Optimization study of a piezoelectric bistable generator with doubled voltage frequency using harmonic balance method

Bistable generator for vibration energy harvesting is one of the most promising solutions to reach practically enhanced performance. Due to the buckled–spring–mass–specific behavior, the deformation of the piezoelectric transducer is nonlinearly dependent on the displacement, especially in the inter-well motion case. An analytical model is developed using harmonic balance analysis for the buckled–spring–mass generator architecture. Contrary to the usual method, a special doubled frequency voltage solution in the inter-well motion case is assumed in harmonic balance analysis to obtain an accurate predictive model, which is validated by experimental results. The influence of five critical parameters on the performance is thoroughly discussed. Design rules are then deduced: low damping ratio, properly high coupling level, matched load, optimal buckling level, and low characteristic frequency are required to get optimal performance in the inter-well motion case. Besides, we show some interesting results about the parameter optimization study.

Harmonic Balance Analysis of Snap-Through Orbits in an Undamped Duffing Oscillator

A simple nonlinear undamped Duffing oscillator has been studied for its snap-through behavior at large-amplitude vibrations. We present an algorithm that uses the harmonic balance (HB) method to find amplitude and frequency relationships in two- and three-term approximations for solutions that lie outside the separatrix in the phase space. Trends of the approximate solution properties are examined with reference to an analysis of the limit as the trajectory approaches the separatrix.