Micro electrical mechanical systems inherently tend to behave nonlinearly in high power handling. Such nonlinearities arise from mechanical and electrical characteristics of the systems. In this study, the mechanical nonlinearities are focused and the longitudinal mode shape of a microbeam resonator with high quality factor is considered. The mechanical nonlinearities for this system are assumed to be cubic and quadratic. the method of multiple scale is used for perturbation analysis which leads us to obtain the function of displacement with respect to frequency which is beneficial to set an upper dynamic limit to avoid instability and, also, facilitates to make the system so-called almost linear.

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