Inductive-resistive Circuits Research Articles

Nonlinear analysis of galloping piezoelectric energy harvesters with inductive-resistive circuits for boundaries of analytical solutions

For nonlinear characterization of the galloping piezoelectric energy harvester with the inductive-resistive circuit, the electromechanical coupled distributed parameter model is concisely retrospected. A general electromechanical decoupled model is proposed for the series and parallel circuits with different algebraic expressions of the electrical damping and modified frequency. The electrical damping corresponding to Hopf bifurcation (EDHB) is derived and noticed to be linearly and positively varied with the wind speed. Galloping occurs when the electrical damping is smaller than EDHB. To analyze the effects of the electrical circuits on Hopf bifurcation, the inductance corresponding to Hopf bifurcation (IHB) is proposed as a function of the load resistance and EDHB. The stable and galloping regions of the inductance and modified frequency varied with the wind speed are determined and found to be strongly dependent on the load resistance. Hopf bifurcation for the small load resistance of the series connection is similar as that for the large load resistance of the parallel case, and vice versa. The time history, phase portrait and power spectrum are introduced to show the differences between the results obtained with the small and large initial conditions. It is found that the large initial condition corresponds to the large electrical damping and the small initial condition relates to the small electrical damping. This is expected to be the reason that the large electrical damping is more difficult to be excited. Different from our common concept, the tip displacement with the small initial condition is larger than that with the large initial condition in some situations. With the galloping region determined by the presented nonlinear analyses, the analytical solutions agree well with the numerical results using the small and large initial conditions.

Optimization study on inductive-resistive circuit for broadband piezoelectric energy harvesters

The performance of cantilever-beam piezoelectric energy harvester is usually analyzed with pure resistive circuit. The optimal performance of such a vibration-based energy harvesting system is limited by narrow bandwidth around its modified natural frequency. For broadband piezoelectric energy harvesting, series and parallel inductive-resistive circuits are introduced. The electromechanical coupled distributed parameter models for such systems under harmonic base excitations are decoupled with modified natural frequency and electrical damping to consider the coupling effect. Analytical solutions of the harvested power and tip displacement for the electromechanical decoupled model are confirmed with numerical solutions for the coupled model. The optimal performance of piezoelectric energy harvesting with inductive-resistive circuits is revealed theoretically as constant maximal power at any excitation frequency. This is achieved by the scenarios of matching the modified natural frequency with the excitation frequency and equating the electrical damping to the mechanical damping. The inductance and load resistance should be simultaneously tuned to their optimal values, which may not be applicable for very high electromechanical coupling systems when the excitation frequency is higher than their natural frequencies. With identical optimal performance, the series inductive-resistive circuit is recommended for relatively small load resistance, while the parallel inductive-resistive circuit is suggested for relatively large load resistance. This study provides a simplified optimization method for broadband piezoelectric energy harvesters with inductive-resistive circuits.

Electromechanical decoupled model for cantilever-beam piezoelectric energy harvesters with inductive-resistive circuits and its application in galloping mode

The electromechanical decoupled distributed parameter model for cantilever-beam piezoelectric energy harvesters with inductive-resistive circuits is proposed. The modified natural frequency and electrical damping for series and parallel inductive-resistive cases are derived, which are functions of the first natural frequency of the cantilever beam, capacitance of the piezoelectric layers, load resistance, inductance and electromechanical coupling term. As a demonstration, we apply the decoupled model to cantilever-beam piezoelectric energy harvesters operated in the galloping mode. The average harvested power is derived as an algebraic expression of the electrical damping in addition to the wind speed, aerodynamic parameters of the bluff body and mechanical properties of the cantilever beam. Besides these impacts, the amplitude of the tip displacement also depends on its modified natural frequency. The electromechanical decoupled model and its analytical solutions are confirmed by the numerical solutions of the coupled model for the galloping mode. The theoretical expressions for the maximal harvested power and corresponding tip displacement at the optimal electrical damping are then developed. The cantilever-beam piezoelectric energy harvester with the inductive-resistive circuit has multiple solution sets of the modified natural frequency and electrical damping. Any optimal electrical damping can be realized by series or parallel inductive-resistive circuit, which cannot be accomplished by pure resistive circuit. By introducing the inductance to the circuit of the galloping piezoelectric energy harvester, the performance of such a system is improved with larger maximal harvested power at high wind speed and smaller amplitude of the tip displacement. This study provides a theoretical approach to capture the intrinsic effects of the inductance in addition to the load resistance on the performance of cantilever-beam piezoelectric energy harvesters.

Pulse mode of operation of a spherical piezoceramic transducer filled with liquid and having a correcting electric circuit

By means of a computational method, the possibility of radiating a short acoustic pulse by a transducer in the form of a piezoceramic sphere internally filled with liquid is investigated. An electric inductive-resistive circuit is connected to the electric input of the transducer. Solution is obtained based on scheme-analogs theory for piezoceramic transducers, and spectral Fourier transform theory. The values of parameters of the system, providing minimal durations of radiated signals, are determined. Computation was carried out for different values of relative thicknesses of the transducer wall. The estimates of durations and amplitudes of the acoustic signals radiated into the external medium are obtained.

Study of the possibility of producing a short acoustic pulse using an inductive-resistive circuit connected to the input of a radiator loaded on a solid through a contact layer

A scheme of radiation is considered that consists of a piezoelectric plate with an RL-circuit connected to its input and that is loaded on a solid through a contact layer. A study of the effect that the system’s characteristic parameters have on the duration and amplitude of radiated pulses for different wavelengths thicknesses, specific acoustic impedance of the contact layers, and different acoustic loads is performed on the basis of numerical calculations. Concrete estimates are presented that show the use of the optimal (from the viewpoint of the minimum duration of radiated pulses) characteristic parameters of the system to obtain short acoustic pulses over a rather wide range of the contact-layer wave thicknesses is made possible.