A simple holographic interferometer for static and dynamic photomechanics

A particular variation of holographic imaging system is described which, when used as a multiple-exposure holographic interferometer, possesses advantages for applications in static and dynamic photomechanics. Large fields of view can be obtained. Rigid-body motions produced by loading are automatically eliminated. The holograms can be recorded on medium-resolution films which have high sensitivity. Specimens manufactured with readily available materials can be used for the determination of isochromatics and isopachics. An attempt is made to describe this contribution in the background of previous developments in interferometry. Operation of the system is interpreted by showing the equivalence of the holographic interferometer to a combination of two systems presently in use in experimental stress analysis: a Fizeau interferometer and an optical spatial filter. The interpretation of isochromatics and isopachis as moiré phenomena is emphasized. Isochromatics and isopachics are presented as illustrations of the applications of the method to the solution of static-stress problems, and they are used in the solution of some not yet solved dynamic-stress problems. Whole-field static isochromatics obtained as absolute-retardation interference are shown. Also shown are whole-field dynamic isopachics.     

Application of the absolute-retardation method to the determination of steady-state dynamic contact stresses

The absolute-retardation method of stress analysis has been developed and extended to the measurement of steady-state dynamic contact-stress distributions in an elastohydrodynamic rolling contact. The method has been shown to be applicable to the plane-strain conditions appearing in such a contact, and many of the difficulties of the technique associated with the use of conventional interferometers have been eliminated by forming the absolute-retardation interferogram from reflections at the front and back surfaces of an optically plane parallel birefringent model using a laser light source. Some results illustrating the success and limitations of the technique in the study of the elastohydrodynamic problem are discussed.     

The determination of elastic parameters of a half-space using a monochromatic vibration field at the surface

The paper presents a method to determine Lamé parameters λ, μ and density ϱ in a layered half-space, using monochromatic vibrations of its surface, excited by a harmonic source which is assumed to be known. The equations governing the vibrations are reduced to the Sturm-Liouville problem in scalar form for Love-type displacements, and in matrix form for the Rayleigh type. The scalar and matrix potentials of the Sturm-Liouville equations can be recovered from the corresponding impedance. Explicit formulas are given to construct the potentials by amplitudes and wavenumbers of normal (progressive) modes and attenuated standing waves. The potentials then are used to determine the elastic parameters and the density. The method can also be used for the acoustic equation.     

Holographic photoelasticity: Determination of absolute retardations by a single hologram

In this paper, real-time holographic interferometry is applied to determine the absolute-retardation fringes in the photoelastic analysis of plane models. The method requires only one hologram recorded with the model unloaded. In the reconstruction process, the mcdel is loaded and the polarizers on the reference and object beams are rotated through the same angle. At the points of the model where the polarization direction is parallel to one of the principal stresses, only the corresponding family of absolute retardations is obtained. The technique is demonstrated experimentally using a deep beam centrally loaded.     

On the limitations of interferometric methods in three-dimensional photoelasticity

The photoelastic response of tinree different epoxy materials was measured. Tensile strips, beams, disks and spheres were loaded and the deformations “frozen in.” Slices from these models were used to calibrate and analyze the absolute retardation of the materials. It was found that the absolute retardation of light vibrating in a given principal direction was directly proportional to the principal strain in that direction and to the deviatoric components of stress in that direction. This result was a consequence of a unique value of the ratio of the absolute-retardation constants and is contrary to published suggestions that absolute-retardation methods could be used to separate normal stresses in the interior of stress-frozen models.     

刚性源项处理方法在爆震模拟中的应用对比

为解决爆震燃烧模拟中出现的刚性问题,对处理刚性源项问题常见的一步法、逼近法、拟稳态逼近法(α qusai steady state, αQSS)和点隐方法进行对比,从稳定性等方面分析源项处理方法应满足的时间步长要求,并探索各方法之间的联系以及适应化学反应特征变化的能力,进一步通过球头激波诱导燃烧算例比较每种方法的计算效率。理论分析和数值计算表明:一步法在积分刚性源项时,积分步长需小于或等于2倍最短反应特征时间,而逼近法、αQSS法和点隐方法对时间步长取值没有影响;αQSS法可根据化学反应特征的变化自动调整α值和时间步长,适用范围较广,而一步法和逼近法则是αQSS方法的特例。点隐等隐式方法在求解数学意义上的刚性问题时稳定性很好,但计算效率较低。相比而言,αQSS法在计算稳定性和适应化学反应变化方面都具有良好的性能,且针对激波诱导燃烧算例,αQSS法消耗的CPU时间仅为点隐方法的一半,是处理刚性源项较好的选择。     

Stochastic stability of non-linear SDOF systems

A semi-analytical procedure for obtaining stability conditions for strongly non-linear single degree of freedom system (SDOF) subjected to random excitations is presented using stochastic averaging technique. The method is useful for finding stability conditions for systems having highly irregular non-linear functions which cannot be integrated in closed form to yield analytical expressions for averaged drift and diffusion coefficients. In spite of numerical methods available for finding stability of SDOF system by determining Lyapunov exponent, the proposed technique may have to be adopted (i) when the excitation is non-white; and (ii) when numerical integration fails due to convergence problem. The method is developed in such a way that it lends itself to a numerical computational scheme using FFT for obtaining numerical values of drift and diffusion coefficients of Its differential equation and the corresponding FPK equation for the system. These values of averaged drift and diffusion coefficients are then fit into polynomial form using curve fitting technique so that polynomials can be used for stability analysis. Two example problems are solved as illustrations. The first one is the Van der Pol oscillator having non-linearities which can be treated purely analytically. The example is considered for the validation of the proposed method. The second one involves non-linearities in the form of signum function for which purely analytical solution is not possible. The results of the study show that the proposed method is useful and efficient for performing stability analysis of dynamic systems having any type of non-linearities.     

Two-wavelength method for full-field automated photoelasticity

A new method for the whole-field determination of the isoclinic angle α and the isochromatic parameter ϕ is presented. The problems appearing during the calculation of these two parameters are solved with the use of two different wavelengths. Indeed, when a monochromatic light is used as an incident light, α is not measurable at the points where ϕ is equal to 2kπ. In this method, each monochromatic light can compensate for the influence of ϕ to obtain the isoclinic angle for the entire model. Also, most of the methods calculate the fractional fringe order that is unwrapped afterward to obtain the isochromatic parameter. This unwrapping process needs an initialization, which cannot be automatic with only one isochromatic fringe pattern. The use of two wavelengths permits a complete automatic unwrapping of the isochromatic parameter, even for the initialization of the process.     

MOIRÉ INTERFEROMETRY WITH ENHANCED RESOLUTION

The implementation of this method is relatively simple. It does not require any modification to interferometric systems already in use. It can be used in the analysis of large as well as very small fields, including measurements under a microscope.
A fringe pattern with a carrier is recorded in a single exposure, just as in the standard procedure. As a consequence, any possible instability of the interferometer does not affect the accuracy of the measurements. Further, the spatial resolution of the measurements is not compromised.
Since only one exposure is needed for a given displacement component this method can be applied to dynamic as well as static measurements.
It should be emphasized that even though the number of electronically generated fringes can be arbitrary, the sensitivity is the same as in ordinary moire interferometry as long as the data are taken at the lines of minimum intensity. The improvement is in the increase of the number of data points taken at the locations of maximum resolution. In other words, all the data are taken at the maximum resolution.
This method applies not only to moire interferometry but to any experimental technique based on two-beam interference, as long as the fringe pattern has good contrast.     

Integration of linear and some model non-linear equations of motion of incompressible fluids

We suggest a new exact method that allows one to construct solutions to a wide class of linear and some model non-linear hydrodynamic-type systems. The method is based on splitting a system into a few simpler equations; two different representations of solutions (non-symmetric and symmetric) are given. We derive formulas that connect solutions to linear three-dimensional stationary and non-stationary systems (corresponding to different models of incompressible fluids in the absence of mass forces) with solutions to two independent equations, one of which being the Laplace equation and the other following from the equation of motion for any velocity component at zero pressure. To illustrate the potentials of the method, we consider the Stokes equations, describing slow flows of viscous incompressible fluids, as well as linearized equations corresponding to Maxwell's and some other viscoelastic models. We also suggest and analyze a differential-difference fluid model with a constant relaxation time. We give examples of integrable non-linear hydrodynamic-type systems. The results obtained can be suitable for the integration of linear hydrodynamic equations and for testing numerical methods designed to solve non-linear equations of continuum mechanics.     

定向约束提高炸药作功能力的实验研究

采用任意反射面激光干涉测速技术,通过测量飞片的自由面速度,对比研究了50 mm50 mm的含铝炸药在10 mm厚的钢筒约束条件下和无约束状态时对50 mm1.5 mm钢飞片的作功效能,实验结果表明,采用钢筒约束装置后,炸药对钢飞片的作功效能明显提高,钢飞片的飞行速度提高了34.8％,动能提高了81.7％。     

A methodology for determining mechanical properties of freestanding thin films and MEMS materials

We have developed a novel chip-level membrane deflection experiment particularly suited for the investigation of sub-micron thin films and microelectro-mechanical systems. The experiment consists of loading a fixed-fixed membrane with a line load applied at the middle of the span using a nanoindenter. A Mirau microscope interferometer is positioned below the membrane to observe its response in real time. This is accomplished through a micromachined wafer containing a window that exposes the bottom surface of the specimen. A combined atomic force microscope/nanoindenter incorporates the interferometer to allow continuous monitoring of the membrane deflection during both loading and unloading. As the nanoindenter engages and deflects the sample downward, fringes are formed and acquired by means of a CCD camera. Digital monochromatic images are obtained and stored at periodic intervals of time to map the strain field. Stresses and strains are computed independently without recourse to mathematical assumptions or numerical calibrations. Additionally, no restrictions on the material behavior are imposed in the interpretation of the data. In fact, inelastic mechanisms including strain gradient plasticity, piezo and shape memory effects can be characterized by this technique.The test methodology, data acquisition and reduction are illustrated by investigating the response of 1-μm thick gold membranes. A Young's modulus of , a yield stress of and a residual stress of are consistently measured. The post-yield behavior leading to fracture exhibits typical statistical variations associated to plasticity and microcrack initiation.     

连续分层流体中垂直薄板的水动力特性

研究了在线性连续分层流体中水波与半潜式刚性垂直薄板相互作用的问题. 在 Boussinesq近似下,基于分离变量法,导出了具有自由面的平面前进波的色散关系,建立 了半潜式刚性垂直薄板的反射与透射能量、水平波浪力的计算方法. 对给定的频率,当它大 于浮力频率时,流场中只有一种模态的平面前进波,当它小于浮力频率时,流场 中有无数多个模态的平面前进波,并证明了对每一种模态的入射波,其它每个模态水波的反射与透射能量是 相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量,以及作用在薄板上的水平波浪力 进行了数值计算分析,表明了流体的线性连续分层效应对这些水动力的影响是不可忽视 的. 特别地,在入射波频率小于浮力频率时,与第1模态入射波的能量转化量及其对薄板产 生的水平波浪力相比,其它模态入射波的能量转化量及其对薄板产生的水平波浪力都要大得 多.     

压剪炮的激光测速系统的研究

压剪炮试验是获取材料超高应变率下本构关系的最常用手段,其中普遍采用的测试方法是利用激光干涉技术同时测量靶板背面一点的纵向和横向速度。但传统的横向位移干涉仪抵抗靶板撞击过程中的运动而引起的光路偏移能力很有限,因而压剪试验成功率很低。本文讨论了撞击过程中靶板运动对横向位移干涉仪试验信号的影响,为提高横向位移干涉仪特别是非理想撞靶情况下的测量能力,对几种不同干涉光路进行详细分析。通过改进传统横向位移干涉光路,研制了一种新干涉光路,并通过试验证明:相对于传统光路,新光路更简单并更可靠。     

参数灵敏度分析的神经网络方法及其工程应用

在系统分析中，参数灵敏度分析不仅为判断各系统参数的重要性大小提供了依据，量化的灵敏度指标也是后续参数估计的前提。然而，在多效实际系统中，系统参数与系统状态间的显式函数关系不易得到，导致一阶灵敏度指标无法直接求取。简化的单因素分析方法亦存在模型粗糙、精度不高的缺点。本文研究采用人工神经网络的高精度泛化映射，通过少量样本的训练，建立复杂系统中多个系统参数与系统状态间的近似映射关系，继而推导得到统一的灵敏度计算列式。简单结构的神经网络方法和解析方法的对比计算显示了方法的有效性和可靠性。最后，应用该法对某斜拉桥结构的荷载参数和刚度参数进行了考查，得到一般性结论。     

Instantaneous phase-stepping interferometry using polarization imaging with a micro-retarder array

An instantaneous phase-stepping and subsequent phase analysis method, using a CCD camera with a form-birefringent micro-retarder array, is proposed for interferometry. An optical setup of a polarization interferometry using a Twyman-Green interferometer with two polarizers is constructed to analyze the distribution of out-of-plane displacement. Light emerging from the interferometer is recorded using a CCD camera that has micro-retarder array on the CCD plane. This micro-retarder array has four different principal directions. That is, an image obtained by the CCD camera contains four types of data corresponding to four different optical axes of the retarder. The four images separated from the image recorded by the CCD camera are reconstructed using gray-level interpolation. Then, the distributions of the Stokes parameters that represent the state of polarization are calculated from the four images. The phase distribution of the interference fringe pattern produced by the Twyman-Green interferometer is then obtained from these Stokes parameters. This method is applicable to time-dependent phenomena because multiple exposures are unnecessary for sufficient data acquisition in the completion of phase analysis.     

A new moiré interferometer for measuring in-plane displacement

This paper proposes a new moiré interferometer to be used for determining in-plane displacement of a body deformed with small strains and small surface slopes. With this interferometer, the grating not only diffracts the incoming beam but also rediffracts the two first orders, each of which is reflected by a mirror, back into the path of the incoming beam. The two rediffracted beams are then directed to the viewer to generate an interference fringe pattern that depends only on the in-plane displacement. Theoretical analysis of this new interferometer is presented. It was determined that the sensivity of the interferometer is twice that of conventional interferometers, and the slightly warped beam wave front coming from the laser source does not affect the measurement result. An experiment was performed by adopting the proposed and conventional interferometers to determine the displacement of a specimen grating. The results confirm the advantages of using this new interferometer.     

The Peculiarities of Linear Wave Propagation in Double Porous Media

The features of propagation of longitudinal and transverse waves (LW and TW) in fractured porous medium (FPM) saturated with liquid are investigated by methods of multiphase mechanics. The mathematical model of FPM accounting for inequality of velocities and pressures of liquid in pores and fractures, liquid mass exchange and nonstationary interaction forces is developed. Processes of monochromatic wave propagation are studied. The dispersion relation is obtained and the effect of model parameters on wave propagation is analysed. It is established that one transverse and three longitudinal waves propagate in FPM saturated with liquid. The fastest LW is a deformational wave and the two others are filtrational. Filtrational waves attenuate much stronger than deformational and transverse waves. Distinction of velocities and pressures in liquid in various pore systems provides an explanation for the existence of the two filtrational waves in porous medium with two different characteristic sizes of pores.     

Application of the extended Kantorovich method to the bending of clamped cylindrical panels

Applicability and performance of the extended Kantorovich method (EKM) to obtain highly accurate approximate closed form solution for bending analysis of a cylindrical panel is studied. Fully clamped panel subjected to both uniform and non-uniform loadings is considered. Based on the Love–Kirchhoff first approximation for thin shallow cylindrical panels, the governing equations of the problem in terms of three displacement components include a system of two second order and one forth order partial differential equations. The governing PDE system is converted to a double set of ODE systems by assuming separable functions for displacements together with utilization of the extended Kantorovich method. The resulted ODE systems are solved iteratively. In each iteration, exact closed form solutions are presented for both ODE systems. Rapid convergence and high accuracy of the method is shown for various examples. Both displacement and stress predictions show close agreement with other analytical and finite element analysis.     

Oscillation pattern of stick-slip vibrations

This paper studies the stick-slip oscillations of discrete systems interacting with translating energy source through a non-linear smooth friction curve. The stick-slip limit cycle oscillations of a single degree-of-freedom model are examined by means of numerical time-integration and analytical methods. Similar approaches are also applied to the model of the coupled friction oscillator. Particularly, it is found that the steady-state response of the coupled oscillator can be divided into two different forms of oscillation (mode-merged and mode-separated oscillations) according to the frequency separation of two modes. The oscillation pattern of the steady-state response is shown to depend on system parameters such as detuning factor, energy source speed, and normal contact load.