Investigation of area mobility of a finite thin plate subject to a uniform velocity excitation

Methods for theoretically calculating area mobility of a finite thin plate are derived for a typical excitation pattern,uniform velocity excitation,over a contact area.In the derivation,the contact area is discretised into sub-regions and the excitation and response continuously distributed over these sub-regions are simplified as acting at the centers of the sub-regions.Therefore,according to the concept of effective point mobility,the theoretical formula for area mobility of a finite thin plate subject to a uniform velocity excitation is obtained.According to the relation between complex power and area mobility,the measurement method of a finite plate is also obtained by means of transfer point mobility.When comparing results generated by theoretical calculation to patterns measured in experiment,consistent patterns are found,suggesting that the proposed methods are practical.The results of calculation show that the accuracy of theoretical calculation increases with the number of sub-regions and is influenced by the moment caused by the experiment device,especially when the excitation frequency is high.     

Error due to two-force excitation in moment mobility measurement

In direct moment mobility measurement, one difficulty is the moment excitation. Two-force configuration excitation is widely used to generate moment in practice. Previous error analysis mainly focused on the initial load of exciters, the matching of the two forces, and the system resonance. In this paper, the distance requirement of two-force configuration in moment excitation is investigated. Based on the numerical calculation, other factors that affect the error in moment mobility measurement are discussed. The influence of the deduced distance requirement on moment mobility measurement is also explained.     

受均布速度作用的有限板面导纳研究

针对接触面积上典型的激励形式,均布速度激励,推导有限薄板上面导纳的理论计算方法。在推导过程中,将接触面积离散为较小的子面积,连续分布的激励和响应简化为作用在子面积中心的激励和响应,再利用有效点导纳的定义,获得有限薄板受均布速度激励的面导纳的理论计算公式;根据接触面积上复功率与面导纳的关系,推导出由传递点导纳获得有限板面导纳的测量方法。通过比较理论计算结果和实验测量结果,证明两种方法可行。对计算结果进行的分析还表明,子面积数的增加可以提高理论计算的精度,而测量精度在激励频率较高时受测量装置产生的弯矩影响较大。      

The measurement of structural mobilities of a circular cylindrical shell

Structural mobility is useful for the estimation of structural power flows in coupled systems. Although the methods of measuring structural mobilities are easily found for one-dimensional beam structures, few are available for cylindrical shells. In this paper, a new method is proposed for the measurement of the structural mobilities of a circular cylindrical shell. A point force excitation is used instead of circumferential modal forces which are difficult to implement in practice. This method utilizes the least squares technique to obtain the transfer function components of different circumferential modes from the measured data. Experiments were carried out on a circular cylindrical shell with different end conditions excited by a point force to verify the feasibility of this proposed method.     

Direct measurement of moment mobility and a moment excitation system

Over the years, a number of investigators have tried to solve the problems in the direct measurement of moment mobility. However, no one has found a moment excitation system that can produce a pure and sufficiently powerful moment. In the past, most investigators tried to solve the problem of impurity in moment by tackling the problem in unmatched shakers in a moment exciter. Su and Gibbs (Su J, Gibbs BM. Measurement of point moment mobility in the presence of non-zero cross mobility. Applied Acoustics 1998;54(1):9-26) have indicated theoretically that compromise between the purity and the power of a moment generated by the moment exciter is greatly affected by the output force impedance of the moment excitation system. In this paper, experiments have been conducted to investigate the effect of output force impedance on direct measurement of moment mobility from which theory of Su and Gibbs has been verified. Methods of improvements of the moment exciter have been proposed in order that the moment exciter can generate a pure and sufficiently powerful moment.     

Swept sine testing of rotor-bearing system for damping estimation

Many types of rotating components commonly operate above the first or second critical speed and they are subjected to run-ups and shutdowns frequently. The present study focuses on developing FRF of rotor bearing systems for damping estimation from swept-sine excitation. The principle of active vibration control states that with increase in angular acceleration, the amplitude of vibration due to unbalance will reduce and the FRF envelope will shift towards the right (or higher frequency). The frequency response function (FRF) estimated by tracking filters or Co-Quad analyzers was proved to induce an error into the FRF estimate. Using Fast Fourier Transform (FFT) algorithm and stationary wavelet transform (SWT) decomposition FRF distortion can be reduced. To obtain a theoretical clarity, the shifting of FRF envelope phenomenon is incorporated into conventional FRF expressions and validation is performed with the FRF estimated using the Fourier Transform approach. The half-power bandwidth method is employed to extract damping ratios from the FRF estimates. While deriving half-power points for both types of responses (acceleration and displacement), damping ratio (ζ) is estimated with different approximations like classical definition (neglecting damping ratio of order higher than 2), third order (neglecting damping ratios with order higher than 4) and exact (no assumptions on damping ratio). The use of stationary wavelet transform to denoise the noise corrupted FRF data is explained. Finally, experiments are performed on a test rotor excited with different sweep rates to estimate the damping ratio.     

A new iterative model updating method using incomplete frequency response function data

A new iterative model updating method is proposed for reduced model using incomplete frequency response function (FRF) data. It uses a modified difference vector between the analytical and experimental FRF data to construct a linear sensitivity updating equation system. To improve the convergence performance of the proposed algorithm, a concept of pseudo master degree-of-freedom (DOF) is put forward and the finite element (FE) model is reduced to the measured and user selected pseudo DOFs. The FRFs at pseudo master DOFs are estimated using the impedance matrix of iteratively modified analytical model and the measured FRFs at master DOFs. They are only used to improve the sensitivity matrix and difference calculation between the analytical and experimental FRF data without introducing additional difference equation. At the end, a 25 truss structure is used to evaluate the performance of the proposed method.     

Atomistic simulation of slow grain boundary motion

Existing atomistic simulation techniques to study grain boundary motion are usually limited to either high velocities or temperatures and are difficult to compare to realistic experimental conditions. Here we introduce an adapted simulation method that can access boundary velocities in the experimental range and extract mobilities in the zero driving force limit at temperatures as low as ～0.2T(m) (T(m) is the melting point). The method reveals three mechanistic regimes of boundary mobility at zero net velocity depending on the system temperature.     

THE ENERGY MOBILITY

The energy mobility method is presented and applied both numerically and experimentally to thin plates of high modal density. The energy mobility is defined as the ratio of the frequency averaged quadratic velocity at one point of a structure to the frequency averaged active power injected at one point of the structure. It can be calculated using only classic input and transfer mobilities. The property of energy additivity of the contributions of several external loads is shown to be a good approximation in the case of a single structure. To quantify the approximations on typical structures one is interested in, numerical simulations are presented on plates. A good agreement is found between the predictions using the energy mobility and the exact calculations. An experiment conducted on a plate with a real excitation confirms that the prediction of the energy mobility approach can be quite satisfactory. Finally, a remarkable property for the energy mobility (contrary to standard mobility) is noted: the insensitivity to the presence of a mass heterogeneity at driving points. This property allows one to simplify considerably the characterization of industrial structures that have in general a lot of heterogeneities. The energy mobility concept is further applied to the vibrational behaviour of an assembly. For each subsystem the connection is described by adding injected power and coupling power into the energy additivity. The equality of the frequency averaged quadratic velocity and the power flow balance at each coupling point allows one to calculate the coupling power at connection points with energy mobilities of uncoupled subsystems. A system of two plates has been used to compare the energy mobility calculation and the exact one given by the classic mobility method. The comparison shows that a connectivity factor must be introduced to keep the same formalism generally used with classic mobilities. A generalized definition for the energy mobility is then established.     

Flow-induced oscillations of a cantilevered pipe conveying fluid with base excitation

It is known that a plain cantilevered pipe conveying fluid loses its stability by a Hopf bifurcation, leading to either planar or non-planar flutter for flow velocities beyond the critical flow velocity for Hopf bifurcation. If an external mass is attached to the end of the pipe (an end-mass), the resulting dynamics become much richer, showing 2D and 3D quasiperiodic and chaotic oscillations at high flow velocities. In this paper, a cantilevered pipe, with and without an end-mass, subjected to a small-amplitude periodic base excitation is considered. A set of three-dimensional nonlinear equations is used to analyze the pipe?s response at various flow velocities and with different amplitudes and frequencies of base excitation. The nonlinear equations are discretized using the Galerkin technique and the resulting set of equations is solved using Houbolt?s finite difference method. It is shown that for a plain pipe (with no end-mass), non-planar post-instability oscillations can be reduced to planar periodic oscillations for a range of base excitation frequencies and amplitudes. For a pipe with an end-mass, similarly to a plain pipe, three-dimensional period oscillations can be reduced to planar ones. At flow velocities beyond the critical flow velocity for torus instability, the three-dimensional quasiperiodic oscillations can be reduced to two-dimensional quasiperiodic or periodic oscillations, depending on the frequency of base excitation. In all these cases, a low-amplitude base excitation results in reducing the three-dimensional oscillations of the pipe to purely two-dimensional oscillations, over a range of excitation frequencies. These numerical results are in agreement with the previous experimental work.     

Acoustic anisotropy and birefringence in fibre-reinforced composite materials

All nine elastic moduli of an orthotropic composite material, namely, polypropylene reinforced with glass fiber, are determined from the measured values of the bulk acoustic wave velocities along specific directions in the planes of symmetry of the material. These data are used to calculate the angular dependences of phase velocities, polarization vectors, and directions of ray velocities of bulk waves in the composite. It is demonstrated that the difference in the velocities of shear waves polarized along and across the glass fiber gives rise to an acoustic birefringence and can lead to an elliptical polarization of waves. The measurement of the phase velocities of shear waves as functions of the wave polarization is suggested as a method for the determination of the fiber orientation in a composite material.     

Vibration testing based on impulse response excited by laser ablation

This paper proposes an innovative vibration testing method based on impulse response excited by laser ablation. In conventional vibration testing using an impulse hammer, high-frequency elements of over tens of kilohertz are barely present in the excitation force. A pulsed high-power YAG laser is used in this study for producing an ideal impulse force on a structural surface. Illuminating a point on a metal with the well-focused YAG laser, laser ablation is caused by generation of plasma on the metal. As a result, an ideal impulse excitation force generated by laser ablation is applied to the point on the structure. Therefore, it is possible to measure high-frequency FRFs due to the laser excitation. A water droplet overlay on the metal is used to adjust the force magnitude of laser excitation. An aluminum block that has nine natural frequencies below 40 kHz is employed as a test piece. The validity of the proposed method is verified by comparing the FRFs of the block obtained by the laser excitation, impulse hammer, and finite element analysis. Furthermore, the relationship between accuracy of FRF measurements and sensitivity of sensors is investigated.     

Visualization of three-dimensional temperature distributions in a large-scale furnace via regularized reconstruction from radiative energy images: numerical studies

In this paper, the possibility of visualization of three-dimensional (3-D) temperature distributions in large-scale boiler furnaces from radiative energy images captured by multiple charge-coupled device (CCD) cameras mounted around the furnace is studied numerically. For the calculation of the radiative energy image formation, a fast algorithm proposed by the authors for pinhole imaging is used in this paper, which is based on the Monte Carlo method and combined with a concept of angular factor effective for image formation. This algorithm is applicable for the emitting, absorbing, and isotropic scattering medium. For the inversion of the 3-D temperature distributions which is an ill-posed problem, a modified Tikhonov regularization method is improved, where the finite difference regularizer is defined and can be used in 3-D cases, and the optimal regularization parameter is suggested to be selected by using a post-treatment method. For a 3-D unimodal temperature distribution, the numerical simulation results show that the reconstruction errors for the 3-D temperature distribution can be maintained at levels similar to the measurement error and the visualization quality of the temperature distribution is satisfactory. For a kind of bimodal temperature distribution, the reconstruction errors are higher than those for the unimodal distribution, but the bimodal feature of the temperature distribution can also be reproduced clearly.     

Three bias errors in the measurement of structural intensity

I.IntroductionTheabilityofstructuralintensitytechniquetomeasureboththemagnitudeanddirectionofpowerflowmakesitanattractivetechniqueforinvestigatingawidevarietyofstructures.However,intensitymeasurementtechniqueispronetoerrors.Theseerrorsdependonthepropertiesofthestructurebeingmeasured,thetypeofwavespresefltedonthestructureandtheinstrumentationusedtomeasuretheintensity.Theerrorscanbeclassifiedasrandomerrorsandbiaserrors.Randomerrorscannotbecalculatedexactlyinanycasesandcouldresultinoverorunderes…     

球几何中子输运保正线性间断有限元格式

针对球几何中子输运方程线性间断有限元方法计算的负中子通量问题,构造了保正线性间断有限元格式,该格式保持中子角通量0阶矩和1阶矩。现有方法计算中子角通量非负时,采用传统的线性间断有限元方法,求解线性方程组;原方法计算出现负通量,则采用构造的保正格式,求解非线性方程组。编制了球几何中子输运问题保正格式程序模块,并集成到应用程序。数值算例表明构造的保正格式计算的中子通量非负,有效降低数值误差,提高数值计算的精度。     

模拟大气风场及其数据处理技术的研究

热层大气风速的测量可以采用干涉法来进行,由于光源（气辉辐射谱线）的强度很弱,故干涉法对测量系统要求很高。利用半导体激光器（LD）的调制特性和法布里-帕罗干涉仪(FPI)的高光谱分辨能力设计了一种用简单设备进行大气风场模拟与测量的方法。改变LD的驱动电流使其输出激光频率改变,从而模拟气辉辐射的多普勒频移,通过分析FPI获得的干涉图可检测出该频移,进而得到等效风速。模拟风速的相对误差不超过6.5%,最小模拟风速为20.01m/s,且测量结果与LD的线性调制特性很相符。使用该方法可以有效地对多普勒风速测量原理、数据处理方法、系统性能以及测量误差进行分析和评估。     

基于CT序列图像的旋转体积测量方法

针对工程应用中常见的轴向变化剧烈工件,研究一种Zernike矩亚像素层间拟合轮廓旋转积分的高精度体积测量算法。首先用Zernike矩方法提取亚像素级轮廓,其次采用多项式拟合切片轮廓,并进行等相角间隔采样;然后对等相位的轮廓点采用多项式拟合并通过外插法自动预测工件顶端,将各拟合轮廓旋转一个相角,对旋转块积分并累加得到待测工件的体积。分别对体积相等的3个试块进行CT扫描测量实验,结果表明该算法的测量误差低于0.7%;对实际含内腔工件进行测量实验,结果表明该算法测量精度是Canny台体法的1.5倍。     

Excitation and propagation of non-axisymmetric guided waves in a hollow cylinder

Excitation and propagation of non-axisymmetric guided waves in a hollow cylinder is studied by using the normal mode expansion method (NME). Different sources such as angle beam, tube end excitation with normal beam, and comb transducer possibilities are discussed based on the derivations of the NME method. Numerical calculations are focused on the case of angle beam partial loading. Based on the NME method, the amplitude coefficients for all of the harmonic modes are obtained. Due to the difference of phase velocities for different modes, the superimposed total field varies with propagating distances and hence makes particle displacement distribution patterns (angular profile) change with distance. This varying non-axisymmetric angular profile of guided waves represents a nonuniform energy distribution around the hollow cylinder and thus has an impact on the inspection ability of guided waves. The angular profiles of an angle beam source are predicted by theory and then verified by experiments. The predicted angular profiles also provide information for determining the transducer location to find defects in a certain position on the hollow cylinder.