Analytical solution for forced vibration of multilayer structures composed of plates with different geometric dimensions

Multilayer system composed of parallel plate components with different geometric dimensions is frequently used to describe engineering objects, such as electronic assembly. In this work, an analytical method was proposed for forced vibration of this type of multilayer system. The proposed method overcomes the limitation that the traditional wave method is only applicable to all plate components must have the same in-plane dimensions. The proposed analytical method has an efficiency advantages in parameter analysis than element-based methods such as finite element method (FEM). The connection joints between two adjacent plate components, such as ball grid array (BGA) solder interconnect, are represented by elastic springs. The vibration of each component are described in terms of general and physical analytical waves, respectively, and the dynamic coupling between them are established by an equivalent dynamic flexibility matrix. The forced responses of the multilayer system are analytically calculated by solving the system equation in wave space. In the numerical examples, the effectiveness of the proposed method is validated by comparing the present results with the FEM results. The influence of number of the defective solder joints on vibration response is also investigated.