Influence of asymmetric potential on multiple solutions of the bi-stable piezoelectric harvester

Influence of potential well asymmetry on the dynamics of magneto-elastic and piezo-magneto-elastic harvesters with symmetric and asymmetric bi-stable potential wells are investigated in this article. An autonomous algorithm is developed which categorizes the response obtained under different harmonic excitations and initial conditions into seven unique-primary attractor solutions. Influence of two small and two moderate levels of asymmetry in potential well is visualized at the different excitation frequencies through the attractor basins and largest Lyapunov exponent of the solutions. The results of the numerical investigations prove that small and moderate levels of asymmetry considered in this investigations have insignificant influence on the desirable cross-well periodic solution. Also, under small asymmetry levels, the cross-well periodic solutions preferably transform into other cross-well solutions only, viz. cross-well subharmonic and chaotic solutions, if attainable. In addition, these asymmetry levels are beneficial in restraining the chaos-prone solutions and even boost up the basin areas of the cross-well periodic solution. A reduction in chaos-prone responses not only implies a simplified and efficient energy harvesting circuitry, but also results in an improved life expectancy of the transduction material as the instances of stress reversals are reduced