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This paper presents the results of numerical simulations of a nonlinear bistable system for harvesting energy from ambient vibrating mechanical sources. Detailed model tests were carried out on an inertial energy harvesting system consisting of a piezoelectric beam with additional springs attached. The mathematical model was derived using the bond graph approach. Depending on the spring selection, the shape of the bistable potential wells was modified including the removal of wells' degeneration. Consequently, the broken mirror symmetry between the potential wells led to additional solutions with corresponding voltage responses. The probability of occurrence for different high voltage/large orbit solutions with changes in potential symmetry was investigated. In particular, the periodicity of different solutions with respect to the harmonic excitation period were studied and compared in terms of the voltage output. The results showed that a large orbit period-6 subharmonic solution could be stabilized while some higher subharmonic solutions disappeared with the increasing asymmetry of potential wells. Changes in frequency ranges were also observed for chaotic solutions. [ABSTRACT FROM AUTHOR]

In this paper, the frequency broadband effect in vibration energy harvesting was studied numerically using a quasi-zero stiffness resonator with two potential wells and piezoelectric transducers. Corresponding solutions were investigated for system excitation harmonics at various frequencies. Solutions for the higher voltage output were collected in specific branches of the power output diagram. Both the resonant solution synchronized with excitation and the frequency responses of the subharmonic spectra were found. The selected cases were illustrated and classified using a phase portrait, a Poincaré section, and recurrence plot (RP) approaches. Select recurrence quantification analysis (RQA) measures were used to characterize the discussed solutions. [ABSTRACT FROM AUTHOR]

A method for selecting dynamic parameters and structures of drive systems using the synthesis algorithm is presented. The dynamic parameters of the system with six degrees of freedom, consisting of a power component (motor) and a two-speed gearbox, were determined, based on a formalized methodology. The required gearbox is to work in specific resonance zones, i.e., meet the required dynamic properties such as the required resonance frequencies. In the result of the tests, a series of parameters of the drive system, defining the required dynamic properties such as the resonance and anti-resonance frequencies were recorded. Mass moments of inertia of the wheels and elastic components, contained in the required structure of the driving system, were determined for the selected parameters obtained during the synthesis. [ABSTRACT FROM AUTHOR]

This paper presents the results of numerical simulations of a non-linear, tristable system for harvesting energy from vibrating mechanical devices. Detailed model tests were carried out in relation to the system consisting of a beam and three permanent magnets. Based on the derived mathematical model and assuming a range of control parameter variability, a three-dimensional image of the distribution of the largest Lyapunov exponent was plotted. On its basis, the regions of chaotic and predictable movement of the considered system exist have been established. With reference to selected plane of the largest Lyapunov exponent cross-sections, possible co-existing solutions were identified. To identify multiple solutions, a diagram of solutions (DS) diagram was used to illustrate the number of existing solutions and their periodicity. The proposed calculation tool is based on the so-called fixed points of Poincaré cross-section. In relation to selected values of the control parameter ω, coexisting periodic solutions were identified for which phase trajectories and basins of attraction were presented. Based on the model tests carried out, it was found that in order to efficiently harvest energy, appropriate transducer adjustment is required. Calibration of the transducer is necessary to obtain the greatest amplitude of vibration of the beam, which corresponds to the phase trajectory limited by external energy potential barriers. As expected, the average voltage induced on the electrodes of the piezoelectric transducer and the average electrical power recorded on the resistive element are directly proportional to the amplitude and average kinetic energy of the beam. [ABSTRACT FROM AUTHOR]