Resonant Shunt Research Articles

Tunable electromagnetic resonant shunt using pulse-width modulation

This article proposes a novel mean for tuning the natural frequency of an electromagnetic resonant shunt, using a pulse-width modulation (PWM) circuit. It is used to modulate the value of the capacitance of the shunt, and the electrical frequency is shown to be proportional to the command parameter of the PWM, the duty cycle. An easy and efficient strategy to tune the resonant shunt in real time is then proposed, thus obtaining a low powered and always stable vibration control device. The article proposes the theory of PWM, giving a robust method to predict the dynamics of the system. Then, an accurate multi-mode theoretical model of the tunable resonant shunt coupled to an elastic structure is proposed and experimentally validated on an elastic multi-mode structure, in the case of two different control strategies. The first one is a standard resonant shunt with both the electrical frequency and damping optimized to reduce a given resonance peak. The second one is based on a resonant shunt with the electrical damping as low as possible, which creates an antiresonance and a “notch” type mechanical response at the driving frequency. Both strategies are experimentally validated with real time variation and adaptation of the electrical frequency, obtaining an efficient vibration control device, able to reduce by a factor 40 the vibration level.

Simultaneous vibration reduction and energy harvesting of a nonlinear oscillator using a nonlinear electromagnetic vibration absorber-inerter

Recently, considerable attention has been given to electromagnetic resonant shunt tuned mass damper-inerters (ERS-TMDI) for simultaneous vibration mitigation and energy harvesting. The application of this design is already well-established for linear structures, however, it is not extensively explored for nonlinear structures. This work, for the first time, aims to achieve both vibration mitigation and energy harvesting for nonlinear oscillating structures using a single device. For this, a novel nonlinear electromagnetic resonant shunt tuned mass damper-inerter (NERS-TMDI) is proposed with two different configurations. The proposed NERS-TMDI is coupled to a nonlinear oscillator via linear and nonlinear springs. For the first configuration, the electromagnetic and the inerter devices are grounded on one side and connected to the nonlinear vibration absorber on the other side. In the second configuration, the electromagnetic device is placed between the nonlinear vibration absorber and the primary structure. The nonlinear governing equations of motion are solved analytically using the method of harmonic balance in conjunction with the fixed arc-length continuation method. The analytical approach is validated using numerical simulations. A detailed parametric analysis for both configurations is conducted to identify the key design parameters that render the best performance of the NERS-TMDI. The results show that the proposed NERS-TMDI configurations perform better than the existing approaches, including the nonlinear tuned mass damper (NTMD), and the ERS-TMDI, in terms of vibration control. The results also show that the first configuration of NERS-TMDI always performs better for simultaneous vibration mitigation and energy harvesting than the second configuration of NERS-TMDI. This implies that grounding the electromagnetic transducer extends the range of effectiveness of the NERS-TMDI. Further, a sensitivity analysis on the optimal Configuration-1 showed that the NERS-TMDI is robust to variations in nonlinear stiffness, but its performance degrades for variations in inertance, resistance, inductance, and capacitance. Additionally, a parametric study demonstrates that higher values of nonlinear stiffness, inertance, and resistance, and lower values of inductance and capacitance render an optimal design of the Configuration-1 of the NERS-TMDI for energy harvesting. The findings are very promising and open a horizon of future opportunities to optimize the design of the NERS-TMDI for superior performance.

Reduction in High-Frequency Wheel Noise/Vibration of Railway Vehicles Using Piezoelectric Shunt

We propose the application of a resonant shunt to wheels to reduce the high-frequency wheel noise generated by railway vehicles. High-frequency wheel noise is caused by the resonance of wheels owing to contact between rails and wheels. A resonant shunt is applied at specific frequencies to reduce wheel resonance. In this work, the high-frequency noise generated by a wheel moving on a curved railway track was analyzed and compared with the dynamic characteristics of the wheel. Further, to reproduce the high-frequency noise of the wheel, an external electric signal was input to a piezoelectric patch connected to the wheel to generate noise and vibration at the natural frequency of the wheel. The optimum mounting position of the piezoelectric patch was determined by numerically analyzing the strain energy of the wheel. Piezoelectric patches were connected to their respective resonant shunts to form a vibration reduction array. A synthetic inductor was tuned to effectively reduce the high-frequency vibration and noise of the wheel generated at its natural frequency. In the wheel excited at its natural frequency, vibration and noise were reduced by approximately 4–10 dB and 8–12 dB(A), respectively. In the wheels that were simultaneously excited at two natural frequencies, vibration and noise were reduced by 5 dB and 5 dB(A), respectively. The results showed that the resonant shunt could effectively reduce the noise and vibration generated by the wheel. Therefore, the resonant shunt is an effective circuit system for reducing noise and vibration even in large structures.

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.

Vibration damping of marine lifting surfaces with resonant piezoelectric shunts

Marine lifting surfaces may undergo flow-induced vibrations due to fluid sources of excitation, leading to shorter life cycles due to structural fatigue and critical to the acoustic performances (e.g hydrofoil singing). As such, accurate understanding of the fluid-structure response of marine structures, as well as vibration control and damping, are critical to many maritime applications. In particular, this work investigates the potential of the electromechanical coupling inherent to piezoelectric materials for passive vibration damping of a cantilever blunt flat plate under hydrodynamic flows. A prototype equipped with piezoelectric ceramics connected to an inductor, in order to act as a resonant piezoelectric shunt, is specifically designed for this study. Its flow-induced vibrations are first assessed within the water tunnel of IRENav to identify the natural frequency of interest to control. It shows that the plate is subjected to von Kármán vortex-shedding with two configurations, namely lock-off for the first-bending mode, and lock-in with the first torsional mode. The latter results in the most extreme vibration cases but is also the most difficult to control. Therefore, the first-bending mode is selected for this first experimental assessment. Second, semi-passive control strategies, using the resonant piezoelectric shunt, have been tested on the targeted natural frequency both in air and in still water. Subsequent comparisons show similar coupling factors, meaning that the performances of the resonant shunt should also be similar in air and in still water. Moreover, a numerical model, based on fluid-structure-piezoelectricity coupling, is also set-up to compute the coupling factors. Hence, a valuable numerical tool is provided for future designs of more complex geometries. Finally, experimental vibration mitigation is achieved both for still water and under hydrodynamic flows, experimentally proving the feasibility and relevance of this control solution for maritime applications.

Improvement in step resolution and response time of ultrasonic motor by using a piezoelectric resonant shunting circuit as damping control.

Ultrasonic motors can be driven by burst voltage to obtain micro-stepping motion, and the corresponding step size depends on the load and cycle number of the applied ac driving voltage in one burst. The rotor of the motor achieves a step motion through a process of startup-acceleration-deceleration-stop. To obtain a large torque (or thrust force) and quick startup, a large vibration amplitude of a stator and a high growth rate are desired; thus, a large mechanical quality factor and a high electromechanical coupling factor are required. However, the stator vibration decays for a long time before it stops because of low mechanical energy loss; meanwhile, the rotor moves a big step. Hence, there is contradiction between thrust force and resolution/response time. This paper presents a new drive method to improve the step resolution and response time while keeping the torque by damping control. By simply adding a switch and a shunting damp circuit and connecting the shunting circuit to ultrasonic motors at the end of a drive burst signal, the stator vibration attenuates more rapidly and the step size is reduced. First, the damping effect of the piezoelectric system with a passive resonant shunting circuit (a resistor and an inductor connected in series) on the free stator of a bar-type rotary traveling wave ultrasonic motor has been tested. Next, a drive circuit comprising electronic switches and the shunting circuit is designed and utilized for measuring the performance of the motor. Experimental results have well proven the proposed method.

A Synthesis Approach to Acoustic Wave Ladder Filters and Duplexers Starting With Shunt Resonator

In this article, we explore how acoustic wave filters starting with shunt resonator require particular reflection phase conditions to ensure that the synthesized filter is feasible. The position of transmission zeros (TZs) along with the phase of the objective filter function might lead to nonfeasible solutions where the first and last resonators require elements with positive reactance slope in the static branch, or equivalently, a nonphysical negative static capacitor. Since the reflection phase of a duplexer-oriented filter is fixed to reduce loading effects, the feasibility problem is solved by bringing the resonance frequency of the first resonator beyond the central frequency of the counter band. However, this entails surpassing the limits of the electromechanical coupling coefficient. We demonstrate how two reactive elements at the input overcome this resonance position limitation and provide a simple rule to decide the right topology. The position of the first TZ of duplexers will play an important role. Moreover, we provide rules on the reflection phase values that ensure that all resonators have a capacitive static branch.

Shunted piezoelectric patches on auxetic microstructures for the enhancement of band gaps

Certain frequency ranges where waves do not propagate, and thus, vibrations are suppressed, are called band gaps. In the present paper, the appearance and the behavior of such areas are investigated on star-shaped auxetic microstructures, which are equipped with shunted piezoelectric elements. The optimal position of the piezoelectric patches is found using genetic algorithms, considering the maximization of the electromechanical coupling coefficient. A genetic algorithm is also used for the calculation of the values of the electrical parameters of the resonant shunt circuit, with objective the maximization of certain band gaps. The results indicate that the proposed technique can be used for the maximization of band gaps at certain frequency ranges, as well as at frequency bands which have not been considered in the optimization problem of the mechanical microstructure.

Modal analysis of finite-size piezoelectric metamaterial plates

Two-dimensional electromechanical metamaterials composed of thin plates with local piezoelectric resonators can display extreme vibration attenuation characteristics at desired frequencies. The typical bandgap analyses in the literature use the assumption of wave propagation in an infinite elastic structure and do not consider the modal characteristics of the structure. However, for practical implementation and design of finite-size electromechanical metamaterials, modal behaviour of the host structure and piezoelectric elements must be coupled with the dynamics of shunt circuits. To this end, we present a system-level modal analysis framework for finite-size thin plates with a segregated array of piezo-patches connected to resonant shunt circuits. The developed model takes into account the spatially discontinuous flexural rigidity of the metamaterial plate due to discrete placement of piezoelectric resonators on the substrate. Using the developed framework, we show that the electrical quality factor of resonators is critical for transitioning from broadband shunt damping to bandgap formation in piezoelectric plate metamaterials. This enables on-demand tailoring of effective dynamic stiffness of metamaterial plates for the targeted task. Lastly, for a fixed number of discrete resonators, we demonstrate the effect of physical gap size between resonators on the bandgap creation. Overall, the modelling frameworks in this study can be used for predicting the dynamics of piezoelectric plate-type metamaterials for applications in waveguiding, attenuation, filtering, and energy harvesting.

Enhancement of a dynamic vibration absorber by means of an electromagnetic shunt

In this study, we address the reduction of structural vibrations by means of an electromagnetic shunt damper (EMSD) combined with a mechanical dynamic vibration absorber (DVA). Two architectures, that differs in the placement of the EMSD with respect to the DVA, are tested, showing that one of them enhances the vibration control. In parallel, three shunt architecture are tested: a resistive shunt, a resonant conservative shunt and a resonant dissipative shunt. Optimal values of the EMSD and DVA parameters are obtained; then, the performances of all architecture, according to relevant criteria, are estimated and compared to a single DVA or a single EMSD. The case of a conservative DVA, that creates an anti-resonance, is particularly targeted. It is shown that the performances rely on two free parameters only: the mass ratio for the DVA and the electromagnetic coupling factor for the EMSD, thus giving generic abacuses that can be applied to any practical cases. Finally, experiments are proposed and a good agreement with the theoretical results is obtained, thus validating them.

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.

Acoustic Radiation Suppression of a Truss Core Sandwich Panel Using Decentralized Resonant Shunt Damping

The aim of the present work was to suppress the free space acoustic radiation of a truss-cored sandwich panel through the use of the decentralized resonant shunt method. First, the finite element model of the structure was established and its sound radiation characteristics were studied using the elemental radiators decomposition method. Then the decentralized modal piezoelectric shunt vibration control strategy of the Kagome sandwich panel was described in detail. In this approach, a small number of rods in the bottom truss of the sandwich panel were replaced by a piezoelectric stack transducer; each transducer was connected to a single resonant shunt which was tuned to suppress the vibration of a specific mode. The biggest advantage of the independent modal resonant shunt method is that the circuits of each mode are independent of each other; thus the large-scale parameter optimization can be decomposed into small-scale optimization problems. The results of the numerical simulation have shown that the approach that has been proposed in this paper is very effective in controlling the sound radiation of the examined structure at its resonant frequency. The results of this study can be useful in the study of the sound radiation suppression of a sandwich panel.

Suppression of Cavity Resonant Coupling by L-Shaped Metal Plate on Microwave Module Lid

This article proposes and implements a novel technique for high spatial isolation that includes the placement of L-shaped metal-plate resonator shunt open-circuited stubs as a band-rejection filter on the lid of a microwave/radio frequency (RF) module. The low-cost, lightweight resonators are realized using a thin metal plate, which is patterned, with high design flexibility, and bent. This article demonstrates that the resonator is equivalent to a quarter-wavelength shunt open-circuited stub in a parallel-plate waveguide, which effectively suppresses the cavity resonant mode in the housed microwave/RF module. In addition, the robust design of the bent section and the determination of the resonator size, from the common ground to the open-circuited end, are presented. The suppression of the coupling level via cavity resonance is demonstrated by the $X$ -band measurements, where the suppressed fractional bandwidth is 46.8% of −63 dB, which is the highest reduction level achieved with an absorber model in this frequency band. These measurement results are in good agreement with the theoretical and electromagnetic simulation results.

Robust project of resonant shunt circuit for passive vibration control of composite structures

Composite structures have been widely used in petroleum, aerospace and automotive industries for which structural components must be designed to support high levels of mechanical disturbances with typically high reliability levels. Moreover, the increasing high-speed and lightweight composite structures subjected to vibrations, and the interest in achieving vibration attenuation becomes capital importance as extensive vibrations can reduce structural life and contribute to mechanical failure. In this sense, smart materials can be used as an excellent alternative, being able to stabilize these structures. Thus, the use of shunted piezoceramics has received major attention in the last decades. The contribution intended herein is the proposition of a robust passive vibration control tool by using resonant shunt circuits. The stochastic finite element method is used, and the uncertain variables are modeled as Gaussian random fields and discretized in accordance with the Karhunen–Loeve expansion method. Numerical applications are presented, and the main features and capabilities of the proposed method are highlighted.

LRLC-shunted piezoelectric vibration absorber

This paper addresses a new approach for mono-modal vibration reduction by means of a piezoelectric shunt. It is based on an innovative shunt impedance which allows to improve the attenuation performance and the robustness to mistuning compared to the use of the classical resonant shunt. This result is achieved by building a network, composed of two inductances, one capacitance and one resistance, which generates two resonances, instead of the single resonance imposed by the classical resonant shunt. All the theoretical results discussed in the paper are validated by an experimental campaign on a tailored set-up. These tests show a good agreement between theoretical and experimental results and thereby validate the benefits of the new approach.

An Experimental Study of a Piezoelectric Metastructure With Adaptive Resonant Shunt Circuits

There is a growing interest for research toward enabling on-demand reconfigurable and readjustable metastructures with dynamic response tailoring capabilities. In this article, a metastructure with piezoelectric unit cells shunted to self-tuning resonant circuits is experimentally explored to enable adaptive behavior in the resulting system dynamics with focus on vibration attenuation. Synthetic inductor circuits are combined with digital potentiometers to enable real-time tuning of the resonant shunts. A microcontroller unit was employed to detect the excitation frequency and properly adjust the resonant circuits. Experimental results are presented for a base-excited, locally resonant, piezoelectric plate following a discussion of the adaptive circuit. For a certain metamaterial configuration, a broad suppression range (102–622 Hz) was observed. The bandwidth of 520 Hz (84% of the upper limiting frequency) could be increased according to the electrical elements of the adaptive circuit.

Wideband Phase Shifters With Miniaturized Size on Multiple Series and Shunt Resonators: Proposal and Synthetic Design

In this article, a new class of wideband phase shifters with very compact size, large phase shift value, low insertion loss (IL), and low cost are presented and developed. The proposed phase shifter consists of N series and shunt resonators, which can achieve the magnitude and phase shift bandwidth of more than 120% thanks to N transmission poles. Besides the wideband property, the proposed phase shifter is able to achieve a small size of nearly 1/10 guided wavelength (λg), which has a size reduction of more than 90% as compared with conventional wideband phase shifters on printed circuit board (PCB). Meanwhile, insertion phases for the both series and shunt resonators are zero at their resonant frequencies; thus, the length of reference line can be also greatly reduced. What is more, a detailed synthesis method with closed-form equations is presented and employed to determine all circuit parameters of the proposed phase shifter with the specified in-band return loss (RL), phase shift value AΦ, and resonator number N. To validate the design concept, three design examples of 90° and 180° phase shifters on N = 3 and N = 5 are synthesized and tested. Theoretical, simulated, and measured results are in a fairly close agreement. In particular, the proposed phase shifters feature very low IL. The measured maximum in-band IL is only 0.38 dB for N = 3 (AΦ = 90°) and 0.50 dB for N = 5 (AΦ = 180°).

Phase Random Metasurface With Diffuse Scattering Based on Subwavelength Unit’s Design of Shunt Resonance Circuit

It is known that metasurface composed of randomly distributed subwavelength unit cells with different reflection phases features some specific electromagnetic behaviors, of which diffuse scattering property can be applied to reduce Radar Cross Section (RCS). In this paper, a subwavelength unit cell based on shunt resonance is designed. Since shunt resonance can provide stable phase distribution within the range between its double resonant frequency points, reflection phase variation of the subwavelength unit cell can be slight. Equivalent transmission line model presented proves effective on extracting reflection phase of a sub-wavelength unit cell. Referring to variation of its normalized reactance versus frequency, we adjusted microstructure layout of the sub-wavelength unit cell until its reflection phase variation become gentle over X and Ku band. Six different scaling unit cells are chosen to form diffuse scattering metasurface. Simulation and experimental results exhibit that monostatic RCS reduction more than 10 dB can be realized over X and Ku band.

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

Abstract 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.

Voltage-Controlled Synthetic Inductors for Resonant Piezoelectric Shunt Damping: A Comparative Analysis

In this paper, the design, simulations, and experimental results related to new analog circuits for voltage controlled synthetic inductors (VCSI) are presented. The new circuits based on a generalized impedance converter (GIC) are proposed for adaptive resonant piezoelectric shunt damping. The VCSIs are implemented using (1) an analog multiplier and (2) an operational transconductance amplifier (OTA) as voltage-controlled resistor. The simulation and experimental results for the new proposed VCSIs are presented and a comparative analysis follows. The proposed VCSIs work in a stable manner in parallel with negative impedance converters (NIC) to enhance structural damping in resonant piezoelectric resistive-inductive shunt applications. The behavior of the synthetic inductor is identical to a real inductor only in a specific frequency range and this situation can explain the reported spreading performance in the literature for resonant piezoelectric shunt damping. The simulation results are validated by a group of experimental investigations that confirm the improved stability and linearity of the new circuits proposed as VCSIs. Experimental results show that the VCSI based on an analog multiplier have an enhanced linearity in comparison with the OTA version in a limited voltage control range.