Exploiting the Internal Resonance for the Vibration Suppression of Beams via Piezoelectric Shunt Circuits

This paper investigates the vibration suppression of cantilevered beams using nonlinear shunted piezoelectric circuits. The beam’s inertia and geometric nonlinearities are considered. A quadratic nonlinear piezoelectric capacitance is used such that there exists a two-to-one internal resonance between the mechanical and electrical modes. The internal resonance coupling is exploited to trigger the saturation phenomenon such that the beam’s vibration reaches a limit beyond an excitation amplitude threshold. The equations governing the nonlinear vibration of the beam coupled with the shunt circuit are derived, and modal analysis is used to obtain a system of two nonlinearly coupled modal equations. The equations are then numerically integrated to obtain the results. A parametric study is performed to assess the significance of system parameters, such as the location of the piezoelectric patch, its size, circuit resistance, and nonlinear gain, on the effectiveness of vibration suppression. The results show that the proposed design effectively suppresses the linear and nonlinear vibrations of the beam. The proposed absorber is space-efficient and does not add mass to the primary system, and hence, it has the potential in systems where the weight matters, such as aerospace applications.