Piezoelectric Shunt Research Articles

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.

Dynamic modeling for rotor-bearing system with electromechanically coupled boundary conditions

In this paper, a method based on Green's function is proposed for the dynamic analysis of a rotor-bearing system with electromechanically coupled boundary conditions. The rotor system is supported by two ring-shaped piezoelectric dampers, which has been manufactured in our previous research. Based on the piezoelectric shunt resonant circuits, e.g., current flowing shunt circuit, the rotor system's boundary condition will become complicated and electromechanically coupled. The Laplace transform method is applied to solve the partial governing equations with such boundary conditions and the steady-state whirl Green's function is derived subsequently. Since the Green's functions are fundamental solutions of the system, the steady-state whirl solutions can be obtained by applying the superposition principle. Owing to the solutions’ concise form, it is convenient and suitable for analysis and computation. Validation of the proposed method is demonstrated by comparison with the finite element method (FEM). The simulated results show that the analytical solutions possess high accuracy and the piezoelectric damper has significant damping 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.

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.

Active control on topological immunity of elastic wave metamaterials

The topology concept in the condensed physics and acoustics is introduced into the elastic wave metamaterial plate, which can show the topological property of the flexural wave. The elastic wave metamaterial plate consists of the hexagonal array which is connected by the piezoelectric shunting circuits. The Dirac point is found by adjusting the size of the unit cell and numerical simulations are illustrated to show the topological immunity. Then the closing and breaking of the Dirac point can be generated by the negative capacitance circuits. These investigations denote that the topological immunity can be achieved for flexural wave in mechanical metamaterial plate. The experiments with the active control action are finally carried out to support the numerical design.

Experimental validation of piezoelectric shunt tuning with residual mode correction: Damping of plate-like structures

The effective vibration mitigation properties of piezoceramic patches with inductive-resistive shunts are investigated experimentally. A shunt tuning method is proposed, in which a consistent correction for the influence from residual vibration modes is included by an effective modal capacitance, evaluated from measured charge and voltage amplitudes in short- and open-circuit conditions, respectively. The robustness of the proposed method is verified experimentally for both a free beam and a free plate structure with four shunted piezoceramic patch pairs. A stable and fully passive inductor is produced by winding a copper wire around a magnetic core, which requires precise inductance tuning to determine the final number of turns. It is demonstrated that the effective modal capacitance interpolates consistently between the blocked and static capacitances, commonly used for single-mode tuning of piezoelectric inductive-resistive shunts. By imposing pseudo-random vibrations, the piezoelectric current and voltage signals are measured and evaluated by their frequency response functions. Spectrum peak values determine the apparent short-circuit charge to open-circuit voltage ratio for each shunt, which directly determines the shunt components by explicit tuning formulas. Good correlation between numerical and experimental results are obtained for the free beam, while for the free plate experiment effective multi-mode shunt tuning is obtained by a modified effective electromechanical coupling coefficient.

Consistent frequency-matching calibration procedure for electromechanical shunt absorbers

Electromagnetic and piezoelectric shunt damping can be represented by an equivalent mechanical vibration absorber with a spring, dashpot, and inerter in series. A common calibration procedure for multiple electromechanical shunt absorbers is obtained by this equivalence, including a correction for the influence from residual vibration modes by additional modal terms, whose coefficients are consistently identified by frequency matching for the system with rigid absorber dashpots. The accuracy and robustness of the calibration procedure are verified numerically for an unsupported truss structure with rigid body modes.

Design of dry friction and piezoelectric hybrid ring dampers for integrally bladed disks based on complex nonlinear modes

This paper investigates a new passive damper coupling the energy dissipative mechanisms of dry friction and piezoelectric shunting circuit for Integrally Bladed Disks (blisks). The idea is to distribute piezoelectric material to the dry friction ring so that the elastic deformation of the dry friction ring is utilized to generate additional damping. Mounting piezoelectric material on the additional structure instead of the host structure is a more practical alternative to install piezoelectric damping devices to realistic mechanical systems. This improves the reliability and maintainability of both dampers and host structures. Based on the concept of Complex Nonlinear Modes (CNMs), the dry friction damping effect of the proposed damper is measured through the modal damping ratio for target modes. Modal Electromechanical Coupling Factor (MEMCF) is extended to nonlinear electromechanical coupling systems in order to quantify the additional piezoelectric damping ratio. The damping effect of the hybrid damper is also evaluated by the maximal response amplitude in the frequency domain by the forced response analysis. On one hand, it validates the results from the nonlinear modal analysis, on the other hand, it serves as a reference to choose the optimum design parameters of the hybrid damper. Steady-state response of the cyclic symmetric structure under engine-order excitation is calculated by the Multi-Harmonic Balance Method (MHBM). A phenomenological lumped parameter model representing a blisk with a hybrid ring damper is firstly studied to demonstrate the methodology. Then a blisk finite element model is used as a demonstrator to quantitatively verify the effectiveness of the idea. It is shown that for those modes that can be damped by the dry friction damper, the addition of piezoelectric material further enhances the damping effect.

A lightweight adaptive hybrid laminate metamaterial with higher design freedom for wave attenuation

In this paper, we design a lightweight adaptive hybrid laminate metamaterial with higher design freedom for wave attenuation. The adaptive hybrid laminate acoustic metamaterials are composed of carbon-fiber-reinforced polymer (CFRP) and a periodic array of piezoelectric shunting patches attached to the laminate. A comprehensive analytical model is first developed to reveal the tunable wave attenuation capability in regard to the equivalent bending stiffness of lightweight adaptive hybrid laminate metamaterial. The tunable wave attenuation behavior has been confirmed through finite element modeling (FEM). Numerical results demonstrate that the lightweight adaptive hybrid laminate metamaterial with the shunting circuits can remarkably suppress wave propagation compared to the un-shunted case. In addition, the effects of the laminate’s parameters as well as the shunting circuits on the bandgap’s location and bandwidth are discussed. By introducing the negative capacitance shunting circuit into the piezoelectric patches, the bandwidth can be enlarged significantly.

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.

Estimation and measurement of effective line mobility on a non-deterministic thin plate excited by a piezoelectric patch

This paper derived the expression to estimate the effective line moment mobility of a non-deterministic thin plate under moment excitation by a piezoelectric patch actuator. The piezoelectric patch actuator is assumed to generate purely line moments at each of its edges and regarded as a finite number of point moments acting on an infinite plate, which is achieved by integration method. The theoretical model is validated using MATLAB simulation and compared with experimental measurements on a randomized thin plate. The derived effective line moment mobility managed to closely estimate high-frequency response while cutting significant computational time and resource. Results from this study can be used in many applications ranging from vibration isolation where power transmission between the isolator with an area distribution and its host structure can be determined more accurately, and to design the optimal shunt circuit of a piezoelectric shunt damper for maximum power dissipation in order to reduce vibration of a non-deterministic thin plate.

Reduction of structural vibrations with the piezoelectric stacks ring

It is known that piezoelectric material shunted with external circuits can convert mechanical energy to electrical energy, which is so called piezoelectric shunt damping technology. In this paper, a piezoelectric stacks ring (PSR) is designed for vibration control of beams and rotor systems. A relative simple electromechanical model of an Euler Bernoulli beam supported by two piezoelectric stacks shunted with resonant RL circuits is established. The equation of motion of such simplified system has been derived using Hamilton’s principle. A more realistic FEA model is developed. The numerical analysis is carried out using COMSOL® and the simulation results show a significant reduction of vibration amplitude at the specific natural frequencies. Using finite element method, the influence of circuit parameters on lateral vibration control is discussed. A preliminary experiment of a prototype PSR verifies the PSR’s vibration reduction effect.

Hybrid control technique for vibroacoustic performance analysis of a smart doubly curved sandwich structure considering sensor and actuator layers

The present approach considers hybrid control strategy to reduce the amount of transmitted sound through a multilayered doubly curved sandwich shell equipped with piezoelectric layer and shunt circuit. The construction is composed of some piezoelectric actuator and sensor layers as an active controller as well as resistance–inductance shunt circuit as passive controller. In addition, a layer made of isotropic material is also sandwiched as a core. Firstly, in order to obtain the electromechanical equations of curved shell integrated with piezoelectric layers, Hamilton’s principle, and shear deformation shallow shell theory are employed. After presenting the sound transmission loss of structure, the reliability of the formulation is checked by the aid of previous outcomes. In the following, the piezoelectric layers coupled with shunt circuit are employed to inspect the influence of these patches on the control of transmitted sound through structure. The results indicate that the shunt circuit is able to enhance the sound transmission loss at resonant frequency with no need source of energy. Since in designing the engineering structures, the transmitted noise control is important especially in the resonant frequency, the influence of using several parallel shunt circuits with each piezoelectric layer is also examined. It is shown that increment of the number of parallel shunt circuits implies substantial reduction of transmitted sound to the structure in the resonant frequency. Finally, the solution process is followed to study the effect of active control on the acoustic transmission. Then, it is found that employing the simultaneous active and passive controllers not only cause to reduce the transmitted noise in the resonant frequency but also make to improve the behavior of sound transmission loss in entire range of frequency.

Multi-mode piezoelectric shunt damping with residual mode correction by evaluation of modal charge and voltage

A resonant, piezoelectric shunt tuning procedure is based on the limiting eigenvalue problems associated with short and open circuiting of the piezoelectric domains attached to a vibrating structure. Whereas short circuit and open circuit frequencies are directly obtained from the eigenvalues, the associated electrical equation further determines a modal charge as an short circuit reaction force and a new modal voltage from the electric deflection in the open circuit limit. By a modal representation with short circuit mode shapes the structural equation fully decomposes, while the inherent contributions from non-resonant vibration modes in the corresponding electrical equation consistently define an effective modal capacitance, conveniently estimated by the modal charge to voltage ratio. The shunt tuning is obtained from the governing characteristic equation for the targeted vibration mode, in which the residual mode correction is explicitly represented by the effective modal capacitance. The tuning procedure with an effective modal capacitance is generalized to multiple piezoelectric domains with independent shunts for simultaneous damping of multiple vibration modes. The accuracy of the proposed shunt tuning methods is demonstrated by a numerical beam example with three piezoceramic patch pairs and independent resistive–inductive shunts. The analysis is carried out in a commercial finite element program, in which the required modal frequencies, charge and voltage are readily available as output to the short circuit and open circuit eigenvalue problems.

A novel ring-shaped vibration damper based on piezoelectric shunt damping: Theoretical analysis and experiments

In this paper, a novel ring-shaped piezoelectric damper is proposed; meanwhile, vibration control on a single-DOF system is performed by using it. This damper, called vibration ring, may be used for vibration control of rotating machinery. It has the appearance of a metal ring and can be installed between supporting structure and bearing house. Damping is achieved using piezoelectric stack connected with series resonant RL shunts as fundamental element. Surrounding the stack is a metal structure, which squeezes the stack along its poled axis when the damper is excited by radial forces. Due to its unique configuration, this damper is stiffer than traditional damping devices and can protect stacks very well. In order to analyze and demonstrate the performance of such damper, the electromechanical coupling equation of this damper is firstly derived. Next, the force transmissibility between simplified rotor/shaft and supporting structure is obtained from the foregoing equation in Laplace form. Then the optimum inductance value of shunt circuit is determined. Finally, the performance of vibration ring is demonstrated through simulations and experiment based on a test rig. The experimental results show that the force transmissibility is reduced about 57.75% at resonant frequency.

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.

Dynamics of space- and time-modulated metastructures

Topology has recently emerged as a principle governing unique wave transport phenomena through interface or edge modes that are impurity-immune and potentially unidirectional. In this context, this presentation illustrates the effect on dispersion topology of modulations of properties in space and time. The two modulation strategies are shown to lead to dual phenomena, which can be described by interchanging frequency and wavenumber, and that manifest themselves as gaps enabling frequency/wavenumber-selective wave manipulation. Time modulation produces narrowband tunable reflection at a frequency determined by the modulation, which is illustrated on a beam waveguide with switching negative impedance piezoelectric shunts. Adiabatic, or slow, space modulation of the stiffness properties of a plate structure drives the transition from a localized state at one boundary, to a bulk state and, finally, to another localized state at the opposite boundary. The presented investigations suggest the application of modulation strategies for single-port tunable filtering devices that may be implemented in acoustic, mechanical or photonic platforms. Moreover, the considered experimental platforms allow the exploration of various unique properties associated with time and/or space modulation, including filtering, frequency conversion, non-reciprocity, and topological pumping for wave redirection.Topology has recently emerged as a principle governing unique wave transport phenomena through interface or edge modes that are impurity-immune and potentially unidirectional. In this context, this presentation illustrates the effect on dispersion topology of modulations of properties in space and time. The two modulation strategies are shown to lead to dual phenomena, which can be described by interchanging frequency and wavenumber, and that manifest themselves as gaps enabling frequency/wavenumber-selective wave manipulation. Time modulation produces narrowband tunable reflection at a frequency determined by the modulation, which is illustrated on a beam waveguide with switching negative impedance piezoelectric shunts. Adiabatic, or slow, space modulation of the stiffness properties of a plate structure drives the transition from a localized state at one boundary, to a bulk state and, finally, to another localized state at the opposite boundary. The presented investigations suggest the application of mo...

Stiffness and damping effects of the rhombic piezoelectric stack transducer with a negative capacitance shunt

The piezoelectric shunt damping (PSD) is widely utilized to control structural vibrations based on its damping performance. Unlike previous studies, this work considers the stiffness and damping effects of a rhombic piezoelectric stack transducer with a negative capacitance shunt. The piezoelectric shunt stiffness (PSS) and the PSD concepts are proposed and theoretically modelled to investigate the stiffness and damping performance. The piezoelectric stack transducer with a negative capacitance can achieve both negative and positive stiffnesses to tune the natural frequency of the host structure. The root locus methods are utilized to judge the stability of the system. Both numerical simulation and experimental results demonstrate that the negative stiffness and the positive stiffness of the system greatly depend on the negative capacitance, while the damping depends on the resistance.

Piezoelectric Shunt Stiffness in Rhombic Piezoelectric Stack Transducer with Hybrid Negative-Impedance Shunts: Theoretical Modeling and Stability Analysis.

Negative-capacitance shunted piezoelectric polymer was investigated in depth due to its considerable damping effect. This paper discusses the novel controlled stiffness performance from a rhombic piezoelectric stack transducer with three hybrid negative-impedance shunts, namely, negative capacitance in series with resistance, negative capacitance in parallel with resistance, and negative inductance/negative capacitance (NINC) in series with resistance. An analytical framework for establishing the model of the coupled system is presented. Piezoelectric shunt stiffness (PSS) and piezoelectric shunt damping (PSD) are proposed to analyze the stiffness and damping performances of the hybrid shunts. Theoretical analysis proves that the PSS can produce both positive and negative stiffness by changing the negative capacitance and adjustable resistance. The Routh–Hurwitz criterion and the root locus method are utilized to judge the stability of the three hybrid shunts. The results point out that the negative capacitance should be selected carefully to sustain the stability and to achieve the negative stiffness effect of the transducer. Furthermore, negative capacitance in parallel with resistance has a considerably better stiffness bandwidth and damping performance than the other two shunts. This study demonstrates a novel electrically controlled stiffness method for vibration control engineering.

Exact Solutions to H∞ and H2 Optimizations of Passive Resonant Shunt Circuit for Electromagnetic or Piezoelectric Shunt Damper

In this work, exact closed-form solutions are derived for optimizing the resonant shunt circuits of electromagnetic shunt dampers (EMSDs), which use an electromagnetic transducer, and piezoelectric shunt dampers (PZSDs), which use a piezoelectric element, shunted with an electric circuit. Modeling of the EMSD and PZSD is unified by nondimensional parameters. The optimization criteria selected for the EMSD and PZSD are H∞-norm minimization, H2-norm minimization, and exponential time-decay rate maximization. The aim of this study is to derive for the first time the exact solutions that have not previously been investigated, including cases that consider the inherent damping of the primary system. This paper comprehensively summarizes the exact solutions based on the optimization criteria together with approximated solutions obtained by the fixed-point method, which is commonly used to optimize the dynamic vibration absorber (DVA).