Periodic response of a nonlinear axially moving beam with a nonlinear energy sink and piezoelectric attachment

Abstract

An efficient semi-numerical framework is used in this paper to analyze the dynamic model of an axially moving beam with a nonlinear attachment composed of a nonlinear energy sink and a piezoelectric device. The governing equations of motion of the system are derived by using the Hamilton's principle with von Karman strain-displacement relation and Euler - Bernoulli beam theory. The nonlinear energy sink is modeled as a lumped - mass system composed of a point mass, a spring with nonlinear cubic stiffness and a linear viscous damping element. The piezoelectric device is placed in the ground configuration. Frequency response curves of the presented nonlinear system are determined by introducing the incremental harmonic balance and continuation method for different values of material parameters. Based on the Floquet theory, the stability of periodic solutions was determined. Moreover, the presented results are validated with the results obtained by a numerical method as well as the results from the literature. Numerical examples show a significant effect of the nonlinear attachment on frequency response diagrams and vibration amplitude reduction of the primary beam structure.