Dynamic analysis of the nonlinear energy sink with local and global potentials: geometrically nonlinear damping

In this paper, the considered two-DOF system consists of a linear oscillator (LO) under external harmonic excitation and an attached lightweight nonlinear energy sink (NES) with local potential and geometrically nonlinear damping. With the application of complex-averaging method, the steady-state dynamical behavior of the system is investigated by the slow invariant manifold, folding singularities and equilibrium points. Different scenarios of strongly modulated responses are presented based on the geometry of SIM, and the numerical simulation results are in consistent with the analytical prediction. The incremental harmonic balance method is applied to detect the frequency response curves of the system around the fundamental resonance, and the accuracy of the theoretical analysis is fully verified by the numerical results obtained by direct integration of equations of motion of the system. It is demonstrated that the increase in external forcing amplitude, global nonlinear stiffness and local nonlinear stiffness can drive the frequency response curves move toward the right and widen the frequency bandwidth of the coexistence of multiple steady-state response regimes, while the increase in nonlinear damping the reverse. The numerical simulation results also show that the addition of geometrically nonlinear damping and local potential in the proposed NES can drastically enhance the capacity of the nonlinear vibration absorber to suppress the shock-induced response of the LO, and the proposed NES is effective for a comparatively broad range of applied impulsive energies, particularly for the high impulsive energies.