Nonlinear Dynamical Responses Of Microbeam Using Nonlinear Galerkin Method

Micro-electro-mechanical systems (MEMS) is a category of micro area with a series of unique nature distinguished from macro area. In aspect of mechanics, adhesion of micro-caused phenomenon is usually easy to be ignored and lead to the design of an error. Micro-beams are being developed as a key component in various resonator based micro-systems, such as resonant accelerometers, micro-electro- mechanical filters, and micro-vibromotors. The design tools, however, have not kept pace with this growth since the geometrical complexity and physical conditions of the devices are not easily incorporated into existing computational programs. The ability of effectively simulating and predicting nonlinear behaviour of MEMS is important in estimating system performance and guiding the reliability verification process. The traditional Galerkin method provides a simple approach to establish a nonlinear dynamic model with lower dimension and predicting the mechanical behaviour of microstructures, but it may lead inaccurate results since it neglect the parts of high frequencies completely as indicated in the literature. The nonlinear Galerkin method projects the parts of higher frequencies onto the parts of lower frequencies through an inertial manifold, takes the parts of higher frequencies into account. In this paper, a brief introduction of MEMS relevant background is addressed at first, and nonlinear Galerkin method is complemented in theoretical description to make it applicable to the general situation. Then, the influence of adhesion in the design of resonator is discussed. Calculate the response of micro-resonator driven by the capillary force, which is the major part of adhesion. Finally, analyze the dynamic behaviour of resonator driven by electric force. Consider the first three modes, use nonlinear Garlekin method to get a model of single degree of freedom. Use multiple scales method calculate the dynamic response of model got by the nonlinear Garlekin method. And draw the amplitude-frequency curve of steady state, compare it to the results obtained by traditional Garlekin method which only consider the first mode. Let the micro-beam dynamic response got by numerical integration of model with three degrees of freedom as a reference standard, validated that nonlinear Galerkin method with higher accuracy compared to traditional Galerkin method.