Dynamical analysis and numerical verification of a non-smooth nonlinear energy sink

The performance of the vibration reduction of a lightweight non-smooth nonlinear energy sink (NES) attached to a two-story linear damped primary structure (PS) is studied through dynamical analysis and numerical verification. First, a three-degree-of-freedom non-smooth nonlinear system is formulated to describe the coupled dynamics involving the PS and non-smooth NES, in which nonlinearity is induced by the piecewise linear restoring force of the NES and described by a non-smooth function. Second, when a 1:1:1 internal resonance case of the coupled system is considered, a modified complex-average technique and the method of multiple scales are employed to obtain a set of algebraic equations between the vibration amplitudes of the PS and attached non-smooth NES. The stability conditions and initial critical energy for activating targeted energy transfer (TET) can be analytically obtained. Finally, the linear stiffness, equivalent viscous damping coefficients and impact clearance of the non-smooth NES are numerically optimized by the peak estimates. The initial critical energy for the TET of NES is numerically verified to show the excellent performance of vibration reduction for the non-smooth NES by comparing with other attached dissipation devices under a wide range of impulsive loads.