Extension of cross-well bandwidths for bistable piezoelectric plate oscillators

Snap-through dynamics between the two potential wells of bistable oscillators are exhibited over a wide frequency range which narrows with decreasing harmonic excitation amplitudes until disappearing at a critical forcing level. However, for efficient conversion from vibrational to electrical energy in harvesting applications, the bistable oscillator must retain its favorable broadband cross-well response while the input excitation is minimized. To maintain effectiveness at low forcing levels, an actuation approach is proposed where external perturbations are used to extend the oscillator’s cross-well bandwidths by switching from co-existing low to high energy attractors. By utilizing Macro Fiber Composites (MFC) in a [ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>MFC</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>90</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>MFC</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mo>]</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> bistable piezoelectric laminate, the application of rectangular voltage pulse signals are cycled through different response phases to continuously alter the basins of attraction until the desired cross-well orbit is sustained at each frequency. The pulse magnitude is where the system exhibits limit point behavior and the resulting snap through actuation mechanism brings consistency between perturbation trials. A multi degree of freedom electromechanical model that captures the stable shapes and cross-well dynamics and finite element analysis in Abaqus/Standard demonstrate the efficacy of the perturbation method. The model is then employed to significantly increase the bandwidths inducing cross-well oscillations.