Vibration Analysis of a Nonlinear Absorber Coupled to a Hand-Held Impact Machine

Exposure of human hands to harmful levels of vibration can lead to severe injuries. To attenuate these hand transmitted vibrations, a nonlinear vibration absorber inerter (NVAI) is proposed in this work. The proposed NVAI is attached to a coupled nonlinear system of a hand-held impact machine and a hand-arm system. The combined coupled nonlinear system is modeled as a lumped parameter model with a combination of cubic and linear stiffness components, linear viscous dampers, and lumped masses. The governing equations of motion are solved analytically using the method of harmonic balance and validated using numerical simulations. A numerical bifurcation diagram of the system reveals the existence of complex solutions such as quasi-periodic and chaotic attractors. The appearances of quasi-periodic and chaotic attractors are later confirmed by Lyapunov exponents. Further, we explore the ability of the proposed NVAI to decrease the area corresponding to unstable quasi-periodic and chaotic motion in the excitation amplitude–frequency space. This observation further implies the delay in the onset of quasi-periodic and chaotic motion for a range of forcing amplitude using Lyapunov exponents. Finally, parametric analyses are carried out to identify the critical design parameters of the NVAI. These analyses reveal that an increase in the damping, mass, and inertance of the absorber ameliorates the performance of the NVAI. Furthermore, the critical value of the external excitation, corresponding to a sudden change in the response of the system, can be controlled using an appropriate selection of absorber parameters.