Abstract
Microelectromechanical Systems (MEMS) is difficult to take transient analysis due to the tight coupling between the multiple energy domains, typically nonlinear. An effective increment-dimensional precise integration method (PIM) combined with the model order reduction (MOR) technique based on Krylov subspace is present to solve large-scale nonlinear finite element dynamics systems. The numerical example of V-beam electro-thermal actuator is shown to demonstrate that the MOR-PIM method can achieve high precision and fast speed when solving the nonlinear dynamic equation with large-scale freedom.
Highlights
The research field of MEMS has seen a rapid growth for the last two decades
If the systems contain the microelectronic devices for switching the non-electric signals to electric signals or some else signal processing units, the traditional finite element and boundary element tools are cumbersome and time consuming, i.e. are inappropriate to perform the transient analysis to overall system
The model order reduction technique has been extensively studied in recent years such as the superposition of basic function based on Galerkin method and the matrix subspace projection based on finite element equations [1]
Summary
The research field of MEMS has seen a rapid growth for the last two decades. During the micro and nano fabrication technology development, more and more micro/nano sensors, actuators and even system-on-chip with complexity structures and functions have been designed and taken into commercial application. The model order reduction technique has been extensively studied in recent years such as the superposition of basic function based on Galerkin method and the matrix subspace projection based on finite element equations [1]. If all reduced order model of non-electric energy domains were build, could be combined with the mature circuit model to take the system-level simulation for whole coupled micro-systems. The key component of the PIM is computing the matrix exponential It can give precise numerical results almost equal to the exact solution at the integration point but it is more or less difficult due to the inverse matrix calculations and memory storage when solving the large-scale problem. We took the increment-dimensional precise integration method combined with the Krylov based approximation algorithm (called MOR-PIM) to solve large-scale nonlinear dynamics micro systems. The transient response result of finite element models for V-beam electro-thermal actuator was verified
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