The constraint behavior of compliant mechanisms can be improved via strengthening the stiffness of their constitutive beams using intermediate elements. This interior element may be assumed to be perfectly rigid or one can consider its compliance as a design parameter. While modeling the static behavior of such systems is state of art, the nonlinear dynamic of such systems have been remained un-investigated. So the objective of this paper is to suggest an analytical framework for modeling nonlinear free and forced vibrations of a simple flexure beam strengthened via a compliant intermediate element. The equations of motion of the system are derived using Hamilton's principle. Based on a single mode approximation, the partial differential equations of motion are transformed into two temporal equations. Employing multiple time-scales perturbation techniques, free vibration time histories and forced vibration response due to base excitation is derived analytically. Different parametric studies are carried out to recognize the effect of the intermediate compliant element on the vibrational behavior of the flexure beam. The results of this paper are expected to develop a new approach in modeling and investigation of load-displacement behavior of compliant mechanisms.

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