Pure Longitudinal Mode Research Articles

Experimental observation of sub-radiant longitudinal mode and anomalous optical transmission in metallic wire meshes

In conventional plasmonic media and plasmonic metamaterials, such as metallic wire meshes, a longitudinal mode of an electromagnetic wave manifests itself in frequency overlapping transverse modes, which impedes clear observation of longitudinal-mode-specific physical effects. Through interlacing two sets of wire meshes, an ideal band for the longitudinal mode is achieved ranging from zero frequency to plasma frequency, where transverse modes are completely forbidden. The unique spectral separation of modes facilitates the observation of pure longitudinal modes and related plasmonic effects in a bulk medium. We report the microwave experiment of anomalous optical transmission, induced solely by electromagnetic longitudinal mode resonance, below the plasma frequency in such a wire mesh medium.

Weld Strength of Longitudinal and Longitudinal-Torsional Mode Horns in Ultrasonic Metal Welding

The ultrasonic metal welding technique has been widely used because of the need to weld different materials for meeting high quality performance requirements. The key part in this type of welding is the horn, which plays an important role in the weld quality. Longitudinal vibration has so far been the most popular vibration mode for ultrasonic horns, but the longitudinal mode coupled with torsional mode is gaining a lot of attention these days owing to its better performance compared to the pure longitudinal mode. Although there are many studies on the performance of these two mode horns, comparative studies based on the performance of these two modes, particularly in ultrasonic metal welding, are very rare. This study focuses on the welding performance comparison of these two horns with 20 kHz resonant frequency. Experimental results show that the performance of the longitudinal-torsional horn is better than that of the longitudinal horn in terms of welding strength.

A simplified analytical model for the investigation of contact acoustic nonlinearity in pipe structures

A simplified analytical model of contact acoustic nonlinearity (CAN) in pipe structures was established and verified by finite element modelling to analyse the multimode second harmonic waves induced by a breathing crack. The analytical model was developed from plate to pipe structures with S-parameter formulation applied for the investigation of second harmonic generation where pure longitudinal wave mode excitation was used. A numerical simulation model with the same excitation condition was developed to confirm the results from the theoretical analysis. Multimode second harmonic waves were obtained in both analytical and simulation models and the proportion of different modes in terms of axial amplitude was also studied. A new nonlinear index was finally proposed for the quantitative assessment of fatigue crack growth in pipe structures.

Anisotropic in elasticity, sound velocity and minimum thermal conductivity of Al–Cu intermetallic compounds

First-principles calculations were utilized to study the anisotropic in terms of elasticity, sound velocity and minimum thermal conductivity of Al–Cu intermetallic compounds (AlCu, c-AlCu3, o-AlCu3, o-Al2Cu, t-Al2Cu, Al3Cu2 and Al4Cu9). There was good agreement between our calculated lattice constants and previous experimental and theoretical results. The compounds' anisotropy of elasticity was estimated. They had different anisotropic elastic properties. The anisotropy in sound velocity showed that the faster mixed mode (v+) is much greater than that of slower mixed mode (v-) and pure transverse mode (vt) for AlCu phase, while the sound velocity of pure longitudinal mode (vl) is the largest in cubic phase (c-AlCu3 and Al4Cu9), orthorhombic phase (o-AlCu3 and o-Al2Cu) and tetragonal phase (t-Al2Cu). The calculated minimum thermal conductivity of the compounds from the Clarke's model indicated that they had obvious anisotropy.

Pure mode axis and the electromechanical coupling coefficients of the 0.67Pb(Mg1/3Nb2/3) O3-0.33PbTiO3 single crystal

Pure mode axes of the 0.67Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 (PMN-0.33PT) single crystals are investigated by slowness surfaces method. It is found only the Z-axis is a pure mode axis. The piezoelectricically stiffened Christoffel equation of the PMN-0.33PT crystal is solved in the rotating coordinate system. All of the single acoustic modes of thickness vibration are obtained. For the pure longitudinal mode of Z-cut crystal, the electromechanical coupling coefficient is up to 0.82. However, it is only 0.34 for the pure shear modes of X-cut or Y-cut crystal. It is along the pure mode axis that the maximum electromechanical coupling coefficients can be achieved.

Lateral Field Excitation of Thickness Longitudinal Mode and Shear Mode With ZnO Based on Solidly Mounted Resonator.

Coplanar electrodes are used with the c-axis-oriented piezoelectric film to form the pure longitudinal mode and the pure shear mode solidly mounted resonators (SMRs). Aluminum and molybdenum are used as electrode materials to achieve different excitation pure shear mode and pure longitudinal mode. There is no need to make a bottom electrode or etch the piezoelectric layer, which simplifies the manufacturing and makes the structure stable. Furthermore, the cycle time of the process is significantly reduced. However, the control of the thickness of the Bragg reflectors, roughness control, and electrode photolithography are all challenging aspects of SMR manufacturing. In this study, ZnO piezoelectric film, which has a good electromechanical coupling factor and low transmission loss, was used as the c-axis-oriented piezoelectric film. An RF magnetron sputtering system was used to sputter a seed layer to encourage the growth of the zinc-oxide piezoelectric film and improve the c-axis orientation. The pure longitudinal mode and pure shear mode resonance signals were excited using the room temperature positive axis method. The quality factor and electromechanical coupling coefficient of the pure shear mode were 398% and 4.43%, respectively. The quality factor and electromechanical coupling coefficient of the pure longitudinal mode were 171% and 3.83%, respectively. Stability and feature recognition were accomplished in the pure longitudinal mode and the pure shear mode via a simplified and accelerated manufacturing process using electrodes with the same specifications.

Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817

In this work, we discuss the polarization contents of Einstein-\ae ther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom. We find the plane wave solutions are then found, and identify the polarizations by examining the geodesic deviation equations. We find that there are five polarizations in Einstein-\ae ther theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einstein-\ae ther theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-\ae ther theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces.

Anisotropy in elasticity, sound velocities and minimum thermal conductivity of zirconia from first-principles calculations

The anisotropies of mechanics and thermodynamics properties of zirconia with three zero-pressure polymorphs were studied by using first-principles calculations. It has been shown that Young’s moduli of three phases strongly depend on directions. The sound velocities of faster mixed mode (v+) is much larger than that of slower mixed mode (v−) and pure transverse mode (vt) in monoclinic phase. For both tetragonal phase and the cubic phase, most pure longitudinal mode (vl) have the greatest sound velocity among the three acoustic modes. According to the Clarke's model, three zero-pressure polymorphs zirconia also have pronounced anisotropic minimum thermal conductivity.

Electronic structure, anisotropic elastic and thermal properties of monoclinic Ca2Nb2O7

The electronic structure, anisotropic elastic and thermal properties of monoclinic Ca2Nb2O7 have been investigated by density functional theory (DFT) calculations and further are verified by experimental results. It has been shown that the monoclinic Ca2Nb2O7 is a direct band gap insulator with the calculated band gap of 3.07eV which is comparable with the experimental value of 3.33eV. The bottom of the conduction band (CB) is dominated by the 4d orbitals of the Nb atoms and the 2p orbitals of O atoms, while the top of valence band (VB) mainly consists of the 2p orbitals of O atoms. Calculated sound velocities of different directions show that the faster mixed mode (v+) is much larger than that of slower mixed mode (v- ) and pure transverse mode (vt ) in both [100] and [001] directions. The pure longitudinal mode vl has the greatest sound velocity among the three acoustic modes in the [010] direction. According to Clarke's model, monoclinic Ca2Nb2O7 has low limit thermal conductivity with 1.43Wm−1K−1 at high temperature, and minimum thermal conductivity in (100), (110), (010) and (001) planes sensitively depends on the directions.

Analysis of Fabry-Perot optical micro-cavities based on coating-free all-Silicon cylindrical Bragg reflectors

We study the behavior of Fabry-Perot micro-optical resonators based on cylindrical reflectors, optionally combined with cylindrical lenses. The core of the resonator architecture incorporates coating-free, all-silicon, Bragg reflectors of cylindrical shape. The combined effect of high reflectance and light confinement produced by the reflectors curvature allows substantial reduction of the energy loss. The proposed resonator uses curved Bragg reflectors consisting of a stack of silicon-air wall pairs constructed by micromachining. Quality factor Q ~1000 was achieved on rather large cavity length L = 210 microns, which is mainly intended to lab-on-chip analytical experiments, where enough space is required to introduce the analyte inside the resonator. We report on the behavioral analysis of such resonators through analytical modeling along with numerical simulations supported by experimental results. We demonstrate selective excitation of pure longitudinal modes, taking advantage of a proper control of mode matching involved in the process of coupling light from an optical fiber to the resonator. For the sake of comparison, insight on the behavior of Fabry-Perot cavity incorporating a Fiber-Rod-Lens is confirmed by similar numerical simulations.

Defect visualization in pipes using a longitudinal guided wave mode

Recently, defect visualization techniques based on guided waves have been developed for pipe inspection. This study advances existing defect visualization techniques in two ways: (1) a fiber-guided laser ultrasonic system, which can operate under high radiation and temperature environments, is used to generate and measure broadband guided waves, and (2) a longitudinal mode instead of a torsional mode is used to detect axial cracks and wall thinning. Using optical fiber probes installed along a circumferential direction of a pipe with equal spacing, a pure longitudinal mode, L(0,2), is launched by axisymmetrically exciting a pipeline structure. The generated L(0,2) subsequently interacts with scattering sources such as defects or pipe boundaries and generate reflected L(0,2) and higher-order modes, L(n,2), (n>0). The reflected modes, L(0,2) and L(n,2), are measured in a pulse-echo manner using the same fiber probes and synthetically processed. By back propagating the dispersive L(0,2) and L(n,2) modes in time and space, this study reconstructs dispersion-compensated L(0,2) and L(n,2) at the scattering sources and thereby visually locates the defects. Numerical simulation and experimental studies are performed to validate the effectiveness of the proposed technique.

Pure modes for elastic waves in crystals: mathematical modeling and search

A universal search method of pure longitudinal and pure transverse modes for elastic wave propagation in crystals, in general piezoelectrics, is presented. A mathematical model of pure modes for elastic waves based on adiabatic state equations for an arbitrary anisotropic piezoelectric medium and its equation of motion under elastic deformations in the rotated Cartesian coordinates is constructed. The condition for longitudinal normals is that all non-diagonal matrix elements of the effective elastic stiffness coefficients in the corresponding wave equation are equal to zero. Equating to zero non-diagonal elements only in one row of this matrix, one can obtain the condition for transverse normals. A computer program is prepared which allows to find the pure modes for elastic waves in crystals and to calculate their characteristics when symmetry class, elastic, piezoelectric, dielectric constants, and crystal density are known.

Analytical study of dual-mode thin film bulk acoustic resonators (FBARs) based on ZnO and AlN films with tilted c-axis orientation

In this paper, we present the analytical study of thin film bulk acoustic wave resonators (FBARs) using ZnO and AlN films with a c-axis tilt angle (off-normal) from 0 degrees to 180 degrees. The tilted c-axis orientation induces normal plane and inplane polarizations, which leads to the coexistence of the longitudinal mode and shear mode in the resonator. The equation for predicting electric impedance of FBARs was derived from the basic piezoelectric constitutive equations. Material properties including elastic, dielectric, and piezoelectric coefficients, bulk wave properties including acoustic velocity and electromechanical coupling coefficient, and impedance of FBARs were calculated and showed strong dependence on the tilt angle. Interestingly, it was found that for ZnO FBARs, pure thickness longitudinal modes occur at 0 degrees and 65.4 degrees, and pure thickness shear modes occur at 43 degrees and 90 degrees. For AlN FBARs, pure longitudinal modes occur at 0 degrees and 67.1 degrees, and pure shear modes occur at 46.1 degrees and 90 degrees for AlN. In other words, pure thickness longitudinal and shear modes exist in ZnO and AlN FBARs at specific tilted polarization angles. In addition, two peaks of shear mode electromechanical coefficient are found at 33.3 degrees and 90 degrees for ZnO, and 34.5 degrees and 90 degrees for AlN. Therefore, ZnO and AlN films with specific tilt angles may provide options in the design and fabrication of FBARs, considering their strong shear resonance with high electromechanical coefficients. The use of dual-mode FBARs for mass sensors is also analyzed; the calculated large resonant frequency shift caused by mass loading shows that they have good prospects for use in sensor applications with high sensitivity. The simulation results agreed well with the reported experiment results, and can be used for design and application of FBARs.

Analysis of dual-mode thin film bulk acoustic resonators based on polar c-axis tilted wurtzite gallium nitride

We present the analytical study of dual-mode thin film bulk acoustic resonators (FBARs) based on wurtzite gallium nitride (GaN) thin films with tilted c-axis orientation. The normal-plane and in-plane electric polarization vector components caused by the titled c-axis orientation induce the coexistence of the thickness longitudinal and thickness shear modes in the thin film resonator. Due to the c-axis orientation dependency of material properties including elastic stiffness, dielectric constants, and piezoelectric coefficients, bulk wave properties of FBARs including acoustic velocity and electromechanical coupling coefficient, and electrical impedance spectra are greatly affected by the tilt angle. It is found that the pure longitudinal mode occurs at θ=0° and 66.4°, and the pure shear mode occurs at θ=42.8° and 90°. In addition, the electromechanical coupling coefficient for thickness shear mode has a maximum value 3.18% at θ=34.2°, which is larger than the maximum value for pure thickness longitudinal mode 2.44% at θ=0°. The calculation results show that FBARs based on tilted c-axis wurtzite GaN thin films are promising for frequency control device design and applications.

Acoustic characteristics of a rocket combustion chamber: Radial baffle effects

This paper describes methods used for determining the characteristic acoustic modes and frequencies of a liquid–propellant rocket–motor combustion chamber and effects of radial baffles on the chamber’s acoustic field. A multi-point sensing experimental setup, including stationary and moving sensors, was used to measure characteristic frequencies and mode shapes of a combustion chamber. A new technique based on the comparison of signal phase angles from stationary sensors to that of a moving sensor was used to map complex characteristic mode shapes of a combustor. A three-dimensional Helmholtz acoustic solver was also developed using an efficient finite volume approach for complex geometries to simulate the acoustic field inside a combustor. Using this approach the effects of the convergent section of the nozzle and the number of radial baffles on the chamber’s dominant acoustic modes with no mean flow were investigated. We have shown that the classical reduction of characteristic frequency of tangential modes caused by radial baffles is due to longitudinalization of tangential modes and is a function of the blade length and weakly dependent on the number of blades. Also, conjugate spinning modes are decoupled and do not spin in any baffled combustor, independent of the number of blades. On the other hand the converging nozzle section of a combustion chamber modifies pure longitudinal modes in the radial direction and pure tangential modes in the longitudinal direction. Existence of some mixed tangential–longitudinal modes in a combustor is dependent on the ratio of the nozzle throat diameter to the combustor head plate diameter.

An analytical, numerical, and experimental study of the axisymmetric vibrations of a short cylinder

This paper presents a study of standing axisymmetric waves in homogeneous, isotropic, linear, and elastic cylinders whose length and diameter are of the same order of magnitude. It is analytically demonstrated that only materials with a Poisson's ratio equal to zero can vibrate in pure radial and longitudinal axisymmetric modes and, hence, the universal frequencies, independent of Poisson's ratio, and the corresponding universal aspect ratios can be accurately calculated. The Ritz method is applied to numerically determine the natural frequencies and the mode shapes of finite cylinders. Vibration of a cylinder in the neighbourhood of the universal point is analysed. Both free and forced vibrations are experimentally detected by using a laser speckle interferometer that allows the determination of the natural frequencies and the mode shapes. From the numerical calculations, it is confirmed that, for materials with Poisson's ratio not equal to zero, no crossings occur between the curves of non-dimensional frequency versus aspect ratio, neither for antisymmetric modes themselves nor for symmetric modes. There is a good agreement between the analytical solutions, the numerical results, and the experimental measurements.

Bulk acoustic wave analysis of crystalline plane oriented ZnO films

Bulk acoustic wave (BAW) properties of piezoelectric layer are very important design parameters for film bulk acoustic wave resonator devices. In this research, BAW properties of all crystalline plane oriented sputtered and epitaxial ZnO films were analyzed theoretically. The (002), (004), and (006) oriented ZnO films provided a pure longitudinal mode. The (100), (110), (200), (210), (300), and (220) oriented ZnO films provided a pure fast shear mode. The (101), (102), (103), (112), (201), (202), (104), (203), (211), (114), (212), (105), (204), (213), (302), (205), (106), and (214) oriented ZnO films provided a quasilongitudinal mode and a quasishear mode. Those bulk acoustic wave properties can be used for further device design and application.

Bulk Acoustic Wave Analysis of Crystalline-Plane-Oriented Aluminum Nitride Films

Bulk acoustic wave analysis of all crystalline-plane-oriented AlN films were studied in this research. Different crystalline-plane-oriented AlN films will form different vibration modes and acoustic properties. (002)-, (004)-, and (006)-oriented AlN films provided a pure longitudinal mode. (100)-, (110)-, (200)-, (210)-, and (300)-oriented AlN films provided a pure fast shear mode. (101)-, (102)-, (103)-, (112)-, (201)-, (202)-, (104)-, (203)-, (211)-, (114)-, (212)-, (105)-, (204)-, (213)-, (302)-, (205)-, (106)-, and (214)-oriented AlN films provided a quasi-longitudinal mode and a quasi-shear mode. These bulk acoustic wave properties can be used for further device design and application.

Large eddy simulation of mean and oscillating flow in a side-dump ramjet combustor

Ramjet flows are very sensitive to combustion instabilities that are difficult to predict using numerical simulations. This paper describes compressible large eddy simulation on unstructured grids used to investigate nonreacting and reacting flows in a simplified twin-inlet ramjet combustor. The reacting flow is compared to experimental results published by ONERA in terms of mean fields. Simulations show a specific flow topology controlled by the impingement of the two air jets issuing from the twin air inlets and by multiple complex recirculation zones. In a second part, all unsteady modes appearing in the reacting LES are analyzed using spectral maps and POD (proper orthogonal decomposition) tools. A Helmholtz solver also computes the frequencies and structures of all acoustic modes in the ramjet. Pure longitudinal, transverse and combined modes are identified by all three diagnostics. In addition, a mode-by-mode analysis of the Rayleigh criterion is presented thanks to POD. This method shows that the most intense structure (at 3750 Hz) is the first transverse acoustic mode of the combustor chamber and the Rayleigh criterion obtained with POD illustrates how this transverse mode couples with unsteady combustion.

A 2H NMR Relaxation Experiment for the Measurement of the Time Scale of Methyl Side-Chain Dynamics in Large Proteins

An NMR experiment is presented for the measurement of the time scale of methyl side-chain dynamics in proteins that are labeled with methyl groups of the (13)CHD(2) variety. The measurement is accomplished by selecting a magnetization mode that to excellent approximation relaxes in a single-exponential manner with a T(1)-like rate. The combination of R(1)((13)CHD(2)) and R(2)((13)CHD(2)) (2)H relaxation rates facilitates the extraction of motional parameters from (13)CHD(2)-labeled proteins exclusively. The utility of the methodology is demonstrated with applications to proteins with tumbling times ranging from 2 ns (protein L, 7.5 kDa, 45 degrees C) to 54 ns (malate synthase G, 82 kDa, 37 degrees C); dynamics parameters are shown to be in excellent agreement with those obtained in (2)H NMR studies of other methyl isotopomers. A consistency relationship is found to exist between R(1)((13)CHD(2)) and the relaxation rates of pure longitudinal and quadrupolar order modes in (13)CH(2)D-labeled methyl groups, and experimental rates measured for a number of proteins are shown to be in excellent agreement with expectations based on theory. The present methodology extends the applicability of (2)H relaxation methods for the quantification of side-chain dynamics in high molecular weight proteins.