This paper proposes a neuro-network-based method for model reduction that combines the generalized Hebbian algorithm (GHA) with the Galerkin procedure to perform the dynamic simulation and analysis of nonlinear microelectromechanical systems (MEMS). An unsupervised neural network is adopted to find the principal eigenvectors of a correlation matrix of snapshots. It has been shown that the extensive computer results of the principal component analysis using the neural network of GHA can extract an empirical basis from numerical or experimental data, which can be used to convert the original system into a lumped low-order macromodel. The macromodel can be employed to carry out the dynamic simulation of the original system resulting in a dramatic reduction of computation time while not losing flexibility and accuracy. Compared with other existing model reduction methods for the dynamic simulation of MEMS, the present method does not need to compute the input correlation matrix in advance. It needs only to find very few required basis functions, which can be learned directly from the input data, and this means that the method possesses potential advantages when the measured data are large. The method is evaluated to simulate the pull-in dynamics of a doubly-clamped microbeam subjected to different input voltage spectra of electrostatic actuation. The efficiency and the flexibility of the proposed method are examined by comparing the results with those of the fully meshed finite-difference method.

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.

The past decade has seen an accelerated growth of technology in the field of microelectromechanical systems (MEMS). The development of MEMS products has generated the need for efficient analytical and simulation methods for minimizing the requirement for actual prototyping. The boundary element method is widely used in the electrostatic analysis for MEMS devices. However, singular elements are needed to accurately capture the behavior at singular regions, such as sharp corners and edges, where standard elements fail to give an accurate result. The manual classification of boundary elements based on their singularity conditions is an immensely laborious task, especially when the boundary element model is large. This process can be automated by querying the geometric model of the MEMS device for convex edges based on geometric information of the model. The associated nodes of the boundary elements on these edges can then be retrieved. The whole process is implemented in the MSC/PATRAN platform using the Patran Command Language (the source code is available as supplementary data in the electronic version of this journal issue).