One-dimensional Piezoelectric Phononic Crystal Research Articles

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.

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.

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

The paper studies the existence of surface acoustic waves in half-infinite one-dimensional piezoelectric phononic crystals consisting of perfectly bonded layers, which are arranged so that the unit cell is symmetric, i.e., is invariant with respect to inversion about its midplane. An example is a bilayered structure with exterior layer being half thinner than the interior layers of the same material. The layers may be generally anisotropic. The maximum possible number of surface acoustoelectric waves referred to a fixed wave number and a given full stop band is established for different types of electric boundary conditions at the mechanically free or clamped surface. In particular, it is proved that the phononic crystal-vacuum interface can support two surface waves in any full stop band. The same statement holds true in the case of a metallized surface of the crystal. This number is greater than that in a purely elastic case. In the presence of crystallographic symmetry, which decouples the sagittally and horizontally polarized surface waves, their separate admissible numbers are obtained. It is shown that the propagation along the normal to the surface is a special case, where the maximum number of surface waves is less than that along oblique directions.

Piezoelectric phononic plates: retrieving the frequency band structure via all-electric experiments

We propose an experimental technique based on all-electric measurements to retrieve the frequency response of a one-dimensional piezoelectric phononic crystal plate, structured periodically with millimeter-scaled metallic strips on its two surfaces. The metallic electrodes, used for the excitation of Lamb-like guided modes in the plate, ensure at the same time control of their dispersion by means of externally loaded electric circuits that offer non-destructive tunability in the frequency response of these structures. Our results, in very good agreement with finite-element numerical predictions, reveal interesting symmetry aspects that are employed to analyze the frequency band structure of such crystals. More importantly, Lamb-like guided modes interact with electric-resonant bands induced by inductance loads on the plate, whose form and symmetry are discussed and analyzed in depth, showing unprecedented dispersion characteristics.

Existence of surface acoustic waves in one-dimensional piezoelectric phononic crystals of general anisotropy

The paper is concerned with the surface acoustic waves propagating in half-infinite one-dimensional piezoelectric phononic crystals of general anisotropy. The phononic crystal is formed of periodically repeated perfectly bonded layers, and its exterior boundary is one of the layer boundaries. The surface waves occurring in the so-called full stop bands are considered. It appears that the number of surface waves existing within a full stop band for a given layered structure is interrelated with their number in the same stop band for the phononic crystal different from the given one only due to the reversed ordering of layers within a period. A series of statements is proved on the maximum possible number of surface waves per full stop band for both these structures in total, i.e., embracing surface-wave occurrences in either one or the other structure. The analysis is performed for the electrically closed, electrically open, and electrically free types of boundary conditions on the mechanically free crystal surface, in which cases it admits a correspondingly different number of surface waves. A subsidiary instance of mechanically clamped surface is addressed as well. It is observed that the piezoelectric coupling can create new surface waves which disappear when piezoelectric coefficients turn to zero. Besides the general case of arbitrary anisotropy, we also consider two specific situations where the crystallographic symmetry allows the existence of sagittally polarized piezoactive surface waves and of shear horizontally polarized piezoactive surface waves. Numerical examples of surface-wave branches under various boundary conditions are provided.

Wave propagation in 1D piezoelectric crystal coupled with 2D infinite network of capacitors

For 1D piezoelectric crystal, the dispersion equation is a simple linear dependence between the frequency and the wave number. After connecting the crystal to the 2D electrical network of variable capacitors, we can obtain very unusual and tunable dispersion diagrams. We present analytic results describing dispersion equations for surface and volume acousto-electric waves and show the corresponding wave simulations. The talk is based on the papers: 1) A. A. Kutsenko, A. L. Shuvalov, and O. Poncelet, “Dispersion spectrum of acoustoelectric waves in 1D piezoelectric crystal coupled with 2D infinite network of capacitors,” J. Appl. Phys. 123, 044902 (2018); 2) A. A. Kutsenko, A. L. Shuvalov, O. Poncelet, and A. N. Darinskii, “Tunable effective constants of the one-dimensional piezoelectric phononic crystal with internal connected electrodes,” J. Acoust. Soc. Am. 137(2), 606–616 (2015).

Influence of temperature on the properties of one-dimensional piezoelectric phononic crystals

The current study investigates the influence of temperature on a one-dimensional piezoelectric phononic crystal using tunable resonant frequencies. Analytical and numerical examples are introduced to emphasize the influence of temperature on the piezoelectric phononic crystals. It was observed that the transmission spectrum of a one-dimensional phononic crystal containing a piezoelectric material (0.7 PMN-0.3PT) can be changed drastically by an increase in temperature. The resonant peak can be shifted toward high or low frequencies by an increase or decrease in temperature, respectively. Therefore, we deduced that temperature can exhibit a large tuning in the phononic band gaps and in the local resonant frequencies depending on the presence of a piezoelectric material. Such result can enhance the harvesting energy from piezoelectric materials, especially those that are confined in a phononic crystal.

Space-time modulation of electric boundary conditions in a one-dimensional piezoelectric phononic crystal

A phononic crystal constituted by a one-dimensional piezoelectric material with a periodic distribution of electrodes submitted to space and time-dependent electrical boundary conditions is considered in this work. Interaction of an incident elastic pulse propagating with such phononic crystal is studied using a specific Finite Difference Time Domain model. Simulations are conducted in the case of periodic grounded electrodes “moving” at constant subsonic or supersonic speed. Various nonlinear phenomena resulting from this interaction are observed: Brillouin-like acoustic scattering, non-reciprocity of transmission at fundamental frequency, parametric amplification of the incident wave. The dispersion curve of the wave propagating in the phononic crystal with space-time modulated electrical boundary conditions is also deduced from simulation results.

Dispersion relations of elastic waves in one-dimensional piezoelectric phononic crystal with initial stresses

The effects of initial stresses on dispersion relations of elastic waves in a one-dimensional piezoelectric phononic crystal are studied in this paper. It is taken into account that initial normal and shear stresses acted on piezoelectric slabs and their influences on constitutive equations, governing equations and boundary conditions under in-plane and anti-plane strain cases. Based on the transfer matrices of ingredient piezoelectric slabs, the total transfer matrix of a single cell is derived. Furthermore, the Bloch theorem is used to obtain the dispersive equation of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. In the case of normal propagation of elastic waves within piezoelectric slabs, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses on the dispersive relations are discussed based on the numerical results. It is found that the initial normal stresses have more evident influences than that of initial shear stresses, no matter that in-plane Bloch waves or anti-plane Bloch wave are concerned. Moreover, the influences of initial stress are more evident on the dispersion curves at high frequency than that at the low frequency.

Dispersion relations of elastic waves in one-dimensional piezoelectric phononic crystal with mechanically and dielectrically imperfect interfaces

The effects of mechanically and dielectrically imperfect interfaces on dispersion relations of elastic waves in a one-dimensional piezoelectric phononic crystal are studied in this paper. Six kinds of imperfect interfaces between two different piezoelectric materials constituting the phononic crystal are considered. These imperfect interfaces include: the mechanically compliant dielectrically weakly conducting interface, the mechanically compliant dielectrically highly conducting interface, the grounded metallized interface, the low dielectric interface, the tangent fixed interface and the tangent slippery interface. Based on transfer matrices of piezoelectric slabs and imperfect interfaces, the total transfer matrix of a typical single cell in the periodical structure is obtained. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. In the case of normal propagation of elastic waves within piezoelectric slabs, the analytical expressions of the dispersion equations are derived and compared with other literatures. The influences of mechanically and dielectrically imperfect interfaces on the dispersive relations are discussed based on the numerical results.

Quasistatic stopband and other unusual features of the spectrum of a one-dimensional piezoelectric phononic crystal controlled by negative capacitance

Normal propagation of the longitudinal wave through the piezoelectric medium with periodically embedded electrodes is considered. Each pair of electrodes is connected via a circuit with capacitance C. The paper analyzes in detail the unusual features of the dispersion spectrum ω(KT) (K is the Floquet–Bloch wavenumber, T is the period) arising in the special case of a negative value of C. The solution of the dispersion equation shows explicitly the evolution of the passbands and stopbands tunable by varying C<0. One of the striking features is the existence of the poles of ImKT (infinite attenuation) and of the corresponding jumps of the phase ReKT from 0 to π in the stopbands for a certain range (C0,C1) of negative C. Besides, for C∈(C0,C∞) where C∞<C1, the spectrum possesses a low-frequency absolute stopband starting from the quasistatic limit ω=0 and including the tunable pole of ImKT inside. This stopband is related to the negative value of the quasistatic effective elastic constant in the range (C0,C∞). At C=C∞, the effective constant is infinite while the spectrum degenerates to the straight line K=0 at any ω. For C close to C∞, the spectrum consists of the branches with high group velocity and of the quasiflat branches.

Tunability of Bragg band gaps in one-dimensional piezoelectric phononic crystals using external capacitances

A one-dimensional stack of identical piezoelectric rods is investigated. The device exhibits a band gap related to electrical boundary condition. A separate control of the central frequency and of the width of the band gap is performed by an electrical boundary condition involving two different variable capacitances. Because the capacitances are grounded, a specific model has been developed and validated. Finally, experiments unambiguously confirmed previous theoretical observations.

Tunable effective constants of the one-dimensional piezoelectric phononic crystal with internal connected electrodes.

One-dimensional propagation of a longitudinal wave through an infinite piezoelectric periodically layered structure is considered. The unit cell consists, in general, of piezoelectric multilayers separated by thin electrodes which are connected through a capacitor with capacity Cj that plays the role of the external electric control providing tunability of the mechanical properties. The main focus of the present study is on the effective properties characterizing the homogenized medium. Due to the electric boundary conditions, the 4×4 transfer matrix M through the period T can be reduced to 2 × 2 dimension governing the mechanical fields only. As a result, the homogenized medium is pure elastic though its effective material parameters depend on the piezoelectric and dielectric coefficients of the actual piezoelectric medium, as well as on Cj. The effective parameters and the impedance in the low-frequency limit ω→0 and at finite frequency are obtained and analyzed.

Piezoelectric-sensitive mode of lamb wave in one-dimensional piezoelectric phononic crystal plate

We investigate the transmission modes in one-dimensional piezoelectric phononic crystal plate, which is consisted of piezoelectric ceramics placed periodically in epoxy. The influences of piezoelectricity and different electrical boundary conditions on the Lamb waves in the composite plate are studied in detail, and an important elastic wave mode named as piezoelectric-sensitive mode (PSM) is defined. Furthermore, the influences of the piezoelectric constants, the filling fraction and the ratio of thickness to lattice pitch on PSM are given, and the physical mechanism of PSM is also discussed. The numerical results show that PSM has a relatively larger frequency shift and significant change in the displacement distribution when piezoelectricity is considered; the electromechanical coupling coefficient of PSM is much larger than the other modes. It reveals that PSM is an important and useful mode in piezoelectric periodic structures. This investigation is helpful in controlling the band gaps and also gives a potential application in design of sensing system and different piezoelectric devices.