Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error

The Fourier transform method, widely applied in photomechanics for the automated analysis of interferometric fringe patterns, has been recently extended to the photoelastic isochromatic fringe patterns analysis. Unfortunately, its use in photoelasticity involves some limitations that have not been completely highlighted in literature. This work deals with the influence of the quarter-wave plate tolerance on the evaluation of the retardation. Both theoretical and experimental analyses have shown that the quarter-wave plate error does not affect the retardation only if the principal stress directions in the model and in the carrier are aligned. In general, instead, the tolerance of the quarter-wave plates leads to an amplification of the retardation error due to the influence of the isoclinics with a subsequent restriction of the field in which the method can be applied. For instance, using common quarter-wave plates and tolerating a maximum retardation error of about 0.03 fringe order, than the Fourier transform method cannot be applied as a full-field technique but only in the model zones in which the misalignment between the principal stresses in the model and in the carrier is less than 15°.     

Determination of isoclinics in photoelasticity with a fast regularized estimator

The determination of isoclinics from photoelastic fringe patterns is a key problem in photoelasticity. Dealing with this problem, however, is not a simple task when isotropic points are present which is common for most experimental situations. Because of this, few researchers have proposed effective and practical solutions. Visualizing this problem as the problem of the determination of the modulo 2π fringe orientation, in this paper it is proposed an efficient regularized algorithm to solve it. Experimental results show that the proposal is effective and can be used with either monochromatic or white light.     

Photoelastic Analysis with a Single Tricolor Image

A new approach to simultaneous measurement of isochromatics and isoclinics from a single image using a tricolor light, called as the tricolor photoelastic technique, is proposed in order to enable and facilitate the analysis of time varying phenomena. Not only an apparatus of experiment but the whole analysis system and procedure are developed. Using a color digital camera and a tricolor light source under linear polarization, fringe order and the principal direction of birefringence are obtained from a piece of color image data by a single shot using the method proposed. It is emphasized that this method can be applicable to time varying phenomena in which good repeatability and reproducibility of experiments are not expected, since multiple exposures are not necessary for sufficient data acquisition in the completion of stress analysis.     

Vibrations of a polygonal plate having orthogonal straight edges by an extended rayleigh-ritz method

An extended Rayleigh-Ritz method is presented for solving vibration problems of a polygonal plate having orthogonal straight edges. The polygonal plate is considered as an assemblage of several rectangular plates. For each element rectangular plate, the transverse displacement is approximated by interpolation functions corresponding to unknown displacements and slopes at the discrete points which are chosen along the edges, and series of trial functions which satisfy homogeneous artificial boundary conditions. By minimizing the energy functional corresponding to the assumed displacement function, the dynamic stiffness matrix of the element rectangular plate, which is similar to that obtained in the finite element method, is derived. The dynamic stiffness matrix of the whole system is obtained by summing up those of the element rectangular plates. Numerical results are presented for the natural frequencies and mode shapes of cantilever L-shaped and T-shaped plates.     

A study of pulsatile jet discharged from pipe end

Noise is generated from a flow field upstream of a shock wave periodically discharged from a pipe end. A vortex ring and an underexpanded jet are periodically formed and diffused downstream. To clarify the mechanism of the noise generation, the flow field was experimentally and numerically studied. The flow field was visualized mainly by the schlieren method and the sound pressure of the noise was measured. The pulsatile flow through the pipe was numerically simulated by Random-Choice Method and using these results as the boundary condition, the pulsatile jet was simulated by TVD scheme. As a result, a good qualitative agreement was found between the flow field obtained by the calculations and that by the experiments. Furthermore, a relation between the behaviour of the vortex ring and the generation of the noise was discussed.     

Hybrid investigation on residual stresses induced by self-drilling screw on polycarbonate plates

The residual stresses induced by using self-drilling screws on polycarbonate plates were investigated by the hybrid method which incorporates the digital photoelastic method and finite element method (FEM). Different types of screws lead to different photoelastic fringe patterns, which provide the boundary conditions needed in the numerical simulation. By changing the two main parameters (pressure and temperature), the FEM results can be matched well with the experimental results for drilling at 0° tilt angle. For drilling at other tilt angles, the photoelastic fringe patterns provide useful information for failure analysis.     

Three-dimensional free vibration analysis of isotropic rectangular plates using the B-spline Ritz method

This paper presents three-dimensional free vibration analysis of isotropic rectangular plates with any thicknesses and arbitrary boundary conditions using the B-spline Ritz method based on the theory of elasticity. The proposed method is formulated by the Ritz procedure with a triplicate series of B-spline functions as amplitude displacement components. The geometric boundary conditions are numerically satisfied by the method of artificial spring. To demonstrate the convergence and accuracy of the present method, several examples with various boundary conditions are solved, and the results are compared with other published solutions by exact and other numerical methods based on the theory of elasticity and various plate theories. Rapid, stable convergences as well as high accuracy are obtained by the present method. The effects of geometric parameters on the vibrational behavior of cantilevered rectangular plates are also investigated. The results reported here may serve as benchmark data for finite element solutions and future developments in numerical methods.     

Analysis and optimization of trimorph ring transducers

The Kirchoff-Love plate theory and electroelasticity theory are combined to simulate the dynamic behaviors of the trimorph ring transducers under different boundary conditions. The transducer consists of an isotropic elastic ring laminated between two identical piezoelectric rings. Their electric current response, resonant frequencies, antiresonant frequencies and electromechanical coupling coefficients (EMCCs) are theoretically formulated and studied by numerical simulation. Also, the resonant frequencies and their corresponding mode shape are simulated by the finite element modelling to verify the theoretical results. Finally, to obtain the maximum energy conversion efficiency, the dynamic EMCC is optimized by varying the proportion of piezoelectric and elastic parts. It is shown that the dynamic EMCC depends on geometric thickness and radii ratios. Optimum settings for a particular transducer to reach the maximum dynamic EMCC are found for different boundary conditions. The trimorph ring transducer for the fixed inner and free outer surfaces boundary condition has slightly lower resonant and anti-resonant frequencies, and larger EMCCs than that for the free inner and fixed outer surfaces boundary condition does.     

Plate impulse response spatial interpolation with sub-Nyquist sampling

Impulse responses of vibrating plates are classically measured on a fine spatial grid satisfying the Shannon-Nyquist spatial sampling criterion, and interpolated between measurement points. For homogeneous and isotropic plates, this study proposed a more efficient sampling and interpolation process, inspired by the recent paradigm of compressed sensing. Remarkably, this method can accommodate any star-convex shape and unspecified boundary conditions. Here, impulse responses are first decomposed as sums of damped sinusoids, using the Simultaneous Orthogonal Matching Pursuit algorithm. Finally, modes are interpolated using a plane wave decomposition. As a beneficial side effect, these algorithms can also be used to obtain the dispersion curve of the plate with a limited number of measurements. Experimental results are given for three different plates of different shapes and boundary conditions, and compared to classical Shannon interpolation.     

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用有限元软件Fluent对EAST超导磁体电流引线中氦气流阻进行了计算。计算中对氦气模型进行了简化和分段,相邻两段模型间采用流量边界条件和压力边界条件进行耦合。计算结果表明:氦气的压力降主要集中在靠近室温端;气体模型厚度越薄,氦气压力降越大;通过电流引线的电流越大,氦气的压力降越大;在引线片凸纹的狭窄处氦气速度很大,在靠近室温端时最大可以达到21m.s-1左右。     

Time-domain simulation of damped impacted plates. I. Theory and experiments

A time-domain formulation for the flexural vibrations in damped rectangular isotropic and orthotropic plates is developed, in order to investigate transient excitation of plates by means of sound synthesis. The model includes three basic mechanisms of damping (thermoelasticity, viscoelasticity and radiation) using a general differential operator. The four rigidity factors of the plate are modified by perturbation terms, each term corresponding to one specific damping mechanism. The first damping term is derived from the coupling between the thermoelastic stress-strain relations and the heat diffusion equation. The second term is obtained from the general differential formulation of viscoelasticity. The third term is obtained through a Pade approximation of the damping factor which governs the coupling of the plate with the surrounding air. The decay factors predicted by the model reproduce adequately the dependence on both dimensions and frequency of the decay factors measured on rectangular plates of various sizes and thicknesses made of four different materials (aluminum, glass, carbon fiber, and wood). The numerical resolution of the complete problem, including initial and boundary conditions, and the comparison between real and simulated sounds are presented in a companion paper.     

数字光弹性相移法中全场等倾角和等差线相位

以径向受压圆盘为例,从弹性力学的角度详细分析了模型全场等倾角相位的情况,分析第一主应力的方向,在六步相移法的基础上提炼出圆盘全场等倾角相位和等差线的真实相位。采用有限元软件MARC与形函数拟合相结合的方法模拟径向受压圆环六步相移图和等差线相位图,可以推广到没有解析解或者解析解复杂的应力模型的光弹性实验模拟。通过径向受压圆盘实验验证了方法的可行性,实现光弹法中自动提取全场等差线的信息。     

精确标定光弹调制器的新方法

针对现有光弹调制器标定方法的不足,提出了一种精确标定光弹调制器的新方法。首先利用起偏器、波片、光弹调制器和检偏器构成标定光路,通过寻找探测信号基频分量的极大值进行粗略标定,使光弹调制器的峰值延迟量处在1.841rad附近。然后撤走波片形成光弹调制器的精确标定光路,在检偏器旋转90°前后获得探测信号的直流分量和二次谐波分量。最后利用这两种探测信号的直流分量和二次谐波分量精确地计算出光弹调制器的峰值延迟量。实验验证了此光弹调制器标定方法,实验结果表明其标定误差仅为0.7%。在此光弹调制器标定方法中,光弹调制器的标定精度和入射光强、电路参量无关。同时,标定要求的峰值延迟量小,非常适合于光弹调制器在其使用波长范围长波段的标定。     

Limitation of carrier fringe methods in digital photoelasticity

The carrier fringes method has been proposed in digital photoelasticity in combination with techniques such as Fourier transform and phase shifting method, without considering the influence of the isoclinics on the isochromatic patterns analysis. Unlike other optical methods as moiré and holographic interferometry, in photoelasticity the light intensity emerging from a circular polariscope is related to both the isochromatic retardation and the isoclinic parameter. As it is shown by the theoretical analysis, owing to the misalignment between the principal stresses in the model and in the carrier, the computed retardation is affected by an error which is the same for all photoelastic methods based on the use of carrier fringes. Consequently, the photoelastic analysis carried out by methods that use carrier fringes cannot be applied as a full-field technique. In detail, numerical simulations show that the retardation error is comparable (less than 0.05 fringe orders) with that of other photoelastic methods provided that the misalignment between the principal stresses in the model and in the carrier is less than 30°. On the contrary, in the model zones where the misalignment is higher than 30°, the retardation measurement can be affected by non negligible errors (up to 0.25 fringe orders).     

Study on Combined Method Based on 3-D ESPI

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Study on Combined Method Based on 3-D ESPI

The finite element method (FEM),whether the calculation is accurate or not,depends closely on object boundary condition.If the three dimensional displacement of the object obtained in experiment is regarded as its boundary condition,a new method combining the results of experiment and calculation,called combined method (CM),is formed.The combined method possess advantages of experiment and calculation.It can correct calculation and improve the accuracy of FEM.Accordingly it has more practicability.In this paper,the three dimensional displacement fields of a typical beam loaded at three points are tested by using 3-D electric speckle pattern interferometry (ESPI).Using the experimental results as boundary condition the whole three-dimensional displacement fields can be calculated by FEM.The beam′s three-dimensional displacement fields obtained by FEM agree very well with those obtained by experiment.This proves that the combined method is effective and practicable.     

柱环腔中的量子电动力学效应

研究以同轴不同半径柱面围成的导体柱环腔体中电磁场真空零点振动模式所给出的宏观量子效应.零点振动模式通过求解柱环空腔边界条件下无源的Maxwell方程组获得.得到了双柱面同心柱环中单位长度和单位面积的且是有限的真空能量，即Casimir能量.这有限的Casimir能量可以分解为独立而且收敛的三部分，它们分别来自内柱面、外柱面和柱环之中.对多柱面同心柱环，Casimir能量可分解为独立的（2n—1）部分（n为柱面数）.柱环是类似于平行板的几何结构.但柱环所给出的Casimir能量和Casimir势能系数是随着 关键词： Casimir效应 柱环腔体 零点能 量子电动力学     

The influence of the quarter wave plates in automated photoelasticity

During the last decades, several methods have been proposed to automate photoelastic analyses. Some procedures are based on the circularly polarised light by using quarter wave plates. However, quarter wave plates are typically matched for a specific wavelength, and an error is introduced at different wavelengths. The error of quarter wave plates affects the measurement of isochromatic and isoclinic data. In this paper, the influence of the errors of quarter wave plates in some of the most common automated photoelastic methods is reviewed. The errors in the photoelastic data are given and the procedures to reduce, or eliminate, them are also suggested.     

An efficient differential quadrature methodology for free vibration analysis of arbitrary straight-sided quadrilateral thin plates

In this paper, a new differential quadrature (DQ) methodology is employed to study free vibration of irregular quadrilateral straight-sided thin plates. A four-nodded super element is used to map the irregular physical domain into a square domain in the computational domain. Second order transformation schemes with relative ease and less computation are employed to transform the fourth order governing equation of thin plates between the two domains. The only degree of freedom within the domain is the displacement, whereas along the boundaries, the displacement as well as the second order derivative of the displacement with respect to associated normal co-ordinate variable in computational domain are the two degrees of freedom. Implementing the method, the formulation for the DQ method for the free vibration analysis of plates of straight-sided shapes was presented together with the implementation procedure for the different boundary conditions. To demonstrate the accuracy, convergency and stability of the new methodology, detail studies are made on isotropic plates at acute angles with different geometries, boundary and loading conditions including DQ free-edge boundary condition implementations. Accurate results even with fewer degrees of freedom than for those of comparable numerical algorithms were achieved.