Nonlinear versus Linear Deflection Analysis of Microcantilever

Abstract

An important aspect in modeling and analysis of MEMS is related to decomposition of the problem to the usual O.D.E's and P.D.E's which are also used in macro scale mechanics. Whereas scaling-down of the macro devices might increase the nonlinearity. It is natural for one to ask the question: how much one could decrease the dimension of a device and still uses the linear form of differential equation for modeling that system? In this research, the difference of linear and nonlinear analysis of a baseline microcantilever which represents the fundamental element of a microstructure is theoretically investigated. This has applications in many MEMS devices like micro-sensors and micro-actuators. In the present work, a comparison in the deflection of a microcantilever subjected to point and distributed forces by nonlinear and linear analysis of the O.D.E's is carried out. Further, the results are compared with finite analysis performed in ANSYS. Another method of solving the O.D.E's is Taylor series expansion; the results of this method are compared by those resulting from the non-linear analysis. For better understanding of the difference between the results of the nonlinear analysis versus the linear analysis, the O.D.E for various initial conditions are solved and results are compared with the ones yielded by the nonlinear approach. Finally, the errors of the linear analysis in comparison with the nonlinear analysis are analyzed and relative error for various dimensions is presented.