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

Response Behavior of Bi-stable Point Wave Energy Absorbers under Harmonic Wave Excitations