Modal coupled vibration behavior of piezoelectric L-shaped resonator induced by added mass

This paper studies the mode coupling behavior and complex nonlinear dynamics of a piezoelectric driven L-shaped beam considering the added mass. To realize natural frequency adjustment and energy exchange among different modes, the added mass is delicately designed. The nonlinear governing equations, representing the first and second modes, are obtained by the Hamilton principle and Galerkin method. Perturbation and bifurcation analyses show that mode coupled vibration can lead to complex dynamic phenomena such as amplitude jump, amplitude saturation, double Hopf bifurcation and amplitude persistence. The physical conditions of amplitude jump, the critical voltage of amplitude saturation and the discriminant formula of double Hopf bifurcation are deduced theoretically and verified numerically. To be more convincing, an experimental test system is set up to observe the nonlinear dynamic behaviors. It is found that when the driving frequency is less than 26.18 Hz or more than 26.52 Hz, the first-order mode vibration jumps under the bifurcation driving voltage, which is qualitatively consistent with the theoretical results. Through mechanism investigation on subcritical Hopf bifurcation induced structure jumping phenomenon, the linear relationship between bifurcation voltage and perturbation mass is deduced. Both theoretical and experimental results demonstrate that small disturbance of added mass can significantly affect the bifurcation voltage of modal coupled vibration, which can realize the detection of micro-mass. The research results of this paper provide theoretical basis and experimental support for the development of micro-resonance device.