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

Microelectomechanical systems (MEMS) are often used in portable electronic products that can be subjected to mechanical shock or impact due to being dropped accidentally. 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 presented. In the first approach, the PCB is modeled as an Euler-Bernoulli beam to which a lumped model of a MEMS device is attached. In the second approach, a special case of a cantilever microbeam is modeled as a distributed-parameter system, which is attached to the PCB. These lumped-distributed and distributed-distributed models are solved numerically by integration of the equation of motion over time using the Galerkin procedure. 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 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 MEMS device. It is observed from the results that in some cases, depending on the different parameters of the problem, the response of the microstructure can be amplified causing early dynamic pull-in and hence possibly failure of the device.