Research On The Adaptation Of Parameterized Model Order Reduction For The Electrostatically Actuated Micro-beam Devices

The characteristics of multi-field coupling of MEMS increase the difficulty of simulation and consume a lot of computing resource.This situation will come to worse especially in the process of optimization design in which the multiple analyses are needed to finding the optimal solutions.Using the model order reduction method can release this burden,in which the reduced order model(ROM)of the device can capture the static or dynamic characteristics of the device with a certain precision meanwhile using less calculating time.However,the existing ROM researches mainly aimed at systems for determining parameters,this is because those types of ROMs have local characteristics,it means that the accuracy of the ROM's simulation will decrease quickly when the parameters of the devices deviate from the initial values from which the ROMs was constructed,So,they are not suitable for the optimal design in which the design space of parameters of devices should be explored and many reanalysis are required.The adaptive parameterized ROM and its construction methods have been studied in this paper,those adaptive ROMs can be used in the process of optimization design.The electrostatically actuated micro-beams are taken as research objects in this paper,and the main focus is on the adaptability of two kinds of Galerkin/ROMs,one is constructed by the undamped modal shape functions,and the other one is constructed by the set of basis functions obtained from the proper orthogonal decomposition(POD)method.For the straight beams of rectangular cross section,the parametric ROMs,constructed by the undamped modal shape functions with analytic forms,have a good adaptability to the changes of load condition and geometric parameters,and can accurately capture the dynamic characteristics of the device due to the changes.Based on existing researches mentioned above,a parametric ROM for the section-changed micro-beam is put forward,and then,it is applied to study the effects of the width parameters on the pull-in phenomenon and natural frequency of the beam.The existing ROM construction technology based on the POD method can be applied to the researches of electrostatic micro beam device system that involved in the field of fluid-solid coupling.However,the construction of the ROM is always based on the data-snapshot technology,which results in a poor adaptability to the ROM.So,after discussing the adaptability of the ROM to the load conditions and the geometric parameters of the device,an adaptive ROM method based on Taylor series approximation and POD modal-sensitivity is proposed.And then,a dynamic simulation is carried out by using the geometric parameters of the micro beam as variables,to investigate the application effect of the adaptive ROM.Finally,the results show that when the length of micro-beam decreases by 20%or increases by 20%,the simulation error of adaptive ROM is about 4.5%,far less than 20%of the initial ROM's;when the width of micro beam increases by 25%,the simulation error of adaptive ROM is about 5.5%,also far less than the 18.2%of the initial ROM's.By reducing the range of parameter variation properly,the simulation accuracy of the adaptive ROM can be further improved,so that,it can be applied to the optimization design of micro beam device.