Resonant Shunt Research Articles

Design of inductors with high inductance values for resonant piezoelectric damping

The resonant piezoelectric shunt requires specific inductance and resistance values in order to reach an optimum in terms of vibration reduction. Yet, practical limits appear in the low frequency range: the required inductance and the corresponding quality factor are often too high to be satisfied with standard passive components. In this paper, inductors are designed with closed magnetic cores made of high permeability materials. Those components are successively integrated into a piezoelectric shunt dedicated to vibration control of a cantilever beam. It is shown that custom designs can definitely extend the application of passive resonant shunt strategies to lower frequency.

Validated linear dynamic model of electrically-shunted magnetostrictive transducers with application to structural vibration control

This paper presents a linear model of the fully-coupled electromechanical behavior of a generally-shunted magnetostrictive transducer. The impedance and admittance representations of the model are reported. The model is used to derive the effect of the shunt’s electrical impedance on the storage modulus and loss factor of the transducer without neglecting the inherent resistance of the transducer’s coil. The expressions are normalized and then shown to also represent generally-shunted piezoelectric materials that have a finite leakage resistance. The generalized expressions are simplified for three shunts: resistive, series resistive-capacitive, and inductive, which are considered for shunt damping, resonant shunt damping, and stiffness tuning, respectively. For each shunt, the storage modulus and loss factor are plotted for a wide range of the normalized parameters. Then, important trends and their impact on different applications are discussed. An experimental validation of the transducer model is presented for the case of resistive and resonant shunts. The model closely predicts the measured response for a variety of operating conditions. This paper also introduces a model for the dynamic compliance of a vibrating structure that is coupled to a magnetostrictive transducer for shunt damping and resonant shunt damping applications. This compliance is normalized and then shown to be analogous to that of a structure that is coupled to a piezoelectric material. The derived analogies allow for the observations and equations in the existing literature on structural vibration control using shunted piezoelectric materials to be directly applied to the case of shunted magnetostrictive transducers.

Coupling between two kinds of band gaps of a shunted tube piezoelectric phononic crystal

A tube-type piezoelectric phononic crystal model is proposed to study interaction between locally resonant and Bragg band gaps, which is arrayed periodically by metal and piezoelectric segments. Each piezoelectric segment consists of a shell with series-connected and opposite directions polarized double layers and a resonant shunting circuit. According to the interaction between Bragg scattering and local electromagnetic oscillation, three regions corresponding to the inductance can be divided as follows: quasi-short circuits region, coupling region, and quasi-open circuits region. Some interesting phenomena are found from the coupling between Bragg scattering and locally resonant of electromagnetic oscillation. (1) In the coupling region, a pass band splits a Bragg band gap into two band gaps. But the cut-off frequency of the second band gap does not change with the inductance. (2) In the quasi-open circuits region, Bragg and locally resonant band gaps exist independently. (3) The first band gap transits from Bragg scattering to local resonance when the inductance increases from quasi-short circuits region to quasi-open circuits region. (4) The cut-off frequency of the first band gap is always less than the estimated resonant frequency of inductor-capacitor oscillators. Finally, the theoretical result is validated by two kinds of finite element models based on ANSYS.

Wind Induced Vibration Control and Energy Harvesting of Electromagnetic Resonant Shunt Tuned Mass-Damper-Inerter for Building Structures

This paper proposes a novel inerter-based dynamic vibration absorber, namely, electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI). To obtain the performances of the ERS-TMDI, the combined ERS-TMDI and a single degree of freedom system are introduced. H2 criteria performances of the ERS-TMDI are introduced in comparison with the classical tuned mass-damper (TMD), the electromagnetic resonant shunt series TMDs (ERS-TMDs), and series-type double-mass TMDs with the aim to minimize structure damage and simultaneously harvest energy under random wind excitation. The closed form solutions, including the mechanical tuning ratio, the electrical damping ratio, the electrical tuning ratio, and the electromagnetic mechanical coupling coefficient, are obtained. It is shown that the ERS-TMDI is superior to the classical TMD, ERS-TMDs, and series-type double-mass TMDs systems for protection from structure damage. Meanwhile, in the time domain, a case study of Taipei 101 tower is presented to demonstrate the dual functions of vibration suppression and energy harvesting based on the simulation fluctuating wind series, which is generated by the inverse fast Fourier transform method. The effectiveness and robustness of ERS-TMDI in the frequency and time domain are illustrated.

Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap

A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method (FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369Hz to 1 687Hz and 2 127Hz to 4 000Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap. Thus, a low-frequency and broad band gap of 369Hz to 4 000Hz is obtained.

Piezoelectric metacomposite structure carrying nonlinear multilevel interleaved-interconnected switched electronic networks

In this article, a new class of piezoelectric phononic meta-composite structure carrying nonlinear multilevel interleaved-interconnected switched electronic networks is proposed, and its electro-elastic coupling between elastic waves and electrical waves is investigated. Normally, distributed multimodal resonant damping can be used to achieve several separate resonant-type band gaps for elastic wave propagation control in electromechanical phononic metamaterials. In the proposed approach, several resonant-type band gaps are induced by the peaks and valleys of electrical waves. Inductances adopted in the electronic network are besides much smaller than those required for generating resonant-type band gaps through conventional resonant circuit shunts. Such feature of requiring less or no inductance contributes to the generation of low-frequency band gaps in a semi-passive way. Numerical results show that the number of band gaps over the primitive pass band (between adjacent primitive stop bands) is determined by the level of the proposed nonlinear interleaved-interconnected electronic network. Compared with broadband wave propagation control, the proposed method is more flexible, and can easily target several discrete frequency domains of interest without significantly affecting other frequency domains. Through the theoretical and experimental investigation on low-frequency damping performance, wave control capability and damping performance are confirmed in the low frequency domain.

Consistent approach to describe and evaluate uncertainty in vibration attenuation using resonant piezoelectric shunting and tuned mass dampers

Undesired vibration may occur in lightweight structures due to low damping and excitation. For the purpose of vibration attenuation, tuned mass dampers (TMD) can be an appropriate measure. A similar approach uses resonantly shunted piezoelectric transducers. However, uncertainty in design and application of resonantly shunted piezoelectric transducers and TMD can be caused by insufficient mathematical modeling, geometric and material deviations or deviations in the electrical and mechanical quantities. During operation, uncertainty may result in detuned attenuation systems and loss of attenuation performance. A consistent and general approach to display uncertainty in load carrying systems developed by the authors is applied to describe parametric uncertainty in vibration attenuation with resonantly shunted piezoelectric transducers and TMD. Mathematical models using Hamilton’s principle and Ritz formulation are set up for a beam, clamped at both ends with resonantly shunted transducers and TMD to demonstrate the effectiveness of both attenuation systems and investigate the effects of parametric uncertainty. Furthermore, both approaches lead to additional masses, piezoelectric material for shunt damping and compensator mass of TMD, in the systems. It is shown that vibration attenuation with TMD is less sensitive to parametric uncertainty and achieves a higher performance using the same additional mass.

Two Kinds Equal Frequency Circuits to Achieve Locally Resonant Band Gap of a Circular Plate Attached Alternately by Piezoelectric Unimorphs

A circular thin plate is proposed for vibration attenuation, which is attached alternately by annular piezoelectric unimorphs with resonant shunt circuits. Two kinds of equal frequency resonant shunt circuits are designed to achieve an integrated locally resonant (LR) band gap (BG) with a much smaller transmission factor: (1) the structure is arrayed periodically while the resonant shunt circuits are aperiodic; (2) the resonant shunt circuits are periodic while the structure is aperiodic. The transmission factor curve is calculated, which is validated by the finite element method. Dependences of the LR BG performance upon the geometric and electric parameters are also analyzed.

Improved shunt damping with two negative capacitances: An efficient alternative to resonant shunt

This paper deals with piezoelectric shunt damping enhanced with negative capacitances. A novel electrical circuit layout is addressed, based on the use of two negative capacitances. It is shown that the shunt performances, in terms of vibration reduction and stability margins, are increased as compared with the classical single negative capacitance layouts. Then, the article focuses on the comparison of a simple resistive shunt, enhanced by a pair of negative capacitances, with a classical resonant shunt. It is shown that the newly proposed enhanced resistive shunt can show equivalent performances in terms of vibration attenuation than the resonant shunt, with at the same time an increased robustness to frequency detuning, in the case of mono-modal damping. The broadband control capability of the resistive shunt coupled to the new negative capacitance layout is also evidenced. The main part of the work is analytical, and then the model is validated by an extensive experimental campaign at the end of the paper.

Exploration of nonlinearly shunted piezoelectrics as vibration absorbers

Practical realization of a nonlinearly shunted piezoelectric vibration absorber is numerically explored in this research. It is widely known that the linear resonant piezoelectric shunting strategy, acting as a tuned mass damper, is limited by the massive inductance required in low-frequency cases and sensitivity to drifts in structural frequencies. In order to overcome this limitation, a nonlinear piezoelectric shunting strategy is proposed based on the nonlinear energy sink theory. The essential idea is to passively absorb vibrational energy from the host structure through the intentional use of nonlinearity in piezoelectric shunting. The nonlinearly shunted piezoelectrics are supposed to work over a broad frequency band with a smaller inductance requirement compared with the linear resonant shunting. The nonlinearly shunted piezoelectric vibration absorber is built and applied in a cantilevered beam. Major challenges coming from the nonlinear tuning design for an effective vibration absorber exempted from high isolated response curves will be covered in this research. This numerical study is supposed to pave the way for experimental investigations that are currently in process.

Vibration reduction of a woven composite fan blade by piezoelectric shunted devices

This study concerns the vibration reduction in the low frequency range of a composite fan blade of a turbojet engine with piezoelectric devices. The interest is to increase lifespan and avoid flutter phenomena by reducing the vibration amplitude. The solution considered in the work consists in using piezoelectric elements connected to a passive electric circuit usually called shunt. The use of woven composite materials for fan blades enables to plan on embedding piezoelectric materials, for instance in the form of patches inserted between the composite and the coating material. The work presented during this conference will illustrate the feasibility of a piezoelectric shunted device integrated in an industrial application that doesn't require electrical supply. For such a structure, it is shown that a purely passive resonant shunt can significantly reduce the level of vibration of the second bending mode and that a good correlation between experiments and simulations validates the best fitting finite element model.

Design of a millimeter‐wave wideband bandpass filter with novel‐slotted substrate integrated waveguide

ABSTRACTA millimeter‐wave (mmW) wideband band‐pass filter (WBF) is proposed and designed by using novel‐slotted unites etched on the metal planes of SIW cavities in this paper. The novel‐slotted SIW cavity consists of two pairs of same size dumbbell slots etched on both the top and bottom metal planes of the SIW, which acts as a shunt resonator. And there is 90‐degree angle rotated between the novel‐slotted unites on top and bottom planes. The novel‐slotted SIW unit can be used to control the transmission zero and the cutoff frequency at upside. Finally, a five‐order millimeter‐wave wideband band‐pass filter is proposed and fabricated. The measured results show that the filter achieves insertion loss of −1.54 dB at 32.5 GHz, return loss of better than 12.5dB and 3dB fractional bandwidth (FBW) of 34.6%. A good agreement between simulated and measured results verifies the validity of this design methodology. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:2406–2410, 2016

Vibration reduction for smart periodic structures via periodic piezoelectric arrays with nonlinear interleaved-switched electronic networks

Smart periodic structures covered by periodically distributed piezoelectric patches have drawn more and more attention in recent years for wave propagation attenuation and corresponding structural vibration suppression. Since piezoelectric materials are special type of energy conversion materials that link mechanical characteristics with electrical characteristics, shunt circuits coupled with such materials play a key role in the wave propagation and/or vibration control performance in smart periodic structures. Conventional shunt circuit designs utilize resistive shunt (R-shunt) and resonant shunt (RL-shunt). More recently, semi-passive nonlinear approaches have also been developed for efficiently controlling the vibrations of such structures. In this paper, an innovative smart periodic beam structure with nonlinear interleaved-switched electric networks based on synchronized switching damping on inductor (SSDI) is proposed and investigated for vibration reduction and wave propagation attenuation. Different from locally resonant band gap mechanism forming narrow band gaps around the desired resonant frequencies, the proposed interleaved electrical networks can induce new broadly low-frequency stop bands and broaden primitive Bragg stop bands by virtue of unique interleaved electrical configurations and the SSDI technique which has the unique feature of realizing automatic impedance adaptation with a small inductance. Finite element modeling of a Timoshenko electromechanical beam structure is also presented for validating dispersion properties of the structure. Both theoretical and experimental results demonstrate that the proposed beam structure not only shows better vibration and wave propagation attenuation than the smart beam structure with independent switched networks, but also has technical simplicity of requiring only half of the number of switches than the independent switched network needs.

Switchable bandpass filter using CRLH cells based on a new kind of admittance inverter

In this paper, a new kind of admittance inverter and design of a switchable microstrip bandpass filter using composite right/left-handed (CRLH) cells has been presented. The proposed filter has two states (or passbands). One of the two passbands, is accessible at each time by on/off state of three PIN diodes. This filter is a three-pole, coupled resonator filter, composed of short-circuited shunt resonators. These resonators are coupled using admittance inverters. With regard to the characteristics of the equivalent circuit of CRLH cells, a new structure of admittance inverter (J-inverter) has been introduced. This novel J-inverter has PI-section equivalent circuit and it consists of both inductive and capacitive elements. In our work, the proposed J-inverter was mathematically studied and the switchable filter was simulated and implemented. The results of simulations for the first and second state of the filter, which are frequency bands of (Δ1 = 0.11 and f1 = 1.26 GHz) and (Δ2 = 0.12 and f2 = 1.5 GHz), are verified by measurements.

電磁トランスデューサのインピーダンスのモデル化に関する一考察:

Electromagnetic shunt damping is a damping technique using an electromagnetic transducer. The damping technique is a simple method since a shunt circuit is only attached to the electromagnetic transducer. The disadvantage of this technique is sensitive to modeling error. Especially, in the case of using a resonant shunt circuit, the impedance model of the electromagnetic transducer in the high-frequency range is very important. However, we observed that the conventional model cannot represent the experimental results of frequency response in the high-frequency range. This paper proposes a novel impedance model that has higher accuracy compared with the conventional model. The proposed model considers eddy currents generated in electromagnetic transducer which has non-uniform physical parameters. Lumped parameter model is derived by spatial discretization. The order of the proposed model can be chosen arbitrarily. The validity of the proposed model is verified by experiments. The experimental result shows that the proposed model has higher accuracy compared with the conventional model.

Application of Shunted Piezoelectric Materials in Aeroelasticity

This paper presents a numerical study on the influence of multimodal shunt circuit parameters in the flutter velocity of a typical section under an unsteady airflow. Flutter on typical sections is a kind of self-excited oscillation which can occur due to the interaction with the airflow. In the flutter point, when the critical dynamic pressure is reached, the vibrations of the typical section become unstable and increase fast and significantly in time. As a result, it can lead the structure to failure. Thus, it becomes important to investigate the possibility of reducing the effects of flutter in order to increase the reliability of composite structures during service. In this work, the aero-electromechanical dynamic model formulation is based on the Hamilton principle. The unsteady aerodynamic forces are calculated based on the linearized thin-airfoil theory, proposed by Theodorsen. The passive element responsible for the energy dissipation is a multimodal resonant shunt circuit in series topology, attached to a piezoelectric patch. An iterative solution algorithm is proposed to solve the resultant nonlinear eigenvalue problem. The optimum shunt tuning is firstly performed using Hagood and Flotow’s propositions; then, it is used an heuristic optimization algorithm, based on Differential Evolution. The preliminary results indicate that the flutter speed can be affected by the passive control, both in its mechanical aspect as electrical.

An Enhanced Plane Wave Expansion Method to Solve Piezoelectric Phononic Crystal with Resonant Shunting Circuits

An enhanced plane wave expansion (PWE) method is proposed to solve piezoelectric phononic crystal (PPC) connected with resonant shunting circuits (PPC-C), which is named as PWE-PPC-C. The resonant shunting circuits can not only bring about the locally resonant (LR) band gap for the PPC-C but also conveniently tune frequency and bandwidth of band gaps through adjusting circuit parameters. However, thus far, more than one-dimensional PPC-C has been studied just by Finite Element method. Compared with other methods, the PWE has great advantages in solving more than one-dimensional PC as well as various lattice types. Nevertheless, the conventional PWE cannot accurately solve coupling between the structure and resonant shunting circuits of the PPC-C since only taking one-way coupling from displacements to electrical parameters into consideration. A two-dimensional PPC-C model of orthorhombic lattice is established to demonstrate the whole solving process of PWE-PPC-C. The PWE-PPC-C method is validated by Transfer Matrix method as well as Finite Element method. The dependence of band gaps on circuit parameters has been investigated in detail by PWE-PPC-C. Its advantage in solving various lattice types is further illustrated by calculating the PPC-C of triangular and hexagonal lattices, respectively.

Automated design of bandpass filters based on open complementary split ring resonators (OCSRRs) using aggressive space mapping (ASM) optimization

AbstractThis paper is focused on the design of bandpass filters based on open complementary split ring resonators (OCSRRs) in microstrip technology. The filters are obtained by coupling the corresponding shunt resonators (OCSRRs) through admittance inverters (quarter wavelength transmission line sections). Different undesirable effects derived from the chosen topology are taken into account and are compensated at the design level. These effects include the reduction in bandwidth (caused by the narrowband functionality of the line sections acting as admittance inverters), and the presence of a spurious band above the filter passband. The proposed technique is based on the well‐known aggressive space mapping algorithm, which is a powerful tool for the synthesis and design of microwave components. The design of the OCSRR‐based filter is provided in a fully automated way as the main result of this paper. Copyright © 2015 John Wiley & Sons, Ltd.

Analytical Solutions to H2 and H∞ Optimizations of Resonant Shunted Electromagnetic Tuned Mass Damper and Vibration Energy Harvester

Abstract When optimized, tuned mass dampers (TMDs) can effectively mitigate the vibration of the primary structure, because additional resonance and damping are introduced by the auxiliary mass-spring-damper system. Similar effect can be realized without auxiliary mass when an electromagnetic transducer shunt with the R-L-C resonant circuit is placed between the primary structure and the base. This paper is to analytically optimize the parameters of the R-L-C circuits for vibration mitigation. Both H2 and H∞ optimization criteria are investigated, which are to minimize the root-mean-square (RMS) vibration under random excitation and the peak magnitude in the frequency domain, respectively. The concise closed-form solutions of the optimal parameters are then summarized together with the ones obtained the using fixed-point method, for practical implementation convenience. The H2 and H∞ optimizations of energy harvesting are also discussed in this paper. Furthermore, we also investigate the sensitivity of system performances to the tuning parameter changes of the electromagnetic shunt circuit.

An adaptive piezoelectric vibration absorber enhanced by a negative capacitance applied to a shell structure

Piezoelectric shunt damping is a well-known technique to damp mechanical vibrations of a structure, using a piezoelectric transducer to convert mechanical vibration energy into electrical energy, which is dissipated in an electrical resistance. Resonant shunts consisting of a resistance and an inductance connected to a piezoelectric transducer are used to damp structural vibrations in narrow frequency bands, but their performance is very sensitive to variations in structural modal frequencies and transducer capacitance. In order to overcome this drawback, a piezoelectric shunt damping technique with improved performance and robustness is presented in this paper. The design of the adaptive circuit considers the variation of the host structure’s natural frequency as a project parameter. This paper describes an adaptive resonant piezoelectric vibration absorber enhanced by a synthetic negative capacitance applied to a shell structure. The resonant shunt circuit autonomously adapts its inductance value by comparing the phase difference of the vibration velocity and the current flowing through the shunt circuit. Moreover, a synthetic negative capacitance is added to the shunt circuit to enhance the vibration attenuation provided by the piezoelectric absorber. The circuitry is implemented using analog components. Validation of the proposed method is done by bonding the piezoelectric absorber on a free-formed metallic shell.