Proper orthogonal decomposition and component mode synthesis in macromodel generation for the dynamic simulation of a complex MEMS device

Abstract

In this paper, we develop a novel method for the macromodel generation for the dynamic simulation and analysis of a structurally complex MEMS device, by making use of proper orthogonal decomposition (POD), also known as the Karhunen-Loève decomposition and classical component mode synthesis. The complex microelectromechanical systems (MEMS) device is divided into interconnected components and each of these components is treated separately using POD to extract its proper orthogonal modes (POMs) and their corresponding proper orthogonal values. The separate component responses are then expressed in generalized coordinates that are defined by the POMs. The requirements of the displacement and force compatibility at the interface of components serve as constraint equations among the component coordinates, and are used to construct a transformation relating the component coordinates to system coordinates. This transformation is used to formulate the low-order macromodel to determine system dynamic responses. Numerical results obtained from the simulation of pull-in dynamics of a non-uniform microbeam MEMS device subjected to electrostatic actuation force with squeezed gas-film damping effect show that the macromodel generated this way can dramatically reduce the computation time while capturing the device behaviour faithfully.