A unified dynamic stiffness modeling of multi-plate coupled systems with discrete spring connections

This work presents a unified dynamic stiffness modeling for the vibration analysis of multi-plate coupled systems with discrete spring connections (MPCS-DSC). First, based on the governing differential equation of the plate, the dynamic stiffness matrix (DS) of transverse and in-plane vibration for a completely free rectangular plate is separately derived by combining the generalized superposition method and the projection method. Then, according to the continuity of displacements at the connection point between the spring and the plate, the projected DS matrix of the discrete spring is developed. Then, using an element assembly concept similar to that in the finite element method (FEM), global DS matrices of various coupled systems are determined by assembling the spring's DS matrice and the transverse or in-plane DS matrices of the plate. In order to verify the accuracy and applicability of the proposed method, the free and forced vibration analysis of four types of coupling systems is carried out. The reliability and applicability of the proposed method are confirmed by comparing the present results with those from open literature and the finite element solutions. This study not only expands the application range of DS modeling theory but also provides a powerful tool to investigate the vibration characteristics of the MPCS-DSC.