Effect of the equivalent stiffness of flexible supports on the MEMS cantilever-based sensors

Small deflections and moments exist on the boundaries of the flexible supports of MEMS cantilever-based sensors. The qualitative dynamical behavior is significantly affected by the non-ideal boundary conditions. Based on the Boussinesq's and Cerruti's displacement equations and the principle of energy equivalence, rigorous theoretical solutions of the normal, tangential and rotational equivalent stiffness are presented in this paper. The proposed model is validated by the fact that the theoretical results remained a good situation consistency with the reported experimental data. The variations of the equivalent stiffness with the geometric dimensions of the cross section of the flexible supports are investigated. It is observed that when the “Hard material” is used as the supports' materials, e.g. Silicon carbide, the equivalent stiffness is large. Yet the equivalent stiffness is small for the “Soft material”, e.g. Silicon and Poly-silicon. In addition, by employing the method of multiple time scales, the non-dimensional differential partial equation of the motion as well as coupled boundary conditions are analytically solved. The results indicate that the resonance frequencies decrease with the flexible supports, however, increase due to the nonlinearity mechanical spring.