Board level drop test: exact solution to the problem of the nonlinear dynamic response of a PCB to the drop impact

Abstract

An analytical predictive model has been developed for the evaluation of the nonlinear dynamic response of a printed-circuit-board (PCB) to the drop impact during board-level testing. The hypothesis of “heavy-and-flexible” PCB is used in the analysis: the surface-mounted-devices (SMDs) are assumed to be small enough not to affect the PCB’s flexural rigidity, but their masses have been considered and accounted for by “spreading out” the SMD total mass over the PCB surface. The analysis is restricted to the fundamental mode of vibrations, and the method of principal coordinates is used to evaluate the response. The exact solution to the nonlinear differential equation for the principal coordinate has been obtained. Another important finding is that the nonlinear amplitudes were determined even without solving the nonlinear differential equation of motion. The main objective of the analysis is to provide design guidelines for constructing a feasible experimental setup. A simply supported board is suggested as the most appropriate structure for an adequate test vehicle: the experimental data for such a board, as far as the behavior of the solder material in the second level of interconnections is concerned, can be easily and reliably interpreted and extrapolated for the practical use. The developed model enables one to predict the induced bending moments and the in-plane (membrane) forces that could be applied in the subsequent analyses to the PCB areas in the proximity of the package and its solder joint interconnections.