Proper orthogonal modes and component mode synthesis in macromodel generation for complex MEMS device simulation

Abstract

In this paper, a novel method for macromodel generation for the dynamic analysis of structurally complex MEMS devices is developed by making use of proper orthogonal decomposition (POD) and classical component mode synthesis (CMS). The complex MEMS device is divided into interconnected components and each of these components is treated separately using POD to extract its proper orthogonal modes (POMs). Component responses are expressed in generalised coordinates that are defined by the POMs. The requirements of the displacement and force compatibility at the interface serve as constraint equations between the component coordinates to determine the system dynamic response. Numerical results obtained from the simulation of a nonuniform beam-beam-beam complex MEMS device shows that the macromodel generated this way can dramatically reduce the computation time while capturing the device behaviour faithfully.