Response behavior of bi-stable point wave energy absorbers under harmonic wave excitations

To expand the narrow response bandwidth of linear point wave energy absorbers (PWAs), a few research studies have recently proposed incorporating a bi-stable restoring force in the design of the absorber. Such studies have relied on numerical simulations to demonstrate the improved bandwidth of the bi-stable absorbers. In this work, we aim to understand how the shape of the bi-stable restoring force influences the effective bandwidth of the absorber. To this end, we use perturbation methods to obtain an approximate analytical solution of the nonlinear differential equations governing the complex motion of the absorber under harmonic wave excitations. The approximate solution is validated against a numerical solution obtained via direct integration of the equations of motion. Using a local stability analysis of the equations governing the slow modulation of the amplitude and phase of the response, the loci of the different bifurcation points are determined as function of the wave frequency and amplitude. Those bifurcation points are then used to define an effective bandwidth of the absorber. The influence of the shape of the restoring force on the effective bandwidth is also characterized by generating design maps that can be used to predict the kind of response behavior (small amplitude periodic, large amplitude periodic, or aperiodic) for any given combination of wave amplitude and frequency. Such maps are critical toward designing efficient bi-stable PWAs for known wave conditions.