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.

Analysis of errors induced by λ/4 wave plate in fiber-optic current sensor system

1/4λ wave plate is a key element in the fiber-optic current sensor system. When a retardation error or an orientation error of birefringence axes of 1/4λ wave plate with respect to the hi-bi fiber axes occurs in the 1/4λ wave plate, the sensor system will output a wrong result of the measured current. The contributions of these two errors to the final result of the whole system were studied and the errors functions were deduced by establishing the measurement function of the current sensor system with Jones matrixes of the optical elements. The results show that that the greater the orientation error or the retardation error, the larger the final error, and that these two errors cannot be compensated each other.

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.

Excitation and Detection of Shear Horizontal Waves with Electromagnetic Acoustic Transducers for Nondestructive Testing of Plates

The fundamental shear horizontal（SH0） wave has several unique features that are attractive for long-range nondestructive testing（NDT）. By a careful design of the geometric configuration, electromagnetic acoustic transducers（EMATs） have the capability to generate a wide range of guided wave modes, such as Lamb waves and shear-horizontal（SH） waves in plates. However, the performance of EMATs is influenced by their parameters. To evaluate the performance of periodic permanent magnet（PPM） EMATs, a distributed-line-source model is developed to calculate the angular acoustic field cross-section in the far-field. Numerical analysis is conducted to investigate the performance of such EMATs with different geometric parameters, such as period and number of magnet arrays, and inner and outer coil widths. Such parameters have a great influence on the directivity of the generated SH0 waves that arises mainly in the amplitude and width of both main and side lobes. According to the numerical analysis, these parameters are optimized to obtain better directivity. Optimized PPM EMATs are designed and used for NDT of strip plates. Experimental results show that the lateral boundary of the strip plate has no perceivable influence on SHO-wave propagation, thus validating their used in NDT. The proposed model predicts the radiation pattern ofPPM EMATs, and can be used for their parameter optimization.

Uplift Pressure of Waves on A Horizontal Plate

Uplift pressures of waves acting on horizontal plates are the important basis for design of maritime hollow-trussed structures. In this paper, an experimental study on the uplift pressures of waves on a horizontal plate is conducted by use of a series of model tests. Detailed analysis has been given to the formation mechanism of uplift pressures of waves. It is considered that the impact pressure intensity is mainly affected by geometrical factors (tangential angle of waves), dynamic factors (wave height, wave velocity, etc.) and air cushion. Based on the test results, an equation for calculation of the maximum uplift pressure intensity of waves on a plate is presented. A large quantity of test data shows good agreement of the present equation with the test results.

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.

Investigation of SH-Wave Fundamental Modes in Piezoelectromagnetic Plate: Electrically Closed and Magnetically Closed Boundary Conditions

It is theoretically considered the propagation (first evidence) of new dispersive shear-horizontal (SH) acoustic waves in the piezoelectromagnetic (magnetoelectroelastic) composite plates. The studied two-phase composites (BaTiO3-CoFe2O4 and PZT-5H-Terfenol-D) possess the piezoelectric phase (BaTiO3, PZT-5H) and the piezomagnetic phase (CoFe2O4, Terfenol-D). The mechanical, electrical, and magnetic boundary conditions applied to both the upper and lower free surfaces of the plate are as follows: the mechanically free, electrically closed, and magnetically closed surfaces. As a result, the fundamental modes of two new dispersive SH-waves recently discovered in book [Zakharenko, A.A. (2012) ISBN: 978-3-659-30943-4] were numerically calculated. It was found that for large values of normalized plate thickness kd (k and d are the wavenumber and plate half-thickness, respectively) the velocities of both the new dispersive SH-waves can approach the nondispersive SH-SAW velocity of the piezoelectric exchange surface Melkumyan (PEESM) wave. It was also discussed that for small values of kd, the experimental study of the new dispersive SH-waves can be preferable in comparison with the nondispersive PEESM wave. The obtained results can be constructive for creation of various technical devices based on (non)dispersive SH-waves and two-phase smart materials. The new dispersive SH-waves propagating in the plates can be also employed for nondestructive testing and evaluation. Also, it is obvious that the plates can be used in technical devices instead of the corresponding bulk samples for further miniaturization.

Hydroelastic Response of A Circular Plate in Waves on A Two-Layer Fluid of Finite Depth

The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the platecovered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.

Wave Attenuation Performance and the Influencing Factors of A Lower Arc-Plate Breakwater

Comprehensive experimental and numerical studies have been undertaken to investigate wave energy dissipation performance and main influencing factors of a lower arc-plate breakwater. The numerical model, which considers nonlinear interactions between waves and the arc-plate breakwater, has been constructed by using the velocity wave- generating method, the volume of fluid (VOF) method and the finite volume method. The results show that the relative width, relative height and relative submergence of the breakwater are three main influencing factors and have significant influence on wave energy dissipation of the lower arc-plate open breakwater. The transmission coefficient is found to decrease with the increasing relative width, and the minimum transmission coefficient is 0.15 when the relative width is 0.45. The reflection coefficient is found to vary slightly with the relative width, and the maximum reflection coefficient is 0.53 when the relative width is 0.45. The transmission and reflection coefficients are shown to increase with the relative wave height for approximately 85% of the experimental tests when the relative width is 0.19 0.45. The transmission coefficients at relative submergences of 0.04, 0.02 and 0 are clearly shown to be greater than those at relative submergences of 0.02 and 0.04, while the reflection coefficient exhibits the opposite relationship. After the wave interacts with the lower arc-plate breakwater, the wave energy is mainly converted into transmission, reflection and dissipation energies. The wave attenuation performance is clearly weakened for waves with greater heights and longer periods.

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.

Dynamic Response of Stiffened Plates with Holes Subjected to Shock Waves and Fragments

The power field of shock waves and fragments is analyzed and set up, and the damage modes of stiffened plates are put forward. According to the structural characters of the stiffened plates investigated and the properties of the shock waves and fragments, the experiments on the shock waves acting on the stiffened plates (penetrated and non-penetrated by fragments) are mainly conducted. The dynamic response rules of stiffened plates with holes under shock waves and fragments loading are obtained. The results show that the penetration of fragments into stiffened plates hardly affects their deformation produced by shock waves..

Numerical Study on the Effect of Submerged Depth on the Horizontal Plate Wave Energy Converter

The growing search for clean and renewable energy sources has given rise to the studies of exploring sea wave energy. This paper is concerned with the numerical evaluation of the main operational principle of a submerged plate employed for the conversion of wave energy into electrical one. The numerical model used to solve the conservation equations of mass, momentum and transport of volume fraction is based on the finite volume method （FVM）. In order to tackle with the flow of mixture of air-water and its interaction with the device, the multiphase model volume of fluid （VOF） is employed. The purpose of this study is the evaluation of a numerical model for improvement of the knowledge about the submerged plate wave energy converter, as well as the investigation of the effect of the distance from the plate to the bottom of the sea （HP） on the performance of the converter. The simulations for several distances of the plate from the seabed show that the optimal efficiency is 64%, which is obtained for HP=0.53 m （88% of the depth）. This efficiency is 17% larger than that found in the worst case （HP=0.46 m, 77% of the depth）.

Draft effect on wave action with a semi-infinite elastic plate

A method for analyzing reflection and transmission of ocean waves from a semi-infinlte elastic plate with a draft is developed. The relation of energy conservation for plates with three different edge conditions （ free, simply supported and built-in） is also derived. It is found that the present method satisfies the energy relation very well. The effects of draft on wave reflection and transmission coefficients as well as on the vertical vibration of the plates are examined through numerical tests. It is demonstrated that the zero draft assumption works well for low wave frequencies, but the effect of plate draft becomes significant for high wave frequencies.

Finite element analysis of controlling the TC4 thin plate weldment wave-like deformation by welding with impacting rotation

The new technology of welding with impacting rotation is put forward to decrease the wave-like deformation of the TC4 thin plate weldment. The thermal stress and strain are vital to understand the mechanism of controlling the wave-like deformation. In order to know the development of internal thermal stress and strain, finite element method is utilized for- the stress and strain are difficult to be investigated by experimental methods during the welding process. Temperature field, thermal stress evolution and distortion of thin plate are compared with the test results such as weld thermal cycle, residual stress sectioning measurement, and the deflection of the thin plate respectively. By the finite element analysis and test results verification, the meehaaism of the technology to control the wave-like deformation is brought forward, non-uniform thermal elastic strain between compressive plastic region and elastic extensive region is diminished by a certain amount of extensive plastic deformation by welding with impacting rotation process.

On the Interaction of Surface Waves with An Elastic Plate of Finite Length in Head Seas

An eigen-function expansion method based on a new orthogonal inner product is proposed by Sahoo et al. (2000) for the study of the hydroelastic response of mat-type VLFS in head seas. However, their main emphasis is on the effect of edge conditions and they assume that the plate is of a semi-infinite length. In reality, the plate is of finite length. For consideration of the finite length effect, the reflection and transmission from the other end must be considered. The effect of this reflection and transmission on the hydroelastic response of VLFS is of interest for practical application. Furthermore, the physical meaning of the new inner product was not given in their paper. In this paper, it is shown that the new inner product can he derived from the governing equation and the bottom boundary conditions. Then the same eigen-function expansion method is adopted for the study of the hydroelastic response of an elastic plate of finite length in surface waves. Detailed comparisons are made between the present finite length model and the semi-infinite model and between the present model predictions and the experimental results. It is found that that the finite length effect is significant and the accuracy of present model is higher than the semi-infinite model. Furthermore, a new phenomenon, which is not mentioned in Sahoo et al. (2000), is found. Taht is, for larger L/h ratios, the reflection and transmission coefficients will oscillate with the non-dimensional parameter k(0) h. Further study is needed for full understanding of this phenomenon.

One-Dimensional Localization of Elastic Waves in Rib-Stiffened Plates

The 1 dimensional localization of elastic waves in disordered periodic multi span rib stiffened plates is investigated. The transfer matrix method is employed to obtain the transfer matrix of the system, and the method for calculating the Lyapunov exponents in continuous dynamic systems presented by Wolf is used to determine the localization factor. As examples, the numerical results of the localization factors are given for a disordered rib stiffened plate. The effects of the degree of disorder of span...

Study on Scattering Wave Force of Horizontal and Vertical Plate Type Breakwaters

The interaction between wave and horizontal and vertical plates is investigated by the boundary element method, and the relations of wave exciting force with plate thickness, submergence and length are obtained. It is found that： 1） The efficient wave exciting force exists while plate submergence is less than 0.5 m, and the plate is very thin with order O（0.005 m）. 2） The maximum heave wave exciting force exists, and it is the main factor for surface and submerged horizontal plate while the roll force can be ignored. 3） The maximum sway wave exciting force exists, it is the main factor for surface or submerged vertical plate, and the roll force is about 20 times of horizontal plate.

Non-Contact Stress Measurement during Tensile Testing Using an Emat for SH₀-Plate Wave and Lamb Wave

The stress on a test specimen during tensile testing is generally measured by a strain gauge. This method has some problems in that it would influence the measurement conditions of the tensile test and can evaluate only the position at which the strain gauge is attached. The acoustoelastic method is proposed as a method replacing the strain gauge method. However, an ultrasonic sensor with a piezoelectric oscillator requires a coupling medium to inject an ultrasonic wave into a solid material. This condition, due to the error factor of the stress measurement, makes it difficult for the ultrasonic sensor to move on the specimen. We then tried to develop a non-contact stress measurement system during tensile testing using an electromagnetic acoustic transducer (EMAT) with an SH0-plate wave and S0-Lamb wave. The EMAT can measure the propagation time in which the ultrasonic wave travels between a receiver and a transmitter without a coupling medium during the tensile testing and can move easily. The interval between the transmitter and the receiver is 10mm and can be moved along the parallel direction or the vertical direction of the tensile load. The transit time was measured by a cross-correlation method and converted into the stress on the test specimen using the acoustoelastic method. We confirmed that the stress measurement using an SH0-plate wave was superior to that with an S0-Lamb wave.

FLEXURAL WAVE PROPAGATION IN NARROW MINDLIN'S PLATE

Appling Mindlin＇s theory of thick plates and Hamilton system to propagation of elastic waves under free boundary condition, a solution of the problem was given. Dispersion equations of propagation mode of strip plates were deduced from eigenfunction expansion method. It was compared with the dispersion relation that was gained through solution of thick plate theory proposed by Mindlin. Based on the two kinds of theories, the dispersion curves show great difference in the region of short waves, and the cutoff frequencies are higher in Hamiltonian systems. However, the dispersion curves are almost the same in the region of long waves.