Propagation Properties of Backward Lamb Waves in Plate Investigated by Dynamic Photoelastic Technique

The dynamic photoelastic technique is employed to visualize and quantify the propagation properties of backward Lamb waves in a plate. Higher energy leakage of second-order symmetric backward wave mode S2b in contrast to third-order anti-symmetric backward mode A3b is shown by the dispersion curve of a plate immersed in water, and then verified by experiments. To avoid the considerable high leakage, the plate is placed in air, both group and phase velocities of modes S2b and A3b in the glass plate are experimentally measured. In comparison with the theoretical values, less than 5% errors are found in experiments.

THEORY AND EXPERIMENTAL INVESTIGAION OF FLEXURAL WAVE PROPAGATION IN THIN RECTANGULAR PLATE WITH PERIODIC STRUCTURE

With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane-wave expansion （PWE） method, and directional band gaps are found in the ΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finite structure is simulated with the finite element method and verified with a vibration experiment. The frequency ranges of sharp drops in the calculated and measured acceleration frequency response curves are in basic agreement with those in the band structures. Thin plate is a widely used component in the engineering structures. The existence of band gaps in such periodic structures gives a new idea in vibration control of thin plates.

Analysis of Second-Harmonic Generation of Low-Frequency Dilatational Lamb Waves in a Two-Layered Composite Plate

We analyze the effect of second-harmonic generation（SHG） of primary Lamb wave propagation in a two-layered composite plate, and then investigate the influence of interfacial properties on the said effect at low frequency. It is found that changes in the interfacial properties essentially affect the dispersion relation and then the maximum cumulative distance of the double-frequency Lamb wave generated. This will remarkably influence the efficiency of SHG. To overcome the complications arising from the inherent dispersion and multimode natures in analyzing the SHG effect of Lamb waves, the present work focuses on the analysis of the SHG effect of low-frequency dilatational Lamb wave propagation. Both the numerical analysis and finite element simulation indicate that the SHG effect of low-frequency dilatational Lamb wave propagation is found to be much more sensitive to changes in the interfacial properties than primary Lamb waves. The potential of using the SHG effect of low-frequency dilatational Lamb waves to characterize a minor change in the interfacial properties is analyzed.

Sub-external cavity effect and elimination method in laser self-mixing interference wave plate measurement system

Laser self-mixing interference（SMI） wave plate measurement method is a burgeoning technique for its simplicity and efficiency. But for the non-coated sample, the reflected light from the surface can seriously affect the measurement results.To analyze the reason theoretically, a self-consistent model for laser operation with a sub-external and an external cavity is established, and the sub-external cavity formed by the sample and a cavity mirror is proved to be the main error source.A synchronous tuning method is proposed to eliminate the sub-external cavity effect. Experiments are carried out on the synchronously tuning double external cavities self-mixing interference system, and the error of the system is in the range of -0.435°~0.387° compared with the ellipsometer. The research plays an important role in improving the performance and enlarging the application range of the laser self-mixing interference system.

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate

We investigate the three-dimensional （3D） scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem. An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes, and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies. The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency. It is also found that the scattering patterns are different from those of the SO wave incidence. Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.

Laser Feedback Technique for Precise Retardation Measurements

A simple and precise retardation measurement based on laser feedback is demonstrated. The measurement principle is based on polarization flipping induced by optical feedback from an external birefringence cavity. The measured wave plate is located in the external cavity. When the length of the external cavity is tuned, the polarization states of laser will flip between two eigenstates, and the position of polarization flipping in one period of intensity modulation will vary with retardation of the wave plate. The duty ratio of two eigenstates is used to determine the retardation. Main advantages of the technique are that it is compact, low cost, fast and flexible. Especially, it is insensitive to a fluctuation of laser intensity and is suitable for on-line measurement. The experimental results have shown that the measurement uncertainty is better than 0.03° in the range 30°-150°.

Ultra-broadband asymmetric acoustic transmission with single transmitted beam

We report both experimentally and numerically that ultra-broadband asymmetric acoustic transmission is realized by a brass plate and a right triangle reflector immersed in water. This exotic phenomenon arises from the asymmetric excitation of the leaky asymmetric zero-order Lamb mode in the brass plate induced by the incident angle of external bulk waves. The results show that the bandwidth of the asymmetric acoustic transmission could reach 2000 k Hz, and the positive transmitted wave is only a single acoustic beam. The device has the advantages of ultra-broadband, single transmitted beam,and simpler structure, which has great potential applications in ultrasonic devices.

Lamb wave topological imaging for blind hole defects in isotropic plates

The research aims at validating the ability of topological imaging to blind holes in isotropic plates using Lamb waves. Due to the defect is not symmetric around the mid- plane of the plate, the effect of Lamb mode conversion will have to be taken into account. The imaging method is based on two computations of ultrasonic fields, one forward and one adjoint, performed for the defect-free reference medium. The excited signal and scattered Lamb waves caused by the blind hole, are used as emitting sources to compute the forward problem and the adjoint problem, respectively. With the help of the finite element simulations, the natural refocusing process of the multimode Lamb waves at the defect location is visually demonstrated by the transient acoustic field snapshots at the different moments to strengthen the physical mechanism of the topological imaging method. The numerical results demonstrate that topological imaging has relatively stronger applicability to the blind hole in contrast to classical Delay And Sum （DAS） method and Time Reversal （TR） method. The topological imaging could handle complex Lamb wave signals containing mode conversions without the imaging quality being affected. The proposed imaging method presents a certain developing potential for detecting and imaging asymmetric defects in plate-like configurations using Lamb waves.

A spectroscopic method for determining thickness of quartz wave plate

A spectroscopic method to determine thickness on chromatic polarization interferometry. With of quartz wave plate is presented. The method is based the polarization-resolved transmission spectrum （PRTS） curve, the phase retardation of quartz wave plate can be determined at a wide spectral range from 200 to 2000 nm obviously. Through accurate judgment of extreme points of PRTS curve at long-wave band, the physical thickness of quartz wave plates can be obtained exactly. We give a measuring example and the error analysis. It is found that the measuring precision of thickness is mainly determined by the spectral resolution of spectrometer.

ANALYSIS OF HYDRODYNAMICS FOR TWO-DIMENSIONAL FLOW AROUND WAVING PLATES

Hydrodynamic characteristics for two-dimensional flow around a waving plate are investigated. Under large Reynolds number approximation, the flow is assumed to be a combination of the outer potential flow and a thin vortex layer, which consists of a boundary layer and a shed free shear layer. A nonlinear mathematical formulation for describing the outer unsteady potential flow coupled with an unsteady boundary layer equation for the inner viscous flow adjacent to the waving plate is developed. A semi-analytical method with a nonlinear Kutta condition imposed at the trailing edge is used to solve the velocity field of the outer flow and the evolution of wake vortex induced by a large-amplitude waving plate. The unsteady boundary layer equation is solved by extending Pohlhausen＇s method to its unsteady counterpart. The thrust and viscous drag coefficients, propulsive efficiency, and the pattern of wake vortex sheet are discussed.

The technique of detecting the laser-ultrasonic vector displacement with a confocal Fabry-Perot interferometer waves in a plate

Generally, a confocal Fabry-Perot interferometer is only able to detect the out-of-plane component of a displacement field; while the in-plane component often has the information about the material which cannot be found in this out-of-plane component. In this paper, based on a confocal Fabry-Perot interferometer set-up for detecting the out-of-plane component of a laser generated acoustic field, a technique is developed to detect both the out-of-plane and in-plane displacement components simultaneously with a novel two-channel confocal Fabry-Perot interferometer.

Experimental analysis of acousto-ultrasonic wave propagation mode in thin plate

in the acousto-ultrasonic technique, a broadband ultrasonic wave is injected onto the surface at one location of the tested plate with the help of a longitudinal transducer and a receiving transducer is coupled to the same surface at another location. Thus, understanding the propagation characteristics of the ultrasonic wave is essential for successful application of the technique. It has been found that the dominant acousto-ultrasonic waves produced experimentally in thin plate are multi-mode Lamb waves. The broadband generation and detection of Lamb waves have been performed in two aluminum plates with different thickness using the acousto-ultrasonic method.

Acoustic streaming induced by ultrasonic quasi-lamb waves in a plate

The speed of the streaming flow in the liquid layer loaded on a thin plate, in which Lamb waves are propagating, was calculated. The results are good agreement with Moroney's experiment

Valley-Chiral Edge States of Antisymmetric Plate Wave in Phononic Crystals with Linear Defect

In this work,two typical interfaces are established for the antisymmetric plate wave by introducing linear defect in between phononic crystals with opposite valley Hall phases.The evolution of projected curves is demonstrated as the defect width increases,which magnifies the occurrence of multiple edge states on both interfaces.The mapping of transmission coefficient is obtained upon the incidence of transversely symmetric and antisymmetric sources,respectively.It is shown that the first edge state contains only symmetric or antisymmetric component regardless the defect width modulation,while other edge states contain both components.When void cavity occurs on the interfaces,the mapping of transmission coefficient shows that the first edge state is topologically protected and its transverse symmetry or antisymmetry is almost unperturbed by the void cavity,while other edge states do not perform the same way.Our work provides useful guidance for the design of topological edge states,and bridges the topological edge states and linear defect modes on the same interface.

Propagation of elastic waves in a plate with rough surfaces

The characteristics of Lamb wave propagating in a solid plate with rough surfaces are studied on the basis of small perturbation approximation. The Rayleigh-Lamb frequency equation expressed with SA matrix is presented. The Rayleigh-Lamb frequency equation for a rough surface plate is different from that for a smooth surface plate, resulting in a small perturbation △k on Lamb wave vector k. The imaginary part of △k gives the attenuation caused by wave scattering. An experiment is designed to test our theoretical predications. By using wedge-shape pipes, different Lamb wave modes are excited. The signals at different positions are received and analyzed to get the dispersion curves and attenuations of different modes. The experimental results are compared with the theoretical predications.

The reflection of the Lamb wave in a semi-infinite plate

The Lamb wave technique is used in the detection of internal defects in plates. The reflection of the Lamb wave at the free edge of the plate has been shown to be rather complicated. The reflected wave is usually composed of infinite number of Lamb wave modes even in the case of incidence of one pure mode. The analysis of the reflection problem is complicated in nature as the orthogonality relations of the eigen modes of the Lamb wave concern both the stresses and displacements. We adopt the principle of the least squares as a new approach to simplify the analysis, in which the eigen-modes are taken as the trial function. It seems to be simple and effective. In most cases a good enough result can be obtained on using an 8- bit microcomputer. Here the coefficients of the various reflected modes are calculated, some interesting phenomena on the mode conversion are indicated and the conditions on the pure mode reflection are given.

Propagation of guided waves in a bonded plate:Antiplane shear modes

The displacement and stress as well as the dispersion equation for the guided waves of antiplane shear (SH) modes in a bonded plate are presented explicitly. The spring model is used to account for the interface rigidity between the layers of the bonded plate. It is found that the dispersion equation is composed of the terms pertinent with the welded and the cracked or slip boundary conditions with the compliance sT of the spring model as the sum-coefficients. Numerical results for an adhesive plate of aluminum and steel whose wave velocities are very close to each other of equal thickness indicate that the modes of odd order are more sensitive than the even ones to the variations of the bond quality, and so are the higher modes than the lower ones for this special layered plate. The phenomena of the cut-off frequency-shift and the phase velocity decrease resulting from the degradation of the bond quality are found to the modes of odd order, which may be used to evaluate the bond states of the adhesive plate. Numerical results for an adhesive plate of rubber and steel whose wave velocities are very different to each other of equal thickness are presented and discussed as well.

The propagation of Lamb waves in an anisotropic plate bordered with liquid layers

Based on elastic wave propagation theory, the dispersion equation for a thin anisotropic plate (such as commonly used Zinc okide in micro-transducers) bordered with liquid layers is derived. Higher symmetry crystals, such as orthorhombic, tetragonal, cubic, isotropic, are included in this analysis as well. For the case of one liquid layer loading, numerical calcu- lations show that the phase velocity changes periodically with the thickness of the liquld layer. When the thickness 2d of the anisotropic plate is very small, mass sensing application of Ao mode Lamb wave is also discussed.

Controlled generation of order-switchable cylindrical vector beams from a Nd:YAG laser

We reporte and demonstrate a solid-state laser to achieve controlled generation of order-switchable cylindrical vector beams(CVBs).In the cavity,a group of vortex wave plates(VWPs)with two quarter-wave plates between the VWPs was utilized to achieve mode conversion and order-switch of CVBs.By utilizing two VWPs of first and third orders,the second and fourth order CVBs were obtained,with mode purities of 96.8%and 94.8%,and sloping efficiencies of 4.45%and 3.06%,respectively.Furthermore,by applying three VWPs of first,second,and third orders,the mode-switchable Gaussian beam,second,fourth,and sixth order CVBs were generated.

Design of broadband terahertz vector and vortex beams: II. Holographic assessment

In this paper,we demonstrate the capabilities of the terahertz pulse time-domain holography in visualisation,simulation,and assessment of broadband THz vortex beam formation dynamics upon its shaping by elements of beam converter,and further propagation and manipulation.By adding Jones matrix formalism to describe broadband optical elements,we highlight the differences in the spatio-spectral and spatio-temporal structure of the formed vortex and vector beams dependence on the modulator used and visualise their modal features.The influence of diffraction field structure from each element in the broadband vortex modulator is revealed in numerical simulation and the formed beams are analysed against the simplified Laguerre-Gaussian beam model.