Piezoelectric Phononic Crystals Research Articles

Investigation of Bandgap Properties of a Piezoelectric Phononic Crystal Plate Based on the PDE Module in COMSOL.

Aiming to address the vibration noise problems on ships, we constructed a piezoelectric phononic crystal (PC) plate structure model, solved the governing equations of the structure using the partial differential equations module (PDE) in the finite element softwareCOMSOL6.1, and obtained the corresponding energy band structure, transmission curves, and vibration modal diagrams. The application of this method to probe the structural properties of two-dimensional piezoelectric PCs is described in detail. The calculation results obtained using this method were compared with the structures obtained using the traditional plane wave expansion method (PWE) and the finite element method (FE). The results were found to be in perfect agreement, which verified the feasibility of this method. To safely and effectively adjust the bandgap within a reasonable voltage range, this paper explored the order of magnitude of the plate thickness, the influence of the voltage on the bandgap, and the dependence between them. It was found that the smaller the order of magnitude of the plate thickness, the smaller the order of magnitude of the band in which the bandgap was located. The magnitude of the driving voltage that made the bandgap change became smaller accordingly. The new idea of attaching the PC plate to the conventional plate structure to achieve a vibration damping effect is also briefly introduced. Finally, the effects of lattice constant, plate width, and thickness on the bandgap were investigated.

Research on targeted modulation of elastic wave bandgap in cantilever-structured piezoelectric Phononic crystals

Piezoelectric phononic crystals (PPCs) have the advantages of simplicity and efficiency in controlling elastic wave bandgaps, which can be utilized to solve NVH problems with varying frequency features, such as the low-frequency vibrations caused by the time-varying power source (i.e., motor) in the subframe and underbody of new energy vehicles. However, most of the previous studies on PPCs bandgap control are qualitative, lacking the knowledge of bandgap targeted modulation. This paper analyzes the locally resonant (LR) bandgap characteristics of PPCs with shunting circuits, and aims to achieve precise control of bandgap position by circuit parameters. A theoretical research model of cantilever-structured PPCs is established firstly, and its accuracy is verified through finite element analysis and experiments. Subsequently, the formation mechanism of the LR bandgap is analyzed, and a bandgap characteristic frequency estimation method is proposed, along with an analysis of the influence of electrical parameters using this method. Finally, from the perspective of bandgap practicality, the variable capacitance method is proposed, which can quickly calculate the capacitance value through an estimation formula under the arbitrary designation of target bandgap in the low-frequency range of 200 Hz∼500 Hz. The results show that the actual bandgap position is very close to the target bandgap position, and the bandgap always keeps enough bandwidth and attenuation amount. This method has broad prospects in the field of vibration attenuation where frequency characteristics are variable.

Experimental design and adaptive modulation of piezoelectric cantilever phononic crystals for vibration attenuation in vehicle subframes

To attenuate the vibrations in the vehicle subframe with changing target frequency, a piezoelectric cantilever phononic crystal (PC) and its adaptive modulation strategy are investigated in this paper. First, based on the cantilever-based PC structure, the bandgap characteristics are obtained by vibration transfer calculation and piezoelectric constitutive modeling. The experimental design of the piezoelectric cantilever PC is further conducted based on the parametric analysis results of structural dimensions and the targeted vibration frequency intervals required by the vehicle subframe. The modal experiments indicate that two local resonant bandgaps and one electromagnetic oscillation bandgap appear in the solved frequency interval, and both of them exhibit excellent consistency with the theoretical calculations. Finally, an adaptive bandgap modulation strategy is proposed by controlling the shunting circuit parameters, and the execution results demonstrate that the PCs employed in the vehicle subframe can effectively achieve vibration attenuation from the powertrain systems. Starting from the experimental design and adaptive modulation of cantilever PCs with piezoelectric materials, this research presents a novel framework for the application of acoustic metamaterials in the vibration mitigation of automotive structures.

Acoustic manipulation of microparticles using a piezoelectric phononic crystal plate

Acoustic tweezer is a promising device for manipulating particles, which does not need contact does not cause damage, or requires transparent materials. They have diverse applications in cell separation, tissue engineering, and material assembly. To control particle movement, this technology relies on the exchange of momentum between the particle and the acoustic field, generating an acoustic radiation force. Achieving high-performance acoustic tweezers necessitates the precise shaping of the acoustic fields. Traditionally, there are mainly two types of acoustic tweezers: bulk acoustic wave (BAW) and surface acoustic wave (SAW). The SAW-based acoustic tweezer operates at high frequencies, realizing precise manipulation. The BAW-based acoustic tweezer operates at lower frequencies and requires artificial structure on the transducer surface to shape the field. However, the separation of the artificial structure from the transducer brings complexity and instability into the manipulation process. In this study, we propose a novel approach to overcoming these challenges, that is, using piezoelectric phononic crystal plates to integrate the transducer and acoustic artificial structure. By designing the thickness, periodicity, and electrode width of the piezoelectric phononic crystal plate, we can excite the <i>A</i><sub>0</sub> Lamb wave mode and the periodic resonant mode, resulting in a periodic gradient field and a periodic weak gradient field, respectively. These fields enable particle to be trapped or levitated on the surface. To validate this approach, an experimental device is constructed, and successful particle manipulation is achieved by using Lamb wave mode or periodic resonant mode through using the piezoelectric phononic crystal plate. This technological breakthrough serves as a crucial foundation and experimental validation for developing the compact, low-energy and high-precision acoustic tweezers.

Ultrahigh frequency vibration control in a piezoelectric phononic crystal beam at the nanoscale considering surface effects

Ultrahigh frequency vibration control in a piezoelectric phononic crystal beam at the nanoscale considering surface effects

Surface acoustic waves in the continuous spectrum of Bloch waves in piezoelectric one-dimensional phononic crystals.

This paper theoretically investigates surface acoustic waves (SAWs) which emerge within the continuous spectrum of bulk Bloch waves in piezoelectric one-dimensional phononic crystals. Accordingly, these SAWs may be treated as an example of the bound states in the continuum (BIC). The equationswhich determine the existence of such BIC-SAWs have been derived. Unlike SAWs in the frequency intervals forbidden for bulk Bloch waves, BIC-SAWs are governed not by a single purely real dispersion equationbut by sets of equations, so BIC-SAWs prove to be robust only to a consistent change of a definite number of free parameters characterizing the wave propagation. The form of the derived equationsallows the establishment of the conditions on the frequency and other parameters under which the BIC-SAW exists. The number of conditions depends on the number of bulk waves in the frequency interval under consideration. In the case of generic crystallographic symmetry, there are three, five, and seven conditions which have to be fulfilled for a BIC-SAWs to coexist with one pair, two pairs, and three pairs of bulk Bloch waves, respectively. It is shown that the crystallographic symmetry may reduce the number of conditions to two, three and four, respectively. Numerical computations confirm analytic results.

Experimental evidence of nonreciprocal propagation in space-time modulated piezoelectric phononic crystals

A nonreciprocal system composed of a one-dimensional piezoelectric phononic crystal whose periodic electrical conditions are modulated in time is presented. One-way longitudinal wave propagation is studied experimentally and compared to finite element temporal simulations. The modulation is performed by prescribing grounded or floating potential conditions on a periodic set of electrodes through external circuits. This approach makes it possible to consider a wide range of modulation speeds, and the large number of unit cells of the phononic crystal allows us to characterize experimentally the full dispersion curves of the system. This permits to observe the presence of directional bandgaps and to follow the shift in frequencies of these bandgaps as a function of the modulation speed. The experiments show the linear evolution of the central position of the bandgaps with the increase in the modulation speed, as well as their progressive closure, over a wide range of frequencies. Experiments are also used to estimate the evolution of bandgaps in a dispersive system, a problem discussed in several theoretical works but never observed experimentally. This work may constitute the foundation for experimental analysis of Floquet acoustic metamaterials, accelerated-modulation space-time metamaterials, or acoustic analog of the event horizon.

Advances in Tunable Bandgaps of Piezoelectric Phononic Crystals.

Bandgaps of traditional phononic crystals (PCs) are determined using structural geometric parameters and material properties, and they are difficult to tune in practical applications. Piezoelectric PCs with lead zirconium titanate piezoelectric ceramics (abbreviated to piezoelectric PCs) have multi-physics coupling effects and their bandgaps can be tuned through external circuits to expand the application range of the PCs. First, the typical structures of piezoelectric PCs are summarized and analyzed. According to the structure, common tunable piezoelectric PCs can be roughly divided into three categories: PCs that only contain piezoelectric materials (single piezoelectric PCs), PCs composed of embedded piezoelectric materials in elastic materials (composite piezoelectric PCs), and PCs that are composed of an elastic base structure and attached piezoelectric patches (patch-type piezoelectric PCs). Second, the tuning methods of bandgaps for piezoelectric PCs are summarized and analyzed. Then, the calculation methods of the bandgaps of piezoelectric PCs are reviewed and analyzed. Finally, conclusions are drawn on the research status of piezoelectric PCs, shortcomings of the existing research are discussed, and future development directions are proposed.

Research on bending vibration characteristics of phononic crystal plates based on Mindlin’s piezoelectric plate theory

Based on Mindlin’s theory and the plane wave expansion method, the formulas are proposed for the governing equations and dispersion relations of bending waves in piezoelectric phononic crystal plates. The shear correction factors can be obtained through transcendental equations based on forced vibrations of the plate. The plates are made of inclusions of different shapes and lattice types, finding that the inclusion shape dramatically affects the mid-to-high frequency band gaps. Piezoelectric materials exhibit distinct eigenfrequencies at the high-symmetry point Γ at low frequencies. Thickness affects the band gap width differently than in two-dimensional models, and cuts influence band gap width significantly.

Tunability of “spring-mass” resonator on band gaps with surface effects of a piezoelectric phononic crystal double-layer nanobeam

A model of piezoelectric phononic crystal (PC) double-layer nanobeam periodically attached by “spring-mass” resonators is proposed. As a comparison, two other simplified models are also proposed. In order to calculate the band structure, the plane wave expansion (PWE) method is improved by introducing the Euler beam and surface piezoelectricity theories. All the results and analysis demonstrate that the tunable advantage is displayed in double-layer nanobeam on account of the antisymmetric and symmetric vibrational modes controlled by adding additional springs between two different nanobeams. Moreover, the influencing rules of parameters related to additional spring and “spring-mas” resonator are also revealed. The bandgap properties can be applied to nano electro-mechanical system (NEMS) to realize active control of vibration.

Vibration isolation of a self-powered piezoelectric pipe conveying fluid composed of laminated fiber-reinforced composites

Based upon the wave manipulating characteristics of phononic crystals (PCs), this paper aims to isolate flexural vibration of laminated composite pipes conveying fluid by introducing a self-powered periodic piezoelectric design. The pipe is composed of three layers of fiber-reinforced composites along the thickness, and is periodically attached with a number of shunted piezoelectric sensor/actuator pairs along the axis. A negative proportional feedback strategy is adopted to amplify the sensing voltage to the actuators, which can generate periodic active stiffness to the pipe and thus enable tunable wave propagation and frequency band gap (BG). The dynamical equation of motion for a single piezoelectric laminated pipe conveying fluid is deduced from classical laminated beam theory as well as one-dimensional piezoelectric constitution. The BG distribution and amplitude transmission of topological structure are obtained by the spectral element method (SEM). Numerical results demonstrate that the present self-powered piezoelectric PC design can achieve excellent vibration isolation effect for the laminated composite pipe conveying fluid. Major parameter regulations including cross-ply angle, lamina sequence, feedback control gain, geometry of piezoelectric layers and fluid effect are examined. Free vibration and stability of the system are also discussed to perfect the vibration isolation design.

Extended topological interface modes with tunable frequency in the piezoelectric phononic crystal

Acoustic metamaterials have provided a versatile platform to explore more degrees of freedom for tunable topological wave manipulation. Recently, extended topological interface modes (ETIMs) with heterostructure have been proposed to extend the spatial degree of freedom. However, the absence of frequency tunability still restricts the application of the wave transports of ETIMs. Here, we propose a one-dimensional piezoelectric topological phononic crystal (PTPC) with electrically tunable working frequency by introducing external capacitor circuit. With the bandgap frequency actively controlled by appropriately tuning the capacitances, we construct the heterostructured PTPCs possessing high-energy-capacity ETIMs with electrically tunable working frequency range and bandwidth. This work paves the way to wide engineering applications on acoustic sensing enhancement, nondestructive testing, energy harvesting, information processing, and reconfigurable topological wave transports.

Electric control of a phononic crystal constituted of Piezoelectric layers using Schottky diode

A one-dimensional piezoelectric phononic crystal (PPC) consisting of a periodic pattern made of two perfectly bonded materials: one active (piezoelectric), the other passive (elastic) and exhibiting a strong acoustic impedance contrast is studied. We are interested in the tunability of piezoelectric inclusions in order to control the propagation of ultrasonic waves in the MHz range from a nonlinear electrical component connected to the terminals of the piezoelectric elements. After modeling the dynamic resistance of the Schottky diode, based on the piezoelectricity equations, a one-dimensional analytical model is proposed to take into account the resistive impedance effect of this diode connected to the electrodes of the active plate. Thus, we have shown that the application of various electrical boundary conditions (EBCs) on the electrodes (open-circuit, short-circuit, connecting an electrical load) allows to change the effective properties of the piezoelectric plate in particular and those of the PPC in general. The dispersion of the waves is then electrically tuned and, depending on the applied EBCs, we have demonstrated numerically the possibility of opening Bragg or hybridization gaps in the PPC band structure.

Bandgap characteristics of a piezoelectric phononic crystal Timoshenko nanobeam based on the modified couple stress and surface energy theories

This paper establishes an analytical model for the size-dependent flexural wave band structures of a piezoelectric phononic crystal (PC) Timoshenko nanobeam, considering the shear deformation and rotational inertia effects. The governing equation is derived based on the surface piezoelectricity energy and modified couple stress theory in the bulk and surface layer of the piezoelectric PC nanobeam, respectively. As a main objective of this article, the surface effects including the surface elasticity, residual surface stress and surface piezoelectricity on the frequency bandgaps in the wave propagation band structures are investigated for a piezoelectric PC Timoshenko nanobeam. Also, the effects of some geometrical parameters on the band structures are studied in details. An analytical approach is proposed for the problem. The obtained results for a piezoelectric PC Timoshenko nanobeam are compared with those of previous researches for a piezoelectric PC Euler-Bernoulli nanobeam. It is concluded that the geometrical parameters and residual surface elasticity affect the location and width of bandgaps in the frequency band structures. Schematic configuration of a piezoelectric PC Timoshenko nanobeam with a surface layer and rectangular cross section.

Complex Band Structure of 2D Piezoelectric Local Resonant Phononic Crystal with Finite Out-Of Plane Extension

In this study, a new type of 2D piezoelectric phononic crystal with a square hollow and convex structures is designed and established. A theoretical study of the piezoelectric phononic crystal is presented in this article to investigate the transmission properties of waves in terms of complex dispersion relations. Based on the finite discretization technique and plane wave expansion, the formula derivation of the real band structure is achieved as well as the complex band diagrams are obtained. The numerical results are presented to demonstrate the multiple broadband complete bandgaps produced by the designed piezoelectric phononic crystal and the propagation characteristics of the elastic waves for different directions. In addition, the transmission loss in the ΓX direction is calculated to verify the band structure. Finally, the effects of the thickness and the square hollow side length on the band structure are discussed.

Influence of the Core Pillar Height on the Bandgap Characteristics of Piezoelectric Phononic Crystals with Ring-Shaped Grooves

Dispersion profiles and surface acoustic wave attenuation characteristics of ring-shaped phononic crystals are investigated as a function of the core pillar height. Finite element method simulations are carried out for both band analyses and transmission spectra calculations. The results reveal that increasing core pillar height results in a decrement in the local resonance band frequency and the corresponding transmission peaks. The obtained dispersion profiles show that the phononic crystal bandgap also expands from 6 MHz to 11 MHz while the pillar height increases from 5 um to 7 um. Similar characteristics are also seen in the transmission spectra for the varying core pillar heights of the ring-shaped periodic grooves. In addition, surface acoustic wave attenuation competency depends on the core pillar height. The frequencies where the investigated phononic crystals are functional can be tuned by adjusting the core pillar height.

Theoretical Investigation of Magneto-Electro-Elastic Piezoelectric Phononic Crystal

We design a magneto-electro-elastic piezoelectric phononic crystal (MPPC) using a one-dimensional piezoelectric superlattice (with a 3m point group) and split-ring resonators. The effect of the split-ring resonators is to enhance the piezoelectric effect of the piezoelectric superlattices. This effect will create elastic anomalies and generate the phononic band gaps. These are first proposed theoretically. We calculate the transmission function of the MPPC through Transfer Matrix Method of the phononic crystal. By using the transmission function, we theoretically study the propagation properties of the acoustic waves in the MPPC. The mechanism for multifield coupling is analyzed. A type of phononic band gap is created, called the multifield coupling phononic band gap. We analyze the possibility of crystals as left-handed metamaterials. We also discuss some potential applications.

Study on broad flexural wave bandgaps of piezoelectric phononic crystal plates for the vibration and noise attenuation

This paper explores a new approach to reducing the interior noise of one vehicle body through the flexural wave bandgap. The phononic crystal is designed by attaching the periodic piezoelectric stacks with the shunting circuits on the host plate. To better implement the frequency-dependent properties, the theoretical model of the piezoelectric stack is improved through capacitance identification. On this basis, the plane wave expansion method is employed to calculate the bandgap. An ultra-wide bandgap is achieved by tuning the shunting circuits and confirmed via the finite element method. The influence of electrical parameters on flexural wave attenuation is investigated. The applicability of the presented resonators for different host plates under the presented design guideline is examined. Subsequently, the concept of phononic crystal with the unique bandgap is exploited to enhance the interior sound performance of one vehicle body. Combining the sound response analysis with the panel acoustic contribution analysis, the numerical study is performed to pick out the critical panels for the arrangement of resonators. Then a circuit control strategy is proposed to activate the wide bandgap. The results demonstrate that the present piezoelectric phononic crystal plate has a significant advantage in hindering the flexural wave propagation and suppressing structure-borne noise over a broadband low-frequency range.

Switchability of a single port SAW resonator using the electrical Bragg band gap

A proof of concept of a new solution for achieving tunable SAW components based on the electrical Bragg band gap concept developed for piezoelectric phononic crystals is presented on a SAW resonator on a LiNbO3 substrate. In this work, it is shown that for a fixed geometry, it is possible to shift the main resonance frequency by modifying the electrical condition on the electrodes that constitute the cavity's mirrors. The concept was validated by both numerical simulations and experimental characterization of single port resonators fabricated on LiNbO3.

Edge states in a non-Hermitian chiral lattice

Non-Hermiticity can alter the topological properties of energy bands and drive topologically trivial systems with Hermitian limits to generate nontrivial topological edge states. Nevertheless, most efforts were devoted to the study of isotropic systems containing multiple pairs of non-Hermitian components, while the influence of distribution of non-Hermitian components was seldom explored. Here, we first investigated a two-dimensional square-lattice non-Hermitian model in which the losses increase in either clockwise or counterclockwise direction, leading to distinct non-Hermitian chiral structures. The effective Hamiltonian satisfied non-Hermitian particle-hole symmetry, which can induce non-Hermitian zero modes. By combing two chiral structures, various edge states emerged from the interface, whose bands strongly depend on the distribution of non-Hermitian components. And the band properties of edge states were analyzed and predicted basing on the non-Hermitian particle-hole symmetry and hypothetical parity-time symmetry. Furthermore, to validate our theory, we proposed a piezoelectric phononic crystal with an external circuit. The band structures were coincident with our theoretical results. And robust wave propagation was also identified. Our study may provide an alternative method to actively engineer propagating waves in non-Hermitian systems.