered plate in unsaturated half-space

The study on the dynamic interaction between plate and foundation is widely concerned. Especially, the dynamic response of plate on unsaturated foundation contains theoretical and practical values. The steady-state response of multi-layered rectangular plate on unsaturated half-space is investigated. Based on the governing equation proposed by the previous literatures, the integral solution for unsaturated half-space is derived by using the integral transformation and elimination method. Meanwhile, a double-cosine form function is proposed for the multi-layered rectangular plate so as to establish the compatibility equation between plate and foundation. Considering the governing equation, boundary conditions and compatibility equation of layered rectangular plate, the amplitudes of vertical displacement and bending moment are calculated. The parameters of foundation and multi-layered plate are selected, and some computed results for steady-state vibration of multi-layered plate are given. To further investigate how the factors of unsaturated soils influence the steady-state response of multi-layered plate, the specific numerical results of displacement of multi-layered plate are calculated, and the rules how the factors influence the deformation of plate are analyzed.