CRACK IDENTIFICATION IN VIBRATING BEAMS USING THE ENERGY METHOD

An energy-based numerical model is developed to investigate the influence of cracks on structural dynamic characteristics during the vibration of a beam with open crack(s). Upon the determination of strain energy in the cracked beam, the equivalent bending stiffness over the beam length is computed. The cracked beam is then taken as a continuous system with varying moment of intertia, and equations of transverse vibration are obtained for a rectangular beam containing one or two cracks. Galerkin's method is applied to solve for the frequencies and vibration modes. To identify the crack, the frequency contours with respect to crack depth and location are defined and plotted. The intersection of contours from different modes could be used to identify the crack location and depth.     

MODELLING OF TRANSVERSE VIBRATION OF SHORT BEAMS FOR CRACK DETECTION AND MEASUREMENT OF CRACK EXTENSION

The method of detection of location of crack in beams based on frequency measurements is extended here to short beams, taking into account the effects of shear deformation and rotational inertia through the Timoshenko beam theory and representing the crack by a rotational spring. Methods for solving both forward (determination of frequencies of beams knowing the crack parameters) and inverse (determination of crack location knowing the natural frequencies) problems are included. A method to estimate crack extension from a change in the first natural frequency is presented. Both numerical and experimental studies are given to demonstrate the accuracy of the methods. The accuracy of the results is quite encouraging.     

Model for continuously scanning ultrasound vibrometer sensing displacements of randomly rough vibrating surfaces

An analytic model is developed for the time-dependent ultrasound field reflected off a randomly rough vibrating surface for a continuously scanning ultrasound vibrometer system in bistatic configuration. Kirchhoff's approximation to Green's theorem is applied to model the three-dimensional scattering interaction of the ultrasound wave field with the vibrating rough surface. The model incorporates the beam patterns of both the transmitting and receiving ultrasound transducers and the statistical properties of the rough surface. Two methods are applied to the ultrasound system for estimating displacement and velocity amplitudes of an oscillating surface: incoherent Doppler shift spectra and coherent interferometry. Motion of the vibrometer over the randomly rough surface leads to time-dependent scattering noise that causes a randomization of the received signal spectrum. Simulations with the model indicate that surface displacement and velocity estimation are highly dependent upon the scan velocity and projected wavelength of the ultrasound vibrometer relative to the roughness height standard deviation and correlation length scales of the rough surface. The model is applied to determine limiting scan speeds for ultrasound vibrometer measuring ground displacements arising from acoustic or seismic excitation to be used in acoustic landmine confirmation sensing.     

激光诱导等离子体的气体动力学和燃烧波扩展速度研究

针对激光对熔石英材料产生致燃损伤过程中存在的激光支持燃烧波,考虑激光作用的温度残余、目标形貌的改变、喷溅物质分布、目标表面气流状况的分布等效应,分阶段对激光支持燃烧波的过程进行建模和仿真研究.通过建立二维轴对称气体动力学模型,模拟研究包含逆韧致辐射、热辐射、热传导和对流过程在内的激光能量传输过程.此外,依据激光支持燃烧波在可见光波段具有明显的辐射特征这一特点,利用阴影法测量了激光对熔石英致燃损伤过程中的燃烧波扩展速度,得到了燃烧波演化过程图像.研究结果表明:在平行激光束作用下,燃烧波的传播是稳态的,气体动力学行为比较稳定;在聚焦激光束作用下,燃烧波的传播是非稳态的.模拟结果中得到的激光支持燃烧波扩展速度及气体动力学结构与实验结果和理论推导结果符合得很好,验证了理论模型的正确性.     

Ultrasonic sizing of short surface cracks

This paper presents a method for ultrasonic sizing of surface cracks based on time domain and frequency domain Rayleigh wave near-field analysis. The procedure allows for the entire range of ratio of crack depth to Rayleigh wavelength a/λ to be covered with one single measurement. In the time domain the time-of-flight method was extended to cracks smaller than the wavelength by correlation of the time delay of the transmitted Rayleigh wave with the crack depth. In the frequency domain, the inverse scattering problem was solved by comparison of the measured scattering coefficients and central frequencies of the reflected and transmitted Rayleigh waves with theoretical curves. The sizing procedure was demonstrated experimentally with narrow slots and real fatigue cracks. The out-of-plane displacement component was measured pointwise in the scattered near field by means of laser interferometry. The determination of the scattering parameters in the near field was enabled by a procedure that allows for the Rayleigh wave to be separated from the other modes scattered at the defect. The experimental results showed good accuracy and repeatability down to the smallest available ratio of crack depth to Rayleigh wavelength a/λ = 0.15.     

Ultrasonic surface crack characterization on complex geometries using surface waves

The characterization of surface cracks on complex geometries using surface waves is investigated numerically and experimentally. The specimen geometry is implemented in a finite difference code by approximation of the contour using a Cartesian grid. In the experiments the out-of-plane surface displacement is measured by means of a heterodyne laser interferometer. Good agreement is shown by comparison of the calculated out-of-plane displacement with experimental results for both cracked and non-cracked specimens. The crack depth is measured down to a size of 0.7 times the surface wavelength using a time delay approach. The many Rayleigh pulses propagating after the crack can be separated from the other modes by a filtering procedure based on the surface wave propagation velocity. Only a detailed analysis of the scattering phenomenon using the simulation allows an identification of the transmitted pulse required for crack depth measurement. Application of the method to a specimen with a real fatigue crack shows a systematical error possibly due to the inclined crack profile.     

The dynamic analysis of a cracked Timoshenko beam by the spectral element method

The aim of this paper is to introduce a new finite spectral element of a cracked Timoshenko beam for modal and elastic wave propagation analysis. The proposed approach deals with the spectral element method. This method is suitable for analyzing wave propagation problems as well as for calculating modal parameters of the structure. In the paper, the results of the change in modal parameters due to crack appearance are presented. The influence of the crack parameters, especially of the changing location of the crack, on the wave propagation is examined. Responses obtained at different points of the beam are presented. Proper analysis of these responses allows one to indicate the crack location in a very precise way. This fact is very promising for the future work in the damage detection field.     

原子光刻中驻波场与基片距离的判定方法研究

原子光刻实验中, 激光驻波场能起到原子透镜的效果, 实现原子汇聚. 激光驻波场与沉积基片间的距离对形成纳米条纹结构的质量具有重要影响. 利用高斯光束传播规律, 提出了一种能够定量判断激光驻波场与沉积基片相对位置的实验方法. 该方法通过调节装载有凸透镜和反射镜的精密位移台改变驻波场距基片的距离, 利用光电探测器接收反射光强的变化, 将位移改变量转变为接收器的电压信号. 利用驻波场激光束光斑直径值, 实现准确定位驻波场与基片的距离. 对上述实验过程进行数值模拟, 数值计算的结果和实验结果高度符合. 该方法实现了准确定位驻波场距基片的距离, 为后续深入研究驻波场和基片间距离对沉积纳米条纹结构质量的影响提供实验基础.     

Detecting damage in vibrating structures with a scanning LDV

It has been demonstrated, through experiments on laboratory-scale structures, that structural defects such as cracks can be detected and located using a continuously scanning laser Doppler vibrometer (LDV) if vibration sufficient to flex the defect can be induced and if the defects are such as to produce localised mode shape discontinuities. This paper describes such a method of defect detection using a short linear scan at the crack location. Through-cracks are easily detected in thin metal plates whereas narrow slots in a solid cantilever beam have no easily identifiable effect unless they extend more than half-way through the thickness. Cracks in a reinforced-concrete beam introduced marked and identifiable discontinuities in mode shapes. Speckle noise affects the measurements, sometimes seriously. A simple low-pass filter may improve the signal quality.     

Beam profile measurements and simulations for ultrasonic transducers operating in air

This paper outlines a method that has been implemented to predict and measure the acoustic radiation generated by ultrasonic transducers operating into air in continuous wave mode. Commencing with both arbitrary surface displacement data and radiating aperture, the transmitted pressure beam profile is obtained and includes simulation of propagation channel attenuation and where necessary, the directional response of any ultrasonic receiver. The surface displacement data may be derived directly, from laser measurement of the vibrating surface, or indirectly, from finite element modeling of the transducer configuration. To validate the approach and to provide experimental measurement of transducer beam profiles, a vibration-free, draft-proof scanning system that has been installed within an environmentally controlled laboratory is described. A comparison of experimental and simulated results for piezoelectric composite, piezoelectric polymer, and electrostatic transducers is then presented to demonstrate some quite different airborne ultrasonic beam-profile characteristics. Good agreement between theory and experiment is obtained. The results are compared with those expected from a classical aperture diffraction approach and the reasons for any significant differences are explained.     

Medium characterization from interface-wave impedance and ellipticity using simultaneous displacement and pressure measurements

The interface-wave impedance and ellipticity are wave attributes that interrelate the full waveforms as observed in different components. For each of the fluid/elastic-solid interface waves, i.e., the pseudo-Rayleigh (pR) and Stoneley (St) waves, the impedance and ellipticity are found to have different functional dependencies on Young's modulus and Poisson's ratio. By combining the attributes in a cost function, unique and stable estimates of these parameters can be obtained, particularly when using the St wave. In a validation experiment, the impedance of the laser-excited pR wave is successfully extracted from simultaneous measurements of the normal particle displacement and the fluid pressure at a water/aluminum interface. The displacement is measured using a laser Doppler vibrometer (LDV) and the pressure with a needle hydrophone. Any LDV measurement is perturbed by refractive-index changes along the LDV beam once acoustic waves interfere with the beam. Using a model that accounts for these perturbations, an impedance decrease of 28% with respect to the plane wave impedance of the pR wave is predicted for the water/aluminum configuration. Although this deviation is different for the experimentally extracted impedance, there is excellent agreement between the observed and predicted pR waveforms in both the particle displacement and fluid pressure.     

Experimental and numerical investigation on structural effects of laser pulses for modal parameter measurement

In this paper it has been described part of the research devoted to the development of a complete non-intrusive experimental modal analysis procedure based on laser techniques both for excitation and for measurement. In particular, attention has been focused on the thermal effects generated by laser pulses on the excited structure. An analytical model of the energy exchange between the light pulse and the target surface is proposed together with a finite element model of thermal and mechanical behaviour of the structure under excitation. Both the models (analytical and numerical) have been experimentally validated by measuring the thermal and the vibration responses induced by the laser pulses. The experimental part of the study has been performed on a cantilever beam excited with laser pulses from an Nd : YAG source (532 nm, 100 mJ/pulse) using an high-speed infrared camera and a scanning laser Doppler vibrometer. Results from this work can be used to improve understanding concerning the features of laser excitation and to establish a mechanical equivalent system of forces and moments, useful in order to increase the accuracy in the measurements of modal parameters when laser pulses are used as excitation sources.     

顶爆和拱腰侧爆同时作用下锚固洞室的动态响应

基于相似模型试验,采用显式非线性动力分析程序LS-DYNA3D研究了地下锚固洞室在拱顶和拱腰侧两处集中装药爆源同时爆炸作用下应力波传播规律、裂纹形成机理以及洞壁围岩位移分布特征。通过对比分析顶爆试验和计算模型的压应力时程曲线,发现模拟与试验结果吻合,且符合应力波的传播规律,表明数值模拟结果可靠。爆源爆炸后,应力波以圆形向周围岩体传播,两应力波相遇处压应力强度明显大于周围岩体;当应力波传到自由面时,会反射形成拉伸波,在地表下方和洞室上方发生“层裂”现象,在拱顶和拱腰侧爆源中间沿洞室径向有裂纹延伸,由于拉伸波的叠加,在爆源下方出现“八”字形的锥形裂纹面。锚杆能够起到加固岩体的作用,锚固洞室比毛洞裂纹分布少,毛洞迎爆侧裂纹主要为横向裂纹,而锚固洞室则为径向劈裂和横向裂纹。两爆源中点洞室径向处的洞壁围岩位移峰值最大,极易产生破坏。     

Crack identification using evolutionary algorithms in parallel computing environment

It is well known that a crack has an important effect on the dynamic behavior of a structure. This effect depends mainly on the location and depth of the crack. To identify the location and depth of a crack in a structure, classical optimization technique was adopted by previous researchers. That technique overcame the difficulty of finding the intersection point of the superposed contours that correspond to the eigenfrequency caused by the crack presence. However, it is hard to select the trial solution initially for optimization because the defined objective function has heavily local minima. A method is presented in this paper which uses a continuous evolutionary algorithm (CEA), which is suitable for solving inverse problems and implemented on PC clusters to shorten calculation time. With finite element model of the structure to calculate eigenfrequencies, it is possible to formulate the inverse problem in optimization format. CEAs are used to identify the crack location and depth minimizing the difference from the measured frequencies. We have tried this new idea on beam structures and the results are promising with high parallel efficiency over about 91%.     

Scattering of obliquely incident shear waves from a cylindrical cavity

Prior work has proposed the use of ultrasonic angle-beam shear wave techniques to detect cracks of varying angular location around fastener sites by generating and detecting creeping waves. To better understand the nature of the scattering problem and quantify the role of creeping waves in fastener site inspections, a 3D analytical model was developed for the propagation and scattering of an obliquely incident plane shear wave from a cylindrical cavity with arbitrary shear wave polarization. The generation and decay of the spiral creeping waves was found to be dependent on both the angle of incidence and polarization of the plane shear wave. A difference between the angle of displacement in 3D and the direction of propagation for the spiral creeping wave was observed and attributed to differences in the curvature of the cavity surface for the tangential and vertical (z) directions. Using the model, practical insight was presented on measuring the displacement response in the far-field from the hole. Both analytical and experimental results highlighted the value of the diffracted and leaky spiral creeping wave signals for nondestructive evaluation of a crack located on the cavity. Last, array and signal processing methods are discussed to improve the resolution of the weaker creeping wave signals in the presence of noise.     

Two-axis-scanning laser Doppler vibrometer for precision engineering

Laser Doppler vibrometer (LVD) has been the most favorite instrument for precision dynamics measurement due to its non-contact, high accuracy and high resolution. However, LDV can only give the dynamic data of a particular location on the entire feature. In order to get the whole field data, a laser beam-scanning mechanism has to be implemented. Currently, motor-driven scanning mirror is used to move the measurement probe from one point to another. The mechanical vibrations of the scanning mirror will reduce the measurement accuracy. This paper introduces a novel scanning LDV optical system embodied in an acousto-optic deflector scanning mechanism. It can improve the measurement accuracy since there is no mechanical motion involved. One main advantage of this system is that it generates a laser scanning beam in parallel that is different from the beam scanning in the conventional scanning laser Doppler vibrometer (SLDV). The new system has a board scanning range. The measurement target size ranges from few tens of millimeters down to 10 μm. We have demonstrated the capability of the novel system on scanning measurements of features as big as ultra-precision cutting tool to features as tiny as AFM cantilever. We believe that the novel SLDV will find profound potential applications in the precision engineering field.     

Temperature and frequency dependence of the visco-elasticity of a poro-elastic layer

Besides their structural complexity, the acoustic behavior of polymer-based poro-elastic layers is complicated also due to their frequency dependent elasticity. In this work, we address the frequency and temperature dependence of the elastic behavior in general, and the shear modulus in particular, of poro-visco-elastic materials. The analysis is based on the monitoring of mechanically excited guided acoustic wave propagation by means of a laser Doppler vibrometer scanning technique. The concept and practical implementation of the experimental method are presented, as well as the signal processing procedure and data analysis. Experimental data are presented for a polyurethane foam. The observed visco-elastic behavior, complemented with dielectric spectroscopy data, is interpreted in the framework of two underlying relaxation processes.     

Modelling of the solid–liquid interface during laser processing using an inverse methodology

This study presents a methodology for estimating the melt depth during laser processing of solid materials. The determination of the melt depth is treated as an inverse heat conduction problem, which includes the solid and liquid phases. The conjugate gradient method is applied to treat the inverse problem using the available temperature measurements. Without the inverse methodology the melt depth is very difficult to obtain with precision. The proposed method can also be applied during microthermal machining to determine the location of the solid–liquid interface and the temperature distributions of the two phases by using scanning thermal microscopy.     

Acoustic field excited by a pulsed laser line source in a cylinder

The excitation and propagation of the acoustic waves in an elastic cylinder are studied by laser ultrasonics both theoretically and experimentally. The theoretical analysis of the two-dimensional acoustic field excited by a pulsed laser line source impacting on the generatrix of an elastic cylinder is presented. The dispersive properties for both cylindrical Rayleigh wave and the higher modes--whispering gallery (WG) modes are analyzed in detail. The numerical transient displacement waveforms for a detecting point located another terminal of the cylinder diameter opposite the source are calculated. The experimental excitation and detection of the acoustic waves in an aluminum cylinder are carried out on a laser ultrasonic system, which mainly consists of a Q-switched Nd:YAG laser and a laser interferometer. The wave components of bulk waves and surface waves (cylindrical Rayleigh waves and WG modes) are analyzed by comparing the numerical and experimental waveforms. The results are in good agreement.     

Proton induced thermal stress-wave measurements using a Laser Doppler Vibrometer

Thermal stress-waves are generated in the solid target material when the proton beam interacts. These stress waves excite natural oscillations of the target or cause plastic deformations. Hence, an experimental setup with a laser Doppler vibrometer [CITE] was developed to investigate free surface vibrations of cylindrical targets. The target configurations for RIB and conventional neutrino beams (CNGS project) were investigated to analyze proton induced thermal stress-wave generation and propagation.