Analytical Solution for Electronic Assemblies Under Vibration

An analytical solution using Ritz method for the electronic assembly vibration problem has been presented in detail. In this solution, a special treatment for plate-mounted-on-standoffs boundary conditions scheme was required, and hence described. Also, a simple equation for estimating ball grid array (BGA) solder joint axial stiffness was developed. The results of the analytical solution were validated with modal analysis measurements and finite element (FE) models data in terms of natural frequencies and mode shapes. Then, the analytical solution was used to estimate the most critical solder joint deformations and stresses. Finally, the so developed solution provided an effective tool to examine the effect of several geometric and material configurations of electronic package structure on the fatigue performance of electronic products under mechanical vibration loadings.