Search Results (57)

This study investigates the coupling mechanism between a parabolic notch and dislocations in one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs) based on the theory of complex variable functions. By applying perturbation techniques and the Cauchy integral, analytical solutions for complex potentials are derived, yielding closed-form expressions for the phonon–phason stress field and electric displacement field. Numerical examples reveal several key findings: significant stress concentration occurs at the notch root, accompanied by suppression of electric displacement; interference patterns between dislocation cores and notch-induced stress singularities are identified; the J-integral quantifies distance-dependent forces, size effects, and angular force distributions reflecting notch symmetry; and the energy-driven dislocation slip toward free surfaces leads to the formation of dislocation-free zones. These results provide new insights into electromechanical fracture mechanisms in quasicrystals. Full article

Defective phononic crystals (PnCs) have garnered significant attention for their ability to localize and amplify elastic wave energy within defect sites or to perform narrowband filtering at defect-band frequencies. The necessity for continuously tunable defect characteristics is driven by the variable excitation frequencies encountered in rotating machinery. Conventional tuning methodologies, including synthetic negative capacitors or inductors integrated with piezoelectric defects, are constrained to fixed, offline, and incremental adjustments. To address these limitations, the present study proposes an active feedback approach that facilitates online, wide-range steering of defect bands in a one-dimensional PnC. Each defect is equipped with a pair of piezoelectric sensors and actuators, governed by three independently tunable feedback gains: displacement, velocity, and acceleration. Real-time sensor signals are transmitted to a multivariable proportional controller, which dynamically modulates local electroelastic stiffness via the actuators. This results in continuous defect-band frequency shifts across the entire band gap, along with on-demand sensitivity modulation. The analytical model that incorporates these feedback gains has been demonstrated to achieve a level of agreement with COMSOL benchmarks that exceeds 99%, while concurrently reducing computation time from hours to seconds. Displacement- and acceleration-controlled gains yield predictable, monotonic up- or down-shifts in defect-band frequency, whereas the velocity-controlled gain permits sensitivity adjustment without frequency drifts. Furthermore, the combined-gain operation enables the concurrent tuning of both the center frequency and the filtering sensitivity, thereby facilitating an instantaneous remote reconfiguration of bandpass filters. This framework establishes a new class of agile, adaptive ultrasonic devices with applications in ultrasonic imaging, structural health monitoring, and prognostics and health management. Full article

Despite extensive research on semiconductor materials, the influence of temperature and magnetic field on the optical quantum transitions within semiconductors remains insufficiently understood. We therefore investigated the Optical Quantum Transition Line Properties (OQTLP), including line shapes (LS) and line widths (LW), as functions of temperature and magnetic field in electron–piezoelectric-phonon-interacting systems within semiconductor materials. A theoretical framework incorporating projection-based equations and equilibrium average projection was applied to GaAs and CdS. Similarly, LW generally increases with magnetic field in a square-well confinement potential across most temperature regions. However, in high magnetic fields at low temperatures, LW decreases for GaAs. Additionally, LW increases with rising temperature. We also compare the LW and LS for transitions within intra- and inter-Landau levels to analyze the quantum transition process. The results indicate that intra-Landau level transitions primarily dominate the temperature dependence of quantum transitions in GaAs and CdS. Full article

The presented article is about the axisymmetric deformation of an annular one-dimensional hexagonal piezoelectric quasicrystal actuator/sensor with different configurations, analyzed by the three-dimensional theory of piezoelectricity coupled with phonon and phason fields. The state space method is utilized to recast the basic equations of one-dimensional hexagonal piezoelectric quasicrystals into the transfer matrix form, and the state space equations of a laminated annular piezoelectric quasicrystal actuator/sensor are obtained. By virtue of the finite Hankel transform, the ordinary differential equations with constant coefficients for an annular quasicrystal actuator/sensor with a generalized elastic simple support boundary condition are derived. Subsequently, the propagator matrix method and inverse Hankel transform are used together to achieve the exact axisymmetric solution for the annular one-dimensional hexagonal piezoelectric quasicrystal actuator/sensor. Numerical illustrations are presented to investigate the influences of the thickness-to-span ratio on a single-layer annular piezoelectric quasicrystal actuator/sensor subjected to different top surface loads, and the effect of material parameters is also presented. Afterward, the present model is applied to compare the performance of different piezoelectric quasicrystal actuator/sensor configurations: the quasicrystal multilayer, quasicrystal unimorph, and quasicrystal bimorph. Full article

A SAW device with a multi-layered piezoelectric substrate has excellent performance due to its high Q value. A multi-layer piezoelectric substrate combined with phononic crystal structures capable of acoustic wave reflection with a very small array can achieve miniaturization and high performance. In this paper, a honeycomb-shaped phononic crystal structure based on 42°Y-X LT/SiO₂/poly-Si/Si-layered substrate is proposed. The analysis of the bandgap distribution under various filling fractions was carried out using dispersion and transmission characteristics. In order to study the application of PnCs in SAW devices, one-port resonators with different reflectors were compared and analyzed. Based on the frequency response curves and Bode-Q value curves, it was found that when the HC-PnC structure is used as a reflector, it can not only improve the transmission loss of the resonator but also reduce the size of the device. Full article

In this work, within the framework of the linear piezoelectricity theory of quasicrystals, the three-dimensional and two-dimensional Green tensors for arbitrary piezoelectric quasicrystals are derived. In the piezoelectricity of quasicrystals, where phonon, phason and electric fields exist, we introduce the corresponding multifields by developing a hyperspace notation for piezoelectric quasicrystals. Using Fourier transform and the multifield formalism, the three-dimensional Green tensor for piezoelectric quasicrystals as well as its spatial gradient necessary for applications, are derived. The solutions for the “displacement”, “distortion” and “stress” multifields in the presence of a “force” multifield in a piezoelectric quasicrystal as well as the solution of the generalised Kelvin problem, are given. In addition, the two-dimensional Green tensors of piezoelectric quasicrystals as well as of quasicrystals, are determined. Full article

Focusing on the bending wave characteristic of plate–shell structures, this paper derives the complex band curve of piezoelectric phononic crystal based on the equilibrium differential equation in the plane stress state using COMSOL PDE 6.2. To ascertain the computational model’s accuracy, the computed complex band curve is then cross-validated against real band curves obtained through coupling simulations. Utilizing this model, this paper investigates the impact of structural and electrical parameters on the bandgap range and the attenuation coefficient in the bandgap. Results indicate that the larger surface areas of the piezoelectric sheet correspond to lower center bands in the bandgap, while increased thickness widens the attenuation coefficient range with increased peak values. Furthermore, the influence of inductance on the bandgap conforms to the variation law of the electrical LC resonance frequency, and increased resistance widens the attenuation coefficient range albeit with decreased peak values. The incorporation of negative capacitance significantly expands the low-frequency bandgap range. Visualized through vibration transfer simulations, the vibration-damping ability of the piezoelectric phononic crystal is demonstrated. Experimentally, this paper finds that two propagation modes of bending waves (symmetric and anti-symmetric) result in variable voltage amplitudes, and the average vibration of the system decreases by 4–5 dB within the range of 1710–1990 Hz. The comparison between experimental and model-generated data confirms the accuracy of the attenuation coefficient calculation model. This convergence between experimental and computational results emphasizes the validity and usefulness of the proposed model, and this paper provides theoretical support for the application of piezoelectric phononic crystals in the field of plate–shell vibration reduction. Full article

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. Full article

Using the piezoelectric (PZT) effect, energy-harvesting has become possible for phononic crystal (PnC). Low-frequency vibration energy harvesting is more of a challenge, which can be solved by local resonance phononic crystals (LRPnCs). A novel three-dimensional (3D) energy harvesting LRPnC is proposed and further analyzed using the finite element method (FEM) software COMSOL. The 3D LRPnC with spiral unit-cell structures is constructed with a low initial frequency and wide band gaps (BGs). According to the large vibration deformation of the elastic beam near the scatterer, a PZT sheet is mounted in the surface of that beam, to harvest the energy of elastic waves using the PZT effect. To further improve the energy-harvesting performance, a 5 × 5 super-cell is numerically constructed. Numerical simulations show that the present 3D super-cell PnC structure can make full use of the advantages of the large vibration deformation and the PZT effect, i.e., the BGs with a frequency range from 28.47 Hz to 194.21 Hz with a bandwidth of 142.7 Hz, and the maximum voltage output is about 29.3 V under effective sound pressure with a peak power of 11.5 µW. The present super-cell phononic crystal structure provides better support for low-frequency vibration energy harvesting, when designing PnCs, than that of the traditional Prague type. Full article

In this paper, a multi-material radial phononic crystal (M-RPC) structure is proposed to reduce the anchor-point loss of piezoelectric micro-electro-mechanical system (MEMS) resonators and improve their quality factor. Compared with single-material phononic crystal structures, an M-RPC structure can reduce the strength damage at the anchor point of a resonator due to the etching of the substrate. The dispersion curve and frequency transmission response of the M-RPC structure were calculated by applying the finite element method, and it was shown that the M-RPC structure was more likely to produce a band-gap range with strong attenuation compared with a single-material radial phononic crystal (S-RPC) structure. Then, the effects of different metal–silicon combinations on the band gap of the M-RPC structures were studied, and we found that the largest band-gap range was produced by a Pt and Si combination, and the range was 84.1–118.3 MHz. Finally, the M-RPC structure was applied to a piezoelectric MEMS resonator. The results showed that the anchor quality factor of the M-RPC resonator was increased by 33.5 times compared with a conventional resonator, and the insertion loss was reduced by 53.6%. In addition, the loaded and unloaded quality factors of the M-RPC resonator were improved by 75.7% and 235.0%, respectively, and at the same time, there was no effect on the electromechanical coupling coefficient. Full article

This paper studies the radial alternating material phononic crystal (RAM-PnC). By simulating the band gap structure of the phononic crystal, a complete acoustic band gap was verified at the resonant frequency of 175.14 MHz, which can prevent the propagation of elastic waves in a specific direction. The proposed alternately arranged radial phononic crystal structure is applied to the thin-film piezoelectric-on-silicon (TPOS) MEMS resonator. The finite element simulation method increases the anchor quality factor (Q_anchor) from 60,596 to 659,536,011 at the operating frequency of 175.14 MHz, which is about 10,000 times higher. The motion resistance of the RAM-PnC resonator is reduced from 156.25 Ω to 48.31 Ω compared with the traditional resonator. At the same time, the insertion loss of the RAM-PnC resonator is reduced by 1.1 dB compared with the traditional resonator. Full article

Quasicrystals endowed with piezoelectric properties belong nowadays to novel piezoelectric materials. In this work, the basic framework of generalized piezoelectricity theory of quasicrystals is investigated by providing an improvement of the existing constitutive modelling. It is shown, for the first time, that the tensor of phason piezoelectric moduli is fully asymmetric without any major or minor symmetry, which has important consequences on the constitutive relations as well as on its classification with respect to the crystal systems and Laue classes. The exploration of the tensor of phason piezoelectric moduli has a significant impact on the understanding of the piezoelectric properties of quasicrystals. Using the group representation theory, the classification of the tensor of phason piezoelectric moduli with respect to the crystal systems and Laue classes is given for one-dimensional quasicrystals. The number of independent components of the phason piezoelectric moduli is determined for all 31 point groups of one-dimensional quasicrystals. It is proven that the 10 centrosymmetric crystallographic point groups have no piezoelectric effects and that the remaining 21 non-centrosymmetric crystallographic point groups exhibit piezoelectric effects due to both phonon and phason fields. Moreover, the constitutive relations for one-dimensional hexagonal piezoelectric quasicrystals of Laue class 9 with point group 6 and Laue class 10 with point group $6mm$ are explicitly derived, showing that the constitutive relations for piezoelectric quasicrystals depend on the considered Laue class as well as on the point group. Comparisons with existing results in the literature and discussion are also given. Full article

This study examines the interference problem between screw dislocation and elliptical inclusion in one-dimensional hexagonal piezoelectric quasicrystals. The general solutions are obtained using the complex variable function method and the conformal transformation technique. When the screw dislocation is located outside or inside the elliptical inclusion, the perturbation method and Laurent series expansion are employed to derive explicit analytical expressions for the complex potentials in the elliptical inclusion and the matrix, respectively. Considering four types of far-field force and electric loading conditions, analytical solutions for various specific cases are obtained by using matrix operations. Expressions for the phonon field stress, phason field stress, and electric displacement are given for special cases, including the absence of a dislocation, the presence of an elliptical hole, and the interference between a screw dislocation and circular inclusion, as well as the case of a circular hole. The design and analysis of quasicrystal inclusion structures can benefit from the results of this work. Full article

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. Full article

Extensive prior research has delved into the localization of elastic wave energy through defect modes within phononic crystals (PnCs). The amalgamation of defective PnCs with piezoelectric materials has opened new avenues for conceptual innovations catering to energy harvesters, wave filters, and ultrasonic receivers. A recent departure from this conventional paradigm involves designing an ultrasonic actuator that excites elastic waves. However, previous efforts have mostly focused on single-defect scenarios for bending-wave excitation. To push the boundaries, this research takes a step forward by extending PnC design to include double piezoelectric defects. This advancement allows ultrasonic actuators to effectively operate across multiple frequencies. An analytical model originally developed for a single-defect situation via Euler–Bernoulli beam theory is adapted to fit within the framework of a double-defect set-up, predicting wave-excitation performance. Furthermore, a comprehensive study is executed to analyze how changes in input voltage configurations impact the output responses. The ultimate goal is to create ultrasonic transducers that could have practical applications in nondestructive testing for monitoring structural health and in ultrasonic imaging for medical purposes. Full article