A study on an estimation technique for the transverse impact of plates

This paper describes a numerical algorithm to determine the response of the structure due to a known force. The inverse dynamics problem in structural dynamics is to estimate the unknown forcing function using dynamic response. Theory of plates is employed to solve inverse problems in elasticity with specific applications to position and force sensing. In this paper, the contact force during the transverse impact of a plate is given and the response is solved. A Kalman filter technique was used to numerically estimate an applied force on the plate with the numerical response by an inverse method. In order to examine the accuracy of the proposed method, the plate is subjected to four type forces, which are triangular, sinusoidal, rectangular and random force. The estimated results have a good agreement with the exact values in all cases tested. Copyright © 2001 John Wiley & Sons, Ltd.     

Vibration analysis and identification of breathing cracks in beams subjected to single or multiple moving mass using online sequential extreme learning machine

In this paper, a novel approach was presented to vibration analysis and identification of breathing cracks in Timoshenko beam under single or multiple moving mass. Dynamic strain energies (DSEs) and translational accelerations in beam structures under moving mass were used as forward problem and application of an emergent learning algorithm called the online sequential extreme learning machine algorithm as inverse problem to predict crack depths and locations. To demonstrate the potential of the proposed vibration analysis over existing ones, two validation studies have been done. To evaluate the proposed method to identify breathing cracks, two examples, namely, clamped–clamped beam and two span continuous beams have been studied. Also, the effect of the discrepancy in stiffness between the finite-element model and the actual tested dynamic system has been investigated. Another examination has been performed in which moving mass with different speeds are utilized. Also, the effect of multi mass passing through the beam has been studied. The obtained results indicated that the proposed method could identify the breathing cracks existence and severity in the beam under moving mass using DSE and accelerations, which may be noisy or noise free.     

An efficient approach for identifying impact force using embedded piezoelectric sensors

In this paper, an efficient technique is proposed for identifying the impact force acting on CFRP laminated plates. First, Chebyshev polynomial is employed to approximate the impact force history. The coefficients in Chebyshev polynomial are directly used as unknown parameters. The relation between these unknown parameters and the strain responses at the specified positions is formulated through the finite element method and the mode superposition method. By comparing the numerically estimated strains and the experimental ones, an optimization model is set up to solve this inverse problem by employing the quadratic programming method. By virtue of this technique, the solution of this inverse problem for identifying the impact force becomes very stable and accurate. Also, by comparing the traditional methods, which employ the values of impact force at the discrete time points in the time domain, the number of unknowns in this proposed method is reduced significantly, which leads to the shortening of identification time for the purpose of real-time identification. After obtaining the impact force history, the impact position is identified by comparing the numerical strains and experimental ones directly. The experimental system for identifying the impact force is set up. Two kinds of CFRP laminates are used to verify the present methodology.     

Direct and sparse construction of consistent inverse mass matrices: general variational formulation and application to selective mass scaling

Classical explicit finite element formulations rely on lumped mass matrices. A diagonalized mass matrix enables a trivial computation of the acceleration vector from the force vector. Recently, non‐diagonal mass matrices for explicit finite element analysis (FEA) have received attention due to the selective mass scaling (SMS) technique. SMS allows larger time step sizes without substantial loss of accuracy. However, an expensive solution for accelerations is required at each time step. In the present study, this problem is solved by directly constructing the inverse mass matrix. First, a consistent and sparse inverse mass matrix is built from the modified Hamiltons principle with independent displacement and momentum variables. Usage of biorthogonal bases for momentum allows elimination of momentum unknowns without matrix inversions and directly yields the inverse mass matrix denoted here as reciprocal mass matrix (RMM). Secondly, a variational mass scaling technique is applied to the RMM. It is based on the penalized Hamiltons principle with an additional velocity variable and a free parameter. Using element‐wise bases for velocity and a local elimination yields variationally scaled RMM. Thirdly, examples illustrating the efficiency of the proposed method for simplex elements are presented and discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

动载荷识别的时间有限元模型理论及其应用

本文利用广义正交多项式作为时间有限元的形函数,推导了基于时间有限元的动载荷识别模型.成功地将时域下动载荷识别的复杂逆卷积关系转变为广义正交域的线性算子逆运算,这种模型识别精度高,抗干扰能力强,具有良好的计算稳定性,尤其适用于具有短时间样本的冲击类型动载荷识别,使该类问题在工程应用时的复杂程度大大降低,具有较高的工程应用价值.该方法为结构动力学逆问题的研究提供了一种新的技术途径.     

Experimental Investigation of Notch-Type Damage Identification with a Curvature-Based Method by Using a Continuously Scanning Laser Doppler Vibrometer System

This paper experimentally investigates a notch-type damage identification methodology for beams by using a continuously scanning laser Doppler vibrometer (CSLDV) system. Velocity response of a beam along a scan line under sinusoidal excitation is measured by the CSLDV system and an operating deflection shape (ODS) of the beam is obtained by the demodulation method from velocity response. The ODS of an associated undamaged beam is obtained by using a polynomial with a proper order to fit the ODS from the demodulation method. The curvature of an ODS (CODS) can be calculated with a high quality due to a dense measurement grid of the ODS. A curvature damage index (CDI) is proposed to identify a notch with a length of 1 mm along a beam and a depth of 0.9 mm under different excitation frequencies. The CDI uses differences between CODSs associated with ODSs that are obtained by the demodulation method and the polynomial fit; an auxiliary CDI obtained by averaging CDIs at different excitation frequencies is defined to further assist identification of damage. An averaging technique is applied to velocity response of the beam to reduce measurement noise. Effects of the number of averages on ODSs, CODSs, and CDIs are investigated. Four scan lines with an equal length of 151 mm and different locations with respect to the notch are used to investigate reliability of the proposed methodology. Finally, a whole scan line with a length of 555 mm along the beam is applied and the notch is successfully identified near regions with consistently high values of CDIs at different excitation frequencies; it can also be identified with the auxiliary CDI by a prominent peak at the location of the notch.     

Low velocity localized impact study of cellular foams

This paper deals with low velocity impact behavior of two densities of ductile polyvinylchloride (PVC) foam manufactured by Divinicell. Low velocity impact tests are carried out on foam beam and panel specimens. A drop-weight rig is used to carry-out the impact tests. The test rig is equipped with a load cell connected to a data acquisition PC computer, which allows the most important dynamic and kinetic parameters, such as the contact force, load–time response, impactor velocity and energy to be measured. Post-impact creep response of the foam is also investigated. Finite element analyzes are also conducted to study the dynamic response of foam specimens subjected to a low velocity impact. The present paper contributes towards the development of a damage tolerance design approach for structural foams.     

Viscoelastic interlaminar shear modulus of fibre reinforced composites

An inverse parameter identification technique using a modified Iosipescu shear test (MIST) has been developed for determining the viscoelastic interlaminar shear modulus of composite laminates. The main component of the technique involves minimising the difference between an experimentally measured and a numerically determined creep response at various elevated temperatures by varying the interlaminar shear modulus terms in the numerical model. Consequently, the ‘optimum’ model for the viscoelastic interlaminar shear modulus can be found at each temperature. These individual models are then combined to form a single ‘master curve’ for which a time-shift function and a Prony-series is fitted. In the present studies, Hexcel F593–18 plain weave pre-preg laminates were investigated. Experimental creep tests were conducted at various temperatures between 40 °C and 150 °C. Through the application of the inverse parameter identification technique, it was determined that the viscoelastic interlaminar shear moduli of the composite material can be effectively modelled by a nine-term Prony series and a third-order polynomial time-shift function.     

Low-velocity heavy-mass impact response of slender metal foam core sandwich beam

The objective of this work is to investigate the dynamic large deflection response of fully clamped metal foam core sandwich beam struck by a low-velocity heavy mass. Analytical solution and ‘bounds’ of dynamic solutions are derived, respectively. Also, finite element analysis is carried out to obtain the numerical solution of the problem. Comparisons of the dynamic, the quasi-static and numerical solutions for the non-dimensional maximum deflection of the sandwich beam with non-dimensional initial kinetic energy of the striker are presented for different cases of mass ratio, impact velocity and location. It is seen that the dynamic solution approaches the quasi-static one as the mass ratio of the striker to the beam is large enough, the quasi-static solution is in good agreement with the numerical results and both solutions lie in the ‘bounds’ of dynamic solutions. The quasi-static and numerical results for the impact force against the maximum deflection of the sandwich beam are obtained. It shows that the quasi-static solution can offer adequate accuracy to predict the low-velocity heavy-mass impact response of fully clamped sandwich beam.     

结构影响线识别：反问题可识别性分析与降维贝叶斯不确定性量化

结构影响线识别是移动荷载下既有结构评估的理论基础,其本质上是基于系统输入-输出含噪数据反向对静力系统指定截面的响应函数进行识别。已有研究虽然取得了进展,但它们在以下两个方面存在局限性：缺乏反问题可识别性分析;缺乏不确定性量化。反问题可识别性分析是为了厘清系统识别的参数的解的情况。不确定性量化是基于测量输入-输出含噪数据估计影响线参数的后验概率密度函数。针对上述两个局限性,该文在贝叶斯概率框架的基础上开展关于影响线识别的反问题可识别性分析与贝叶斯不确定性量化。该文进行基于直接参数化的影响线识别,包括系统输入与输出、反问题可识别性分析、参数最优值。经分析得出：一方面,直接参数化无法保证全局模型可识别;另一方面,现有方法即使是全局模型可识别的情况下也无法进行不确定性量化。为保证反问题是全局模型可识别且同时获取参数后验概率密度函数,该文提出基于降维贝叶斯不确定性量化的影响线后验识别,包括系统输入与输出重构、反问题可识别性分析、后验概率密度函数。该文进行模拟数据下新光大桥吊杆拉力影响线识别,与实测及模拟数据下简支梁桥应变影响线识别,验证提出方法的有效性。     

Impact dynamics of composite beams

The dynamics of a composite beam subject to transverse impact is investigated. A linearized contact law based on an elastic-plastic contact is shown to yield excellent results for the impact response. A dynamic ratio which is defined as the ratio of the maximum impact force obtained from the dynamic simulation to the one obtained from a half-space analysis (i.e., local contact) is used to characterize the type of impact response i.e., whether it is locally dominated, quasi-static or dynamic. It is found that this ratio depends on a single nondimensional parameter called ‘dynamic impact number’, which also governs the initial impact response until the waves are reflected back from the boundaries.     

Application of tomographic techniques to the spatial-response mapping of antenna-coupled detectors in the visible

A tomographiclike method based on the inverse radon transform is used to retrieve the irradiance map of a focused laser beam. The results obtained from multiple knife-edge measurements have been processed through a kriging technique. This technique allows us to map both the beam irradiance and the uncertainty associated with the measurement method. The results are compared with those achieved in the standard fitting of two orthogonal knife-edge profiles to a modeled beam. The application of the tomographiclike technique does not require any beam model and produces a higher signal-to-noise ratio than the conventional method. As a consequence, the quality of the estimation of the spatial response map of an antenna-coupled detector in the visible is improved.     

低速冲击下RC梁的动态响应和破坏机理研究

考虑材料非线性和应变率相关性等因素的影响,运用LS_DYNA非线性有限元软件对RC梁横向低速冲击试验进行了数值模拟,从动态损伤扩展、冲击能量转化等方面研究了RC梁的冲击响应过程和破坏机理。结果表明:RC梁的冲击响应过程可分为局部响应、整体响应和回弹变形三个阶段;RC梁的损伤主要发生在局部响应阶段,梁体变形主要发生在整体响应阶段;局部响应阶段的冲击力完全由梁体惯性力平衡,整体响应阶段的变形模式和截面弯矩分布与刚塑性模型基本相同;受拉钢筋变形耗能是RC梁最主要的冲击耗能机制。     

动载荷识别时域方法的研究现状与发展趋势

与动态载荷识别的频域方法相比,时域方法不仅适用于线性系统,还适用于非线性系统以及能有效处理瞬态冲击激励的识别问题,近年来时域方法愈发受到学者们的关注。目前广泛应用的几种时域方法主要有-反卷积法、计权加速度法、函数逼近法、卡尔曼滤波器和递归最小二乘法、逆系统法以及新兴的智能方法等等。在对各方法研究现状的概述与总结中,分析了各自的优缺点。从研究对象、研究方法、应用领域三方面分析,非线性系统、线性时变系统将成为分析研究的重点。结论显示,与现代智能算法相结合的逆系统方法将成为新的研究热点,将其相应的载荷识别方法应用于机械设备的故障诊断也将成为今后发展的新趋势。     

三次样条函数在桥梁移动荷载识别中的应用

基于欧拉梁模型，介绍了移动荷载识别的一般原理，提出采用三次样条曲线拟合来识别桥梁移动荷载的方法，用三次样条函数逼近桥梁挠度，对逼近函数微分求得桥梁挠曲速度和加速度，并根据模态叠加原理将挠度、速度、加速度转换为模态响应，由模态坐标方程和最小二乘法识别桥上移动荷载。通过计算机仿真，利用算例测试识别误差，获得的结果较理想。     

Multiple impact of beam-to-beam

Based on the rigid-plastic string model, the problem of a beam impacted sequentially by numerous beams with a high velocity is investigated using the wave propagation approach. Attention is focused on the response of the stricken beam. The closed-form expressions for deflection and tensile strain are obtained in the double impact case. In the multiple impact case, a general recursion formula for the tensile strain as a function of the number of the striking beam is derived. By assuming the tensile necking failure mode, the critical impact velocity to fracture the stricken beam is predicted with the impact number specified. Alternatively, with the impact velocity given, the critical impact number of the striking beam is determined. Asymptotic analyses for two limiting cases with infinite and infinitesimal time interval are performed.     

Instrumented low-velocity impact of CFRP beams

Low velocity impact of carbon fiber reinforced epoxy (AS4/3502 by Hercules) was conducted with 48 and 40 layered beams of different combinations of 0°, 90°, 45° and −45° stacking sequences. The test set-up included an instrumented drop weight and data acquisition system. Beams of two lengths were tested: “long” (100 mm) and “short” (55 mm), under impact and quasi-static loading conditions. The acceleration pulse was analysed in the frequency domain to determine the source of high frequency vibrations and a simple two-degrees-of-freedom model was used to distinguish between the force on the striker and the force applied to the beam. It is shown that the elastic response of the beams is the same under the two loading regimes. However, there is a difference in the strength of the beams according to the loading mode: both load and energy at failure under impact are lower than under quasi-static conditions. Nevertheless, the kinetic energy that is required to initiate fracture of the beam must be at least equal to the fracture energy under quasi-static conditions. The relative loss energy is related to the decrease in the rigidity of the beam.     

火炮磁流变阻尼器试验分析与动态模型

火炮磁流变阻尼器工作在高速高冲击条件下,其动力特性及其力学模型与常用的磁流变阻尼器存在较大不同。针对某型号火炮设计了反后坐用磁流变阻尼器,并进行了5种不同电流下的动态测试,验证了该阻尼器对反后坐控制的可行性。由试验分析得,火炮磁流变阻尼器的输出力不仅与控制电流和后坐速度有关,还与高冲击条件下的磁流变效应的复杂性、惯性力、腔体内气体压力等因素有关。提出了用改进的多项式模型描述火炮磁流变阻尼器,该模型具有形式简洁,易于求解逆模型,便于实时控制等优点。通过参数辨识后的模型能较好的描述火炮反后坐过程中阻尼器的输出力。     

Estimation of the surface normal velocity of high frequency ultrasound transducers

This paper is concerned with the characterization of the true locally resolved surface normal velocity of an assumed piston-type ultrasonic transducer. Instead of involving a very complicated direct pointwise measurement of the velocity distribution, an inverse problem is solved which yields a spatially discretized weighting vector for the surface normal velocity of the transducer. The study deals with a spherically focused high frequency transducer, which is driven in pulse-echo mode. As a means of posing the inverse problem, the active transducer surface is divided into annuli of equal surface so that for each annulus the spatial impulse response can be calculated. An acrylic glass plate acts as a simple structured target. The resulting ill-posed nonlinear inverse problem is solved with an iterative regularized Gauss-Newton algorithm. The solution of the inverse problem yields an estimated weight for the surface normal velocity for each annulus. Experimental results for a thin copper wire target are compared to simulation results for both uniform and estimated surface normal velocities.     

A technique for dielectric measurement of cylindrical objects in arectangular waveguide

In this paper, the inverse scattering problem of a homogeneous dielectric post in a rectangular waveguide is considered. A novel inversion algorithm, based on the method of moments and eigen analysis, for computation of the dielectric constant of the post (ϵ) from the measured voltage reflection coefficient is introduced. In this method the integral equation for the polarization current induced in the dielectric post is cast into a matrix equation, and then the contribution of ϵ to the resulting reflection coefficient is expressed explicitly using the eigen analysis. It is shown that the dielectric constant can be obtained from the solution of a complex polynomial function which in turn can be obtained numerically using the conjugate gradient method. Practical aspects of dielectric measurement using this technique are discussed. The HP-8510 network analyzer is used to measure the reflection coefficient of dielectric posts in an X-band waveguide sample holder. Metallic and known dielectric posts are used to determine the accuracy of the dielectric measurement technique