Vibration frequency of a curved beam with tip mass

In flexible blade auto cooling fans, the first vibration frequency is of fundamental importance. These fan blades are usually curved and have a tip mass in the form of a strip along one edge. For the first frequence, the blade can be modelled as a curved beam with a tip mass. This paper reports on an investigation of the vibration frequency of a curved beam with a tip mass, in which both theoretical finite element and experimental methods were used. In the finite element methods, both the normal and tangential displacements are approximated by cubic polynomials to ensure that rigid body displacements are closely represented. The effect of the tip mass is incorporated into the mass matrix. The results show that the curvature has a slight effect on the first mode natural frequencies but has great influence on the higher frequencies, and that the coupling effect between the tip mass and the curvature is insignificant.     

Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique

A hybrid finite element–boundary integral–characteristic basis function method (FE-BI-CBFM) is proposed for an efficient simulation of electromagnetic scattering by random discrete particles. Specifically, the finite element method (FEM) is used to obtain the solution of the vector wave equation inside each particle and the boundary integral equation (BIE) using Green's functions is applied on the surfaces of all the particles as a global boundary condition. The coupling system of equations is solved by employing the characteristic basis function method (CBFM) based on the use of macro-basis functions constructed according to the Foldy–Lax multiple scattering equations. Due to the flexibility of FEM, the proposed hybrid technique can easily deal with the problems of multiple scattering by randomly distributed inhomogeneous particles that are often beyond the scope of traditional numerical methods. Some numerical examples are presented to demonstrate the validity and capability of the proposed method.     

Modal flexibility-based damage detection of cantilever beam-type structures using baseline modification

This paper presents a new damage detection approach for cantilever beam-type structures using the damage-induced inter-storey deflection (DIID) estimated by modal flexibility matrix. This approach can be utilized for damage detection of cantilever beam-type structures such as super high-rise buildings, high-rise apartment buildings, etc. Analytical studies on the DIID of cantilever beam-type structures have shown that the DIID abruptly occurs from damage location. Baseline modification concept was newly introduced to detect multiple damages in cantilever beam-type structures by changing the baseline to the prior damage location. This approach has a clear theoretical base and directly identifies damage location(s) without the use of a finite element (FE) model. For validating the applicability of the proposed approach to cantilever beam-type structures, a series of numerical and experimental studies on a 10-storey building model were carried out. From the tests, it was found that the damage locations can be successfully identified by the proposed approach for multiple damages as well as a single damage. In order to confirm the superiority of the proposed approach, a comparative study was carried out on two well-known damage metrics such as modal strain-based damage index approach and uniform load surface curvature approach.     

含损伤黏弹性阻尼加筋层合板声功率和指向性变异*

该文旨在研究损伤位置和程度对自由阻尼加筋层合板声辐射功率和指向性的影响。基于Mindlin和Timoshenko梁理论,建立了自由阻尼层合板-梁组合结构有限元模型。数值求解四边简支边界条件自由阻尼加筋层合板振动响应,继而通过Rayleigh积分计算加筋层合板辐射声功率和指向性。将计算得到的前4阶模态固有频率、声辐射功率与指向性与已有文献进行了对比基本一致,验证了数值模型的正确性。最后,详细讨论了损伤位置和程度对自由阻尼加筋层合板固有频率、振型、声辐射功率和指向性的影响,结果表明：随着结构损伤程度的增大,声辐射功率峰值向低频移动,在更多角度上出现明显的指向性;声辐射功率和指向性对损伤位置比损伤程度更加敏感。     

光弹材料载荷过程中红外辐射特征机理的计算分析

基于材料的热力学关系和能量守恒定律,给出弹性体形变过程中红外辐射温度改变量和辐出度变化的物理计算方程.并结合有限元方法进行物理建模,对光弹材料三点弯载荷实验过程中的红外辐射出射度的分布进行数值计算和模拟.结果与实验结果吻合较好,表明模型及其相关理论是合理的,可以用来量化揭示实验中的红外辐射特征.从而得到一种能够利用计算机量化分析固体材料载荷过程中红外辐射特征机理的计算方法.     

Vibro-acoustic design sensitivity analysis using the wave-based method

Conventional element-based methods, such as the finite element method (FEM) and boundary element method (BEM), require mesh refinements at higher frequencies in order to converge. Therefore, their applications are limited to low frequencies. Compared to element-based methods, the wave-based method (WBM) adopts exact solutions of the governing differential equation instead of simple polynomials to describe the dynamic response variables within the subdomains. As such, the WBM does not require a finer division of subdomains as the frequency increases in order to exhibit high computational efficiency. In this paper, the design sensitivity formulation of a semi-coupled structural-acoustic problem is implemented using the WBM. Here, the results of structural harmonic analyses are imported as the boundary conditions for the acoustic domain, which consists of multiple wave-based subdomains. The cross-sectional area of each beam element is considered as a sizing design variable. Then, the adjoint variable method (AVM) is used to efficiently compute the sensitivity. The adjoint variable is obtained from structural reanalysis using an adjoint load composed of the system matrix and an evaluation of the wave functions of each boundary. The proposed sensitivity formulation is subsequently applied to a two-dimensional (2D) vehicle model. Finally, the sensitivity results are compared to the finite difference sensitivity results, which show good agreement.     

陶瓷和仿珍珠母陶瓷/聚脲复合结构的冲击损伤对比

建立了陶瓷梁受平头弹撞击的有限元模型,模拟了其冲击损伤演化过程,模拟结果与实验结果吻合较好,验证了模型的合理性。在此基础上,建立了仿珍珠母陶瓷/聚脲复合梁受相同弹体撞击的有限元模型,将其损伤演化过程与陶瓷梁进行了对比,并且分析了弹体撞击速度对两者损伤过程的影响。结果表明:在高速撞击下,陶瓷梁的损伤呈锥状扩展,梁发生整体性破坏,而仿珍珠母复合梁的损伤沿纵向(冲击方向)呈圆柱状扩展,梁发生局部性破坏,能更好地保持结构完整性;随着弹体撞击速度的增加,陶瓷梁的损伤范围加大,损伤程度加剧,而仿珍珠母复合梁的损伤范围在撞击速度高于一定值后变化不大,仅损伤程度增加。     

Identification of embedded horizontal cracks in beams using measured mode shapes

Mode shapes (MSs) have been extensively used to detect structural damage. This paper presents two new non-model-based methods that use measured MSs to identify embedded horizontal cracks in beams. The proposed methods do not require any a priori information of associated undamaged beams, if the beams are geometrically smooth and made of materials that have no stiffness discontinuities. Curvatures and continuous wavelet transforms (CWTs) of differences between a measured MS of a damaged beam and that from a polynomial that fits the MS of the damaged beam are processed to yield a curvature damage index (CDI) and a CWT damage index (CWTDI), respectively, at each measurement point. It is shown that the MS from the polynomial fit can well approximate the measured MS and associated curvature MS of the undamaged beam, provided that the measured MS of the damaged beam is extended beyond boundaries of the beam and the order of the polynomial is properly chosen. The proposed CDIs of a measured MS are presented with multiple resolutions to alleviate adverse effects caused by measurement noise, and cracks can be identified by locating their tips near regions with high values of the CDIs. It is shown that the CWT of a measured MS with the n-th-order Gaussian wavelet function has a shape resembling that of the n-th-order derivative of the MS. The crack tips can also be located using the CWTs of the aforementioned MS differences with second- and third-order Gaussian wavelet functions near peaks and valleys of the resulting CWTDIs, respectively, which are presented with multiple scales. A uniform acrylonitrile butadiene styrene (ABS) cantilever beam with an embedded horizontal crack was constructed to experimentally validate the proposed methods. The elastic modulus of the ABS was determined using experimental modal analysis and model updating. Non-contact operational modal analysis using acoustic excitations and measurements by two laser vibrometers was performed to measure the natural frequencies and MSs of the ABS cantilever beam, and the results compare well with those from the finite element method. Numerical and experimental crack identification can successfully identify the crack by locating its tips.     

Statistical damage identification of structures with frequency changes

Model updating methods based on structural vibration data have being rapidly developed and applied to detect structural damage in civil engineering. But uncertainties existing in the structural model and measured vibration data might lead to unreliable damage detection. In this paper a statistical damage identification algorithm based on frequency changes is developed to account for the effects of random noise in both the vibration data and finite element model. The structural stiffness parameters in the intact state and damaged state are, respectively, derived with a two-stage model updating process. The statistics of the parameters are estimated by the perturbation method and verified by Monte Carlo technique. The probability of damage existence is then estimated based on the probability density functions of the parameters in the two states. A higher probability statistically implies a more likelihood of damage occurrence. The presented technique is applied to detect damages in a numerical cantilever beam and a laboratory tested steel cantilever plate. The effects of using different number of modal frequencies, noise level and damage level on damage identification results are also discussed.     

A study of process parameters during pulsed Nd:YAG laser notching of C70S6 fracture splitting connecting rods

This paper reports on the laser notching technology in C70S6 steel for fracture splitting connecting rod using a Nd:YAG pulsed laser. The effects of process parameters on starting notch (SN) dimension and morphology were investigated by both finite element method (FEM) simulations and physical experiments for various process parameters. Optical microscopy and the scanning electron microscope (SEM) were used for the measurement of SN dimension and the observation of SN morphology in the experiment. The results were compared with the predictions. It was found that the FEM simulations results showed good consistency with the experiments, which indicates that the finite element model is feasible and reliable. Based on the principal findings from the two methods, optimum ranges of process parameters for different fracture splitting connecting rods were predicted, which are a flexibly adjusting notch depth, a curvature radius less than 0.08 mm and an opening angle within the range 18–26°. The results indicate that the predicting ranges are suitable for making good SNs, which has also been proved by the fracture splitting experiments.     

Finite Element Analysis of Field Pattern in Multiple Groove Guide

Rectangular groove guide with multiple grooves has been analyzed by finite element method (FEM) in this paper. The electrical field patterns of the dominant mode and the first higher-order TE mode have been presented for groove guide with single-, double-, triple-, and quadruple-rectangular grooves. The electromagnetic field of the dominant mode is distributed with a concentration in the groove regions, while the electromagnetic field of the first higher-order TE mode is mainly distributed in regions between grooves. The low loss characteristic has been found not only in single-groove guide, but also in multiple groove guide.     

激光辐照受拉铝板破坏行为的时空多尺度数值模拟

推导耦合过渡区内参变量信息交换的元/网格动量传递多尺度算法,建立离散元与有限元耦合时空多尺度计算模型,并应用于激光辐照下受拉铝板破坏行为的数值模拟中.通过对比有限元计算模型、空间多尺度计算模型与时空多尺度计算模型在激光辐照下受拉铝板破坏算例的模拟结果,验证离散元与有限元耦合时空多尺度计算模型的准确性和数值计算高效率优势.使用该多尺度计算模型从宏观和细观尺度对铝板破坏行为进行数值模拟,模拟结果与实验结果基本一致.     

Dynamic analysis of a multi-span uniform beam carrying a number of various concentrated elements

This paper employs the numerical assembly method (NAM) to determine the “exact” frequency–response amplitudes of a multiple-span beam carrying a number of various concentrated elements and subjected to a harmonic force, and the exact natural frequencies and mode shapes of the beam for the case of zero harmonic force. First, the coefficient matrices for the intermediate concentrated elements, pinned support, applied force, left-end support and right-end support of a beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact dynamic response amplitude of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force is determined by solving the simultaneous equations associated with the last overall coefficient matrix. The graph of dynamic response amplitudes versus various exciting frequencies gives the frequency–response curve for any point of a multiple-span beam carrying a number of various concentrated elements. For the case of zero harmonic force, the above-mentioned simultaneous equations reduce to an eigenvalue problem so that natural frequencies and mode shapes of the beam can also be obtained.     

Meshless formulation using NURBS basis functions for eigenfrequency changes of beam having multiple open-cracks

This paper presents a meshless formulation using non-uniform rational B-spline (NURBS) basis functions, and its applications to evaluate natural frequencies of a beam having multiple open-cracks. Node-based NURBS basis functions are used to construct the approximation function. The characteristic differentiability of the NURBS basis functions allows it to represent a function having specific degrees of smoothness and/or discontinuity. The discontinuity can be incorporated simply by assigning multiple knots at those locations. Hence, it can yield exact solutions having interior discontinuous derivatives. These advantages of NURBS are well known, and have been used extensively in graphical approximation of geometrical surfaces. However, it is seldom used in other engineering applications. To model the multiple open-cracks in a beam, quartic NURBS basis functions are employed and quadruplicate knots are assigned at the crack locations. Hence, it is capable to model the abrupt changes of slope (the first derivative of displacement) across a crack. In the present applications, additional equivalent massless rotational springs are inserted at the crack locations to represent the local flexibility caused by the cracks. As such, the cracked beam can be treated in the usual manner as a continuous beam. By adopting the meshless Petrov–Galerkin formulation, a generalized stiffness matrix for the cracked beam can be derived. Compared to the conventional finite element method, the present method does not require a finite element mesh for the purposes of interpolation and numerical integration. The advantages and effectiveness of the present method is illustrated in solving the eigenfrequencies of a beam having multiple open-cracks of different depths.     

Fluid-Structure Interaction in Microchannel Using Lattice Boltzmann Method and Size-Dependent Beam Element

Fluid-structure interaction (FSI) problems in microchannels play prominent roles in many engineering applications. The present study is an effort towards the simulation of flow in microchannel considering FSI. Top boundary of the microchannel is assumed to be rigid and the bottom boundary, which is modeled as a Bernoulli-Euler beam, is simulated by size-dependent beam elements for finite element method (FEM) based on a modified couple stress theory. The lattice Boltzmann method (LBM) using D2Q13 LB model is coupled to the FEM in order to solve fluid part of FSI problem. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.     

A generalized flexibility matrix based approach for structural damage detection

In this paper, a new structural damage detection approach based on changes in the generalized flexibility matrix is presented. The generalized flexibility matrix is first introduced; its sensitivity and change are then used to detect structural damage location and damage extent. Compared with the original flexibility matrix based approach, the effect of truncating higher-order modes can be considerably reduced in this new approach. Finally, a numerical example for a simply supported beam is used to illustrate the effectiveness of this proposed method.     

Study on Combined Method Based on 3-D ESPI

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用有限元法分析多波导耦合系统本征模的模式特性

本文应用有限元法(FEM),计算和分析了多波导耦合系统的本征模(超模)的模式特性及其变化规律,得到了强度均匀分布的基超模,克服了微扰理论计算这类问题的局限性.     

STRUCTURAL DAMAGE DETECTION BASED ON A MICRO-GENETIC ALGORITHM USING INCOMPLETE AND NOISY MODAL TEST DATA

This paper describes a procedure for detecting structural damage based on a micro-genetic algorithm using incomplete and noisy modal test data. As the number of sensors used to measure modal data is normally small when compared with the degrees of freedom of the finite element model of the structure, the incomplete mode shape data are first expanded to match with all degrees of freedom of the finite element model under consideration. The elemental energy quotient difference is then employed to locate the damage domain approximately. Finally, a micro-genetic algorithm is used to quantify the damage extent by minimizing the errors between the measured data and numerical results. The process may be either of single-level or implemented through two-level search strategies. The study has covered the use of frequencies only and the combined use of both frequencies and mode shapes. The proposed method is applied to a single-span simply supported beam and a three-span continuous beam with multiple damage locations. In the study, the modal test data are simulated numerically using the finite element method. The measurement errors of modal data are simulated by superimposing random noise with appropriate magnitudes. The effectiveness of using frequencies and both frequencies and mode shapes as the data for quantification of damage extent are examined. The effects of incomplete and noisy modal test data on the accuracy of damage detection are also discussed.     

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.