Modeling the effects of the PCB motion on the response of microstructures under mechanical shock

Microelectromechanical systems (MEMS) are often used in portable electronic devices that are vulnerable to mechanical shock or impact, such as that induced due to accidental drops on the ground. This work presents a modeling and simulation effort to investigate the effect of the vibration of a printed circuit board (PCB) on the dynamics of MEMS microstructures when subjected to shock. Two models are investigated. In the first model, the PCB is modeled as an Euler-Bernoulli beam to which a lumped model of a MEMS device is attached. In the second model, a special case of a cantilever microbeam is studied and modeled as a distributed-parameter system, which is attached to the PCB. These lumped-distributed and distributed-distributed models are discretized into ordinary differential equations, using the Galerkin method, which are then integrated numerically over time to simulate the dynamic response. Results of the two models are compared against each other for the case of a cantilever microbeam and also compared to the predictions of a finite-element model using the software ANSYS. The influence of the higher order vibration modes of the PCB, the location of the MEMS device on the PCB, the electrostatic forces, damping, and shock pulse duration are presented. It is found that neglecting the effects of the higher order modes of the PCB and the location of the MEMS device can cause incorrect predictions of the response of the microstructure and may lead to failure of the device. It is noted also that, for some PCB designs, the response of the microstructure can be amplified significantly causing early dynamic pull-in and hence possibly failure of the device.