Temporal heterodyne shearing speckle pattern interferometry

Shearing speckle pattern interferometry is a full-field speckle interferometric technique used to determine surface displacement derivatives. In this paper, a new measurement system of real-time heterodyne shearography interferometry is presented. This system combined with heterodyne measurement, shearography interferometry and time domain signal processing technology can dynamically detect the out-of-plane displacement gradient. The principles and system arrangement are described. Using the Jones matrix, the mathematical expression of light intensity distribution passing through this system is deduced. A preliminary experiment was performed to demonstrate the performance of this new device, and simulations were conducted using the finite element method. Comparison of results shows that quantitative measurement of the displacement derivative has been achieved.     

标量波传播问题的双互易精细积分法

为避免使用计算多种特征频率下的声场响应,采用双互易方法将边界积分方程中时间二次导数项的域积分转化为边界积分.首先,将计算场点配置在边界上并考虑边界条件,可以获得由内部节点上声压量线性表示的边界节点上的物理量;其次,将计算场点配置于域内离散节点上,将所得边界积分方程组中关于边界物理量用内部节点的声压量线性表示,获得关于声压量的二阶常微分方程组;第三,引入声压变化速度作为未知量,将二阶常微分方程组转化为一阶常微分方程组;最后,采用精细积分法精确求解常微分方程组.数值算例验证了双互易精细积分法的正确性和稳定性.     

The extended Fourier pseudospectral time-domain method for atmospheric sound propagation

An extended Fourier pseudospectral time-domain (PSTD) method is presented to model atmospheric sound propagation by solving the linearized Euler equations. In this method, evaluation of spatial derivatives is based on an eigenfunction expansion. Evaluation on a spatial grid requires only two spatial points per wavelength. Time iteration is done using a low-storage optimized six-stage Runge-Kutta method. This method is applied to two-dimensional non-moving media models, one with screens and one for an urban canyon, with generally high accuracy in both amplitude and phase. For a moving atmosphere, accurate results have been obtained in models with both a uniform and a logarithmic wind velocity profile over a rigid ground surface and in the presence of a screen. The method has also been validated for three-dimensional sound propagation over a screen. For that application, the developed method is in the order of 100 times faster than the second-order-accurate FDTD solution to the linearized Euler equations. The method is found to be well suited for atmospheric sound propagation simulations where effects of complex meteorology and straight rigid boundary surfaces are to be investigated.     

The Linear KdV Equation with an Interface

The interface problem for the linear Korteweg–de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each domain. The location of the interface is known and a number of compatibility conditions at the boundary are imposed. We provide an explicit characterization of sufficient interface conditions for the construction of a solution using Fokas’s Unified Transform Method. The problem and the method considered here extend that of earlier papers to problems with more than two spatial derivatives.     

A parallel Vlasov solver based on local cubic spline interpolation on patches

A method for computing the numerical solution of Vlasov type equations on massively parallel computers is presented. In contrast with Particle In Cell methods which are known to be noisy, the method is based on a semi-Lagrangian algorithm that approaches the Vlasov equation on a grid of phase space. As this kind of method requires a huge computational effort, the simulations are carried out on parallel machines. To that purpose, we present a local cubic splines interpolation method based on a domain decomposition, e.g. devoted to a processor. Hermite boundary conditions between the domains, using ad hoc reconstruction of the derivatives, provide a good approximation of the global solution. The method is applied on various physical configurations which show the ability of the numerical scheme.     

Surpassing the standard quantum limit for optical imaging using nonclassical multimode light

Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement measurement of a light beam below the standard quantum limit. Multimode squeezed light is obtained by mixing a vacuum squeezed beam and a coherent beam that are spatially orthogonal. Although the resultant beam is not squeezed, it is shown to have strong internal spatial correlations. We show that the position of such a light beam can be measured using a split detector with an increased precision compared to a classical beam. This method can be used to improve the sensitivity of small displacement measurements.     

Immersed boundary method for the simulation of 2D viscous flow based on vorticity–velocity formulations

A new immersed boundary method based on vorticity–velocity formulations for the simulation of 2D incompressible viscous flow is proposed in present paper. The velocity and vorticity are respectively divided into two parts: one is the velocity and vorticity without the influence of the immersed boundary, and the other is the corrected velocity and the corrected vorticity derived from the influence of the immersed boundary. The corrected velocity is obtained from the multi-direct forcing to ensure the well satisfaction of the no-slip boundary condition at the immersed boundary. The corrected vorticity is derived from the vorticity transport equation. The third-order Runge–Kutta for time stepping, the fourth-order finite difference scheme for spatial derivatives and the fourth-order discretized Poisson for solving velocity are applied in present flow solver. Three cases including decaying vortices, flow past a stationary circular cylinder and an in-line oscillating cylinder in a fluid at rest are conducted to validate the method proposed in this paper. And the results of the simulations show good agreements with previous numerical and experimental results. This indicates the validity and the accuracy of present immersed boundary method based on vorticity–velocity formulations.     

Identification of stiffness and damping properties of plates by using the local equation of motion

This paper deals with the identification of stiffness and damping properties of vibrating structures by an inverse method inspired from the Force Analysis Technique (FAT). The proposed approach uses a local equation of motion assumed a priori, which provides a relative straightforward relationship between the displacement field and material properties. The spatial derivatives of the displacement in the equation are calculated using finite differences. As this operation amplifies measurement noise, a regularization step is applied before solving the inverse problem. A procedure is proposed to automatically adjust the level of regularization. The method also allows one to identify local stiffness and damping on a heterogeneous structure. Illustrations for both homogeneous and heterogeneous cases are shown using simulated and measured displacement fields.     

纳米接触行为的三维多尺度数值模拟

应用分子动力学与有限元耦合的桥域多尺度算法,模拟三维刚性球形压头与光滑基体表面的纳米尺度接触行为,并与全原子分子模拟结果比较.考察在一定载荷下的系统弛豫行为、两种模型桥接区位移和应力的连续性、法向力和接触面积随压头位移变化等,结果表明:一定外载荷下,桥域多尺度算法能较快达到平衡状态,且压头的振荡幅度更小,系统初始温度为0 K时该算法的相对误差最小.在准静态加载过程中,该算法能够将原子区的位移、应力等连续的过渡到连续介质区,具有较好的耦合效果;法向力-压头位移和接触半径-压头位移曲线几乎与分子模拟结果重合,表明算法具有较高的计算精度.     

Reconstruction of dynamic displacement and velocity from measured accelerations using the variational statement of an inverse problem

This paper presents two types of finite impulse response (FIR) filters to reconstruct dynamic displacement induced by structural vibration from measured acceleration. The governing equation for the reconstruction is derived by taking the variation of a minimization problem, which defines an inverse problem on displacement. A regularization function for overcoming the ill-posedness of the inverse problem is included in the minimization problem. The governing equation of the inverse problem becomes the same type of differential equation as that of a beam on an elastic foundation. The conventional FIR (CFIR) filter directly approximates the transfer function of the governing equation, while the FEM-based FIR (FFIR) filter is formulated by the discretization of the minimization problem with the finite element method. For the finite element discretization, the Hermitian shape function is utilized. The proposed FFIR filter is capable of reconstructing displacement and velocity simultaneously. The fundamental characteristics of the proposed filters are investigated in the frequency domain using the transfer and accuracy functions. It is shown that the proposed FIR filters suppress low frequency noise components in measured accelerations effectively, and reconstruct physically meaningful displacement accurately. The validity of the proposed filters is demonstrated through a numerical simulation study, a field experiment and an evaluation of flutter derivatives using measurements taken from a wind tunnel test.     

A Weak Form of the Conjugate Gradient FFT Method for Two-Dimensional Elastodynamics

The problem of two-dimensional scattering of elastic waves by an elastic inclusion can be formulated in terms of a domain integral equation, in which the grad-div operator acts on a vector potential. The vector potential is the spatial convolution of a Green's function with the product of the density and the displacement over the domain of interest. A weak form of the integral equation for the unknown displacement is obtained by testing it with rooftop functions. This method shows excellent numerical performance.     

Depth-Encoded Spectral Domain Phase Microscopy for Simultaneous Multi-Site Nanoscale Optical Measurements

Spectral domain phase microscopy (SDPM) is an extension of spectral domain optical coherence tomography (SDOCT) that exploits the extraordinary phase stability of spectrometer-based systems with common-path geometry to resolve sub-wavelength displacements within a sample volume. This technique has been implemented for high resolution axial displacement and velocity measurements in biological samples, but since axial displacement information is acquired serially along the lateral dimension, it has been unable to measure fast temporal dynamics in extended samples. Depth-Encoded SDPM (DESDPM) uses multiple sample arms with unevenly spaced common path reference reflectors to multiplex independent SDPM signals from separate lateral positions on a sample simultaneously using a single interferometer, thereby reducing the time required to detect unique optical events to the integration period of the detector. Here, we introduce DESDPM and demonstrate the ability to acquire useful phase data concurrently at two laterally separated locations in a phantom sample as well as a biological preparation of spontaneously beating chick cardiomyocytes. DESDPM may be a useful tool for imaging fast cellular phenomena such as nervous conduction velocity or contractile motion.     

Modeling of acoustic wave propagation in time-domain using the discontinuous Galerkin method – A comparison with measurements

Simulations of acoustic wave propagation in time-domain are presented. In the simulations, the discontinuous Galerkin method for spatial derivatives and the low-storage Runge–Kutta approach for time derivatives are used. Three different simulation cases are studied. First, the directivity of loudspeaker is simulated. In the second case, acoustic wave propagation in free space is studied using a short pulse. In the last case, acoustic wave scattering from a metallic cylinder is simulated. All simulation results are compared with measurement results. The measurements for the acoustic wave scattering from the metallic cylinder are made in 2D planes using an automated measurement system. Comparison between the simulation and measurement results are made both temporally and spatially and a good agreement between the simulation and measurement results is found. The results suggest that the discontinuous Galerkin method coupled with the low-storage Runge–Kutta approach is a viable tool for modeling acoustic wave propagation in the time-domain.     

Reducing measurement time for a laser Doppler vibrometer using regressive techniques

In the last decade the laser Doppler vibrometer (LDV) has become a widely spread instrument for measuring vibrations. It often offers accurate measurements with a high spatial resolution. However, the measurement time of the LDV and especially for the scanning LDV is long. Therefore, reducing the measurement time is an attractive objective. A way to achieve this is to use a single sine excitation (on a resonance frequency). However, this technique has two major drawbacks: the inability to provide information on the damping and a operational deflection shape that can differ from the true mode shape. In this article two methods will be introduced to reduce measurement time without these defaults. In the first method introduced in this article a narrow band multisine is used as excitation signal and the measured vibration signal in the time domain is represented by a model using sines and cosines with these fixed narrow band frequencies. The coefficients of those sines and cosines are then estimated on a global scale by means of a least-squares estimator. An important advantage of this particular technique is that one does not have to measure a full period of the signal, reducing time. The second method accelerates the measurement time for scanning LDV measurements. Using the time domain sequence from each previous scan point and a limited number of time samples from the current scan point, the full time domain sequence of the current scan point can be estimated. Both these methods are a key benefit for in-line quality control, which can have upwards of 1000 spatial measurement locations. The proposed techniques will be validated on both simulations and experiments of varying complexity.     

A leap-frog discontinuous Galerkin time-domain method of analyzing electromagnetic scattering problems

Several major challenges need to be faced for efficient transient multiscale electromagnetic simulations, such as flexible and robust geometric modeling schemes, efficient and stable time-stepping algorithms, etc. Fortunately, because of the versatile choices of spatial discretization and temporal integration, a discontinuous Galerkin time-domain(DGTD) method can be a very promising method of solving transient multiscale electromagnetic problems. In this paper, we present the application of a leap-frog DGTD method to the analyzing of the multiscale electromagnetic scattering problems. The uniaxial perfect matching layer(UPML) truncation of the computational domain is discussed and formulated in the leap-frog DGTD context. Numerical validations are performed in the challenging test cases demonstrating the accuracy and effectiveness of the method in solving transient multiscale electromagnetic problems compared with those of other numerical methods.     

Nonlinear response of shear deformable beams on tensionless nonlinear viscoelastic foundation under moving loads

In this paper, a boundary element method is developed for the geometrically nonlinear response of shear deformable beams of simply or multiply connected constant cross-section, traversed by moving loads, resting on tensionless nonlinear three-parameter viscoelastic foundation, undergoing moderate large deflections under general boundary conditions. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse moving loading as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Three boundary value problems are formulated with respect to the transverse displacement, to the axial displacement and to a stress functions and solved using the Analog Equation Method, a Boundary Element based method. Application of the boundary element technique yields a system of nonlinear Differential-Algebraic Equations, which is solved using an efficient time discretization scheme, from which the transverse and axial displacements are computed. The evaluation of the shear deformation coefficient is accomplished from the aforementioned stress function using only boundary integration. Analyses are performed to illustrate, wherever possible, the accuracy of the developed method, to investigate the effects of various parameters, such as the load velocity, load frequency, shear deformation, foundation nonlinearity, damping, on the beam displacements and stress resultants and to examine how the consideration of shear and axial compression affects the response of the system.     

An explicit time-domain finite element method for room acoustics simulations: Comparison of the performance with implicit methods

This paper presents the applicability of an explicit time-domain finite element method (TD-FEM) using a dispersion reduction technique called modified integration rules (MIR) on room acoustics simulations with a frequency-independent finite impedance boundary. First, a dispersion error analysis and a stability analysis are performed to derive the dispersion relation and the stability condition of the present explicit TD-FEM for three-dimensional room acoustics simulations with an infinite impedance boundary. Secondly, the accuracy and efficiency of the explicit TD-FEM are presented by comparing with implicit TD-FEM using MIR through room acoustics simulations in a rectangular room with infinite impedance boundaries. Thirdly, the stability condition of the explicit TD-FEM is investigated numerically in the case with finite impedance boundaries. Finally, the performance of the explicit TD-FEM in room acoustics simulations with finite impedance boundaries is demonstrated in a comparison with the implicit TD-FEM. Although the stability of the present explicit TD-FEM is dependent on the impedance values given at boundaries, the explicit TD-FEM is computationally more efficient than the implicit method from the perspective of computational time for acoustics simulations of a room with larger impedance values at boundaries.     

基于层流动能湍流模型的数值模拟方法

从层流动能出发提出数值模拟原则;综合考虑自然、旁路和分离流转捩的因素构建实用的层流动能湍流模型,结合预处理和基本求解技术发展出适于转捩流动的数值模拟方法和程序.针对预处理技术,以Weiss-Smith矩阵为基础,考虑湍流粘性的影响;针对基本离散格式和边界条件,结合模型方程进行对角占优强化等特殊处理.最后通过平板边界层和典型翼型,特别是低雷诺数翼型的数值模拟,验证数值方法的有效性和鲁棒性.算例表明本文的方法能够为求解更复杂的流动提供参考.     

A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x-and y-axis directions are obtained with a phaseshifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.