A study for the effect of the PCB motion on the dynamics of MEMS devices under mechanical shock

We present a theoretical and experimental investigation into the effect of the motion of a printed circuit board (PCB) on the response of microelectromechanical systems (MEMS) devices to shock loading. For the theoretical part, a 2-DOF model is used, where the first degree of freedom accounts for the PCB. The second degree of freedom represents the motion of the MEMS microstructure. Low-g acceleration pulses are applied to the MEMS-PCB assembly base to simulate shock pulses generated from a drop-table test. Simulation data are presented to show the effects of the natural frequency of the PCB, the natural frequency of the microstructure, and the shock pulse duration. Universal 3-D spectra representing the effect of these parameters are presented. It is found that neglecting the PCB effect on the design of MEMS devices under shock loads can lead to undesirable motion of their microstructures. The effects of electrostatic force and squeeze film damping are investigated. It is found that the amplification of motion due to the PCB can cause early pull-in instability for MEMS devices implementing electrostatic forces. The effect of higher order modes of a microbeam is studied through a continuous beam model coupled with a lumped model of the PCB. The limitations of the 2-DOF model are discussed. An experimental investigation is conducted to verify the theoretical results using a capacitive accelerometer. Experimental data for the response of the accelerometer while it is mounted on two representative PCBs due to different low-g shock conditions are shown.