A nonlinear piezoelectric shunt absorber with 2:1 internal resonance: experimental proof of concept

An experimental proof of concept of a new semi-passive nonlinear piezoelectric shunt absorber, introduced theoretically in a companion article, is presented in this work. This absorber is obtained by connecting, through a piezoelectric transducer, an elastic structure to a resonant circuit that includes a quadratic nonlinearity. This nonlinearity is obtained by including in the circuit a voltage source proportional to the square of the voltage across the piezoelectric transducer, thanks to an analog multiplier circuit. Then, by tuning the electric resonance of the circuit to half the value of one of the resonances of the elastic structure, a two-to-one internal resonance is at hand. As a result, a strong energy transfer occurs from the mechanical mode to be attenuated to the electrical mode of the shunt, leading to two essential features: a nonlinear antiresonance in place of the mechanical resonance and an amplitude saturation. Namely, the amplitude of the elastic structure oscillations at the antiresonance becomes, above a given threshold, independent of the forcing level, contrary to a classical linear resonant shunt. This paper presents the experimental setup, the designed nonlinear shunt circuit and the main experimental results.

Guidelines for the layout and tuning of piezoelectric resonant shunt with negative capacitances in terms of dynamic compliance, mobility and accelerance

This paper addresses the vibration attenuation provided by the resonant piezoelectric shunt enhanced by means of negative capacitances. The shunt impedance is composed by one or two negative capacitances, a resistance and an inductance. It is shown that closed analytical formulations, common to all the possible connections of the negative capacitances, can be derived for the tuning of the circuit components and for the prediction of the attenuation in terms of dynamic compliance, mobility and accelerance. The paper also compares the attenuation performance provided by the two possible layouts for the electrical link between the resistance and the inductance, that are series and parallel. Furthermore, this work evidences which shunt configurations offer advantages in terms of practical implementation and the benefits provided by the use of negative capacitances in the shunt circuit. In the last part of the paper, guidelines for the use of resonant shunt are given to the reader and, finally, the theoretical results are validated by means of an experimental campaign showing that it is possible to cancel the resonance on which the resonant shunt is targeted.

Simultaneous Vibration Mitigation and Energy Harvesting for a Nonlinear Oscillator

Considerable attention has been recently given to electromagnetic resonant shunt tuned mass damper-inerter (EH-TMDI) for simultaneous vibration mitigation and energy harvesting. However, only linear structures have been investigated. Hence, in this paper, we aim at simultaneously achieving vibration mitigation and energy harvesting for nonlinear oscillators. To do so, we attach a nonlinear electromagnetic resonant shunt tuned mass damper-inerter (NEH-TMDI) to a single degree of freedom nonlinear oscillator (Duffing Oscillator). The nonlinear oscillator is coupled to the tuned mass damper via a linear and a nonlinear spring. Both the electromagnetic and the inerter devices are grounded on one side and connected to the nonlinear vibration absorber on the other side. This is done so to relax the trade off between energy harvesting and vibration suppression. The electromagnetic transducer is shunted to a resistor-inductor circuit. The governing equations of motion are derived using Newton’s method. Numerical simulations are carried out to examine the performance of the proposed NEH-TMDI. Comprehensive parametric analyses are conducted to identify the key design parameters that render the best performance of the NEH-TMDI. The results show that selected parameters offer regions were maximum energy dissipated and maximum energy harvested coincide. The findings are very promising and open a horizon of future opportunities to optimize the design of the NEH-TMDI for superior performance.

High-voltage synthetic inductor for vibration damping in resonant piezoelectric shunt

Resonant piezoelectric shunts are a well-established way to reduce vibrations of mechanical systems suffering from resonant condition. The vibration energy is transferred to the electrical domain through the bonded piezoelectric material where it is dissipated in the shunt. Typically, electrical and mechanical resonance frequencies are several orders apart. As such, finding a suitable high inductance component for the resonant shunt is not feasible. Therefore, these high inductance values are mimicked through synthetic impedances, consisting of operational amplifiers and passive components. A downside of these synthetic impedances is that standard operational amplifiers can only handle up to 30 V peak to peak and the state-of-the-art amplifiers up to 100 Vpp. However, as mechanical structures tend to become lighter and more flexible, the order induced voltages over the piezoelectric material electrode voltages increase above these limitations. In this research, a high-voltage synthetic inductor is proposed and built by combining the bridge amplifier configuration and the output voltage boost configuration around a single operational amplifier gyrator circuit, effectively quadrupling the range of the synthetic inductor to 400 Vpp. The impedance of the circuit over a frequency range is numerically and experimentally investigated. The synthetic inductor is then connected to a piezoelectric material bonded to a cantilever beam. Numerical and experimental investigation confirms the high-voltage operation of the implemented circuit and its suitability as a vibration damping circuit.

Analysis and Numerical Evaluation of H∞ and H2 Optimal Design Schemes for an Electromagnetic Shunt Damper

The electromagnetic coupling effect can generate electromagnetic damping to suppress disturbance, which can be utilized for vibration serviceability control in civil engineering structures. An electrodynamic actuator is used as a passive electromagnetic damper (EMD). Ideally, the EMD is assumed to be attached between the ground and the structure. The kinetic energy of the vibrating structure can be converted to electrical energy to activate the electromagnetic damping. To induce appropriate damping, the two terminals of the damper need to be closed and cascaded with a resonant shunt circuit as an electromagnetic shunt damper (EMSD). In this study, an resistance–inductance–capacitance (RLC) oscillating circuit is chosen. For determination of optimal circuit components and comparing against the tuned mass damper (TMD), existing H∞ design formulae are applied. This work extends this with a detailed development of an H2 robust optimization technique. The dynamic properties of a footbridge structure are then selected and used to verify the EMSD optimal design numerically. The vibration suppression performance is analytically equivalent to the dynamic characteristic of the TMD and has feasible installation and better damping enhancement. To further evaluate the potential application of the EMSD, multi-vibration mode manipulation via connecting multiple RLC resonant shunt circuits is adopted. The multiple RLC shunt circuit connecting to EMD is an alternative to the single mode control of a traditional TMD. Therefore, the EMSD can, in principle, effectively achieve suppression of single and multiple vibration modes.