Experimental Method to Evaluate Effective Dynamic Properties of a Meta-Structure for Flexural Vibrations

In this study, a laboratory method to evaluate the effective dynamic properties for flexural vibrations of a meta-structure is presented. The flexural vibration of a beam with periodically spaced resonators was investigated using wave propagation analysis. After analyzing vibration interactions between the resonators and the homogeneous beam, the effective dynamic properties of the meta-structure were evaluated using the transfer function method. The comparison of the measured and predicted results allowed for an understanding of the proposed vibration control mechanism. The effective bending stiffness was not affected by the attached resonators. The effective mass exhibited significant frequency-dependent variation near the natural frequency of the resonators. The effective mass becomes complex when the stiffness of the resonators is viscoelastic. The reflected wave from the metamaterial was completely blocked when the real part of the effective mass became negative. The effective mass decreased as the loss factor of the attached resonators increased. The proposed evaluation method can be used to analyze the effects of resonators on structural vibrations.     

Damping of Structural Vibration Using Lightweight Granular Materials

An investigation of the vibration damping capability of granular treatments is presented. Cavities in aluminum and sandwich beams were filled with the lightweight particles made of polyimide. For analysis of vibration damping, the complex stiffness of structures before and after damping treatment was measured. Particles of different sizes, weights and polymer composition were used in the damping treatments. Large, frequency-dependent variations in structural loss factor depending on the types of particles were observed. This behavior was predicted by the Rayleigh-Ritz method. The frame wave propagation characteristics of the particles were measured and used in the numerical simulation. The acoustic–structure interaction between particles and structures enhances the dissipation of vibration energy.     

阶梯压电层合梁的波动动力学特性

采用行波理论系统地研究了压电阶梯梁的自由振动分析以及强迫响应的分析方法. 基于分布 参数理论研究了压电阶梯梁的波传播特性，忽略柔性梁横向剪切和转动惯量的影响，给出了 梁的轴向和横向的简谐波解. 将压电阶梯梁离散化为单元，考虑压电片的刚度和质量的影响， 建立了节点散射模型. 应用位移连续和力平衡条件，推导了节点的波反射和波传递矩阵，在 此基础上，引入波循环矩阵的概念，给出波循环矩阵、波传递系数矩阵的确定方法. 应用波 循环矩阵可以有效地计算结构的固有频率. 另外，应用波传递系数研究了压电陶瓷作动器位 置对其驱动能力的影响. 得出两个主要结论：1)作动器靠近悬臂梁固定端将有较强的驱动 能力，悬臂梁边界反射行波产生弯曲消失波有利于增大压电波的模态传递系数；2)模态传 递系数与固有频率的灵敏度密切相关，波传递系数越大, 对应该处固有频率变化灵敏度越大. 另外，数值算例表明了行波方法比有限元方法具有更高的计算精度.     

Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.     

管道联接件参数识别的行波法

基于结构振动的行波理论,提出了一种管道联接件物理参数识别的新方法.以未充液直管在平面内的弯曲振动为例,建立了入射波和出射波在联接件处的散射关系,并结合波模式幅值系数的识别,得到一组包含待识别参数的非线性方程组.在每一个频率下求解该方程组得到联接件的动刚度,最后采用最小二乘法一次识别得到联接件的物理参数.数值仿真结果表明,行波法在管道联接件参数辨识中,识别精度高,而且采用矩阵条件数小的传感器阵列,可以提高参数辨识的精度.     

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针对连续Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵,分析了在使用连续梁单元 进行结构动态特性分析中的数值问题. 基于连续梁单元的运动方程,导出了连续 Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵. 分析了影响动态刚度矩阵中双曲函 数自变量的各个独立变量及其产生的影响,并给出了初估连续梁单元合理长度的方法. 使用 单一连续Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵分别进行了悬臂梁频响曲线 的数值求解. 研究表明,在合理选择连续梁单元的长度时,大多数工程结构的动态特性分析 中都不会产生数值问题.     

Dynamic response of a reinforced concrete slab subjected to air blast load

Reinforced concrete is the principal material for military engineering and nuclear power plant containment. However, impacts and explosions could completely destroy such structures, causing tremendous casualties and property loss. Hence, this study conducts an analysis on the propagation law of a blast pressure wave and the dynamic response of reinforced concrete structures under explosive pressure wave effects. This study uses proper state material parameters and equations and then applies the nonlinear finite element analysis software LS-DYNA to conduct a numerical simulation of a free-field explosion model. After comparison with the computed results from empirical equations and validating the reliability of the numerical analysis model, the destruction and influencing factors on reinforced concrete slabs, under the effects of a blast pressure wave, are investigated. The results can serve as a reference for future analysis and design.     

Enhancement of wave damping within metamaterials having embedded negative stiffness inclusions

The wave dissipation properties of layered periodic structures are modelled by FE as well as analytical approaches. A linear oscillator incorporating a negative stiffness element and having exceptional energy dissipation properties is exhibited and incorporated within the modelled structures. The structural dynamic stability of both the oscillator and the modelled waveguides is discussed and ensured. The numerical results provide evidence of a drastic increase of several orders of magnitude for the damping ratio of the flexural waves propagating within the structures.     

The application of interferometric techniques to the nondestructive inspection of fiber-reinforced materials

A method for increasing the sensitivity of dynamic materials evaluation (DME) to localized damage in fiber-reinforced composites was examined. To obtain this improved sensitivity, different aspects of DME were examined. These included an increase in the frequency used to evaluate the dynamic properties, utilization of mode-shape information and different procedures for evaluating the experimental data.The extent of the internal damage was determined using measured changes in the dynamic properties of the system (loss factor, dynamic stiffness and mode shape). To obtain the response information at higher frequencies a modalanalysis system was built around the performance characteristics of a laser doppler vibrometer (LDV) and an electronic speckle pattern interferometer (ESPI). These two devices provided complementary information for the determination of the dynamic characteristics of each vibration mode. With this system, damage-induced changes in the dynamic characteristics of composite materials were measured at frequencies up to 10 kHz.The results of this study showed the following. (1) Torsion modes provide the most sensitivity to localized internal damage. (2) The evaluation of higher frequency NDI data requires the ability to correlate the measured loss factor and resonant frequencies with the actual mode shape. (3) The data obtained over the frequency range of the test could be reduced to a series of slopes that provide a sensitive indication of the material condition. (4) The sensitivity of the dynamic method to localized damage is limited by the measurement of the loss factor.     

Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements

This paper presents a formulation of an approximate spectral element for uniform and tapered rotating Euler–Bernoulli beams. The formulation takes into account the varying centrifugal force, mass and bending stiffness. The dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain, where two different interpolating functions for the transverse displacement are used for the element formulation. Both free vibration and wave propagation analysis is performed using the formulated elements. The studies show that the formulated element predicts results, that compare well with the solution available in the literature, at a fraction of the computational effort. In addition, for wave propagation analysis, the element shows superior convergence.     

多体系统齐次矩阵方法在浮桥运动响应中的应用研究

浮桥的抗弯刚度和受弯变形位移波的传播速度都比一般钢桥或混凝土桥小得多。在快速移动重载作用下,荷载移动速度有可能接近甚至超过浮桥位移波的传播速度,这样就会造成移动荷载前方浮桥位移波的堆积效应。介绍了多体系统齐次矩阵方法,并用齐次矩阵方法对浮桥进行建模和求解,通过数值模拟和已有的模型试验表明:当荷载的移动速度较大时,浮桥多体系统的运动呈现明显的波动现象,速度越大位移波的堆积越明显。     

Wave propagation in circular cylindrical shells with periodic axial curvature

The propagation of longitudinal and flexural waves in axisymmetric circular cylindrical shells with periodic circular axial curvature is studied using a finite element method previously developed by the authors. Of primary interest is the coupling of these wave modes due to the periodic axial curvature which results in the generation of two types of stop bands not present in straight circular cylinders. The first type is related to the periodic spacing and occurs independently for longitudinal and flexural wave modes without coupling. However, the second type is caused by longitudinal and flexural wave mode coupling due to the axial curvature. A parametric study is conducted where the effects of cylinder radius, degree of axial curvature, and periodic spacing on wave propagation characteristics are investigated. It is shown that even a small degree of periodic axial curvature results in significant stop bands associated with wave mode coupling. These stop bands are broad and conceivably could be tuned to a specific frequency range by judicious choice of the shell parameters. Forced harmonic analyses performed on finite periodic structures show that strong attenuation of longitudinal and flexural motion occurs in the frequency ranges associated with the stop bands of the infinite periodic structure.     

Shock initiated instabilities in underwater cylindrical structures

An experimental investigation to understand the mechanisms of dynamic buckling instability in cylindrical structures due to underwater explosive loadings is conducted. In particular, the effects of initial hydrostatic pressure coupled with a dynamic pressure pulse on the stability of metallic cylindrical shells are evaluated. The experiments are conducted at varying initial hydrostatic pressures, below the critical buckling pressure, to estimate the threshold after which dynamic buckling will initiate. The transient underwater full-field deformations of the structures during shock wave loading are captured using high-speed stereo photography coupled with modified 3-D Digital Image Correlation (DIC) technique. Experimental results show that increasing initial hydrostatic pressure decreases the natural vibration frequency of the structure indicating loss in structural stiffness. DIC measurements reveal that the initial structural excitations primarily consist of axisymmetric vibrations due to symmetrical shock wave loading in the experiments. Following their decay after a few longitudinal reverberations, the primary mode of vibration evolves which continues throughout later in time. At the initial hydrostatic pressures below the threshold value, these vibrations are stable in nature. The analytical solutions for the vibration frequency and the transient response of cylindrical shell are discussed in the article by accounting for both (1) the added mass effect of the surrounding water and (2) the effect of initial stress on the shell imposed by the hydrostatic pressure. The analytical solutions match reasonably well with the experimental vibration frequencies. Later, the transient response of a cylindrical shell subjected to a general underwater pressure wave loading is derived which leads to the analytical prediction of dynamic stability.     

混凝土率型内时损伤本构模型

混凝土是一种典型的率敏感材料,为了更好地描述混凝土结构在动力、冲击荷载作用下的强度和变形特征,本文结合内时理论和损伤理论建立了一种考虑混凝土率效应的内时损伤本构模型。该模型的特点:将混凝土材料的受力软化效应分解为密实状态的塑性效应和由微裂缝扩展引起的刚度退化效应。前者由内时理论来描述,这使该模型摆脱了一般弹塑性模型中屈服面的概念,从而更符合混凝土的变形特性,并且简化了非线性计算过程;后者由损伤理论来描述,根据混凝土的动力试验结果建立了增量型的损伤演变方程,从而使该模型能够较好地反映混凝土的动力特性。最后,应用本文建议的模型对一钢筋混凝土简支梁进行了非线性分析,结果表明:当结构承受快速荷载作用时,应变率对结构的受力性能影响较大,在进行结构分析时必须予以考虑。     

The SEA Approach to Vibration Localization in a Nearly Periodic Structure

Abstract

The phenomenon of vibration localization occurring in a nearly periodic structure was investigated through a statistical energy analysis (SEA) approach. The phenomenon has been examined mostly through a wave propagation approach, where a localization factor was often employed to evaluate the strength of vibration localization. The wave propagation approach properly predicted the factor close to Monte Carlo calculations in nearly periodic structures for both weak and strong couplings. In this analytical study, the localization factor was derived from the SEA approach for a nearly periodic structure monocoupled with a weak coupling. The SEA approach sequentially breaks the structure into two-oscillator blocked substructures and proposes a way of determining the vibration localization factor with equations of energy balance. This article shows that the SEA approach is quite appropriate for calculating the vibration localization factor compared to the wave propagation approach.     

Wave dispersion in gradient elastic solids and structures: A unified treatment

Analytical wave propagation studies in gradient elastic solids and structures are presented. These solids and structures involve an infinite space, a simple axial bar, a Bernoulli–Euler flexural beam and a Kirchhoff flexural plate. In all cases wave dispersion is observed as a result of introducing microstructural effects into the classical elastic material behavior through a simple gradient elasticity theory involving both micro-elastic and micro-inertia characteristics. It is observed that the micro-elastic characteristics are not enough for resulting in realistic dispersion curves and that the micro-inertia characteristics are needed in addition for that purpose for all the cases of solids and structures considered here. It is further observed that there exist similarities between the shear and rotary inertia corrections in the governing equations of motion for bars, beams and plates and the additions of micro-elastic (gradient elastic) and micro-inertia terms in the classical elastic material behavior in order to have wave dispersion in the above structures.     

Experimental investigation of transient flexural waves in beams with discontinuities of cross section

There has been little experimental work on flexural wave propagation in general and on flexural wave propagation in beams with discontinuities of cross section in particular. Experimental data are obtained for various test beams subjected to eccentric longitudinal impact. The bending strain versus time results are presented for several positions along a uniform beam and finite beams (of circular cross section) with discontinuities of cross section. Bending strain histories are recorded at several positions before and after the discontinuity. The effect of reflections on the propagated flexural wave is illustrated. The dispersion of the traveling flexural wave caused several alternating peaks within the duration of the original positive input pulse. The importance of investigating discontinuities of cross section in structures subjected to impact loading is clearly manifested.     

微差爆破振动波速度峰值-位移分布特征的延时控制

为了通过振动波传播规律研究微差爆破延时控制,改善爆破振动和提高爆炸能利用,选取普通雷管和澳瑞凯高精度雷管进行不同段别延期起爆对比实验,试爆过程对振动波测振。基于振动波函数优化理论基础,对实测数据和波状谱处理分析,总结了不同微差时间下振动波传播规律及速度峰值、主频、频带能量、总能量等变化特征,根据该特征发现振动波速度图谱和该速度积分所得位移图谱中两者最大值对应时间点相同。依据此速度峰值-振动位移分布特征,对某实测简单振动波进行高斯多峰拟合,结果表明:该波段能量最大化时间点为60 ms左右,振动最小的时间点为25 ms左右。     

钢轨轨底垂直振动模式导波检测技术的实验研究

现有铁路钢轨超声探伤车技术无法检测线路钢轨轨底缺陷,给铁路运输安全带来很大隐患.本文开展了钢轨轨底超声导波传播特性和垂直振动模式导波检测技术研究,采用半解析有限元方法分析了我国60型钢轨轨底的各振动模态导波频散曲线和波结构.应用模态锤技术对自由状态钢轨轨底垂直振动模态导波传播特性进行了实验测量,结果表明,在0～100kHz频率范围内,钢轨轨底垂直振动模态优势模式与厚度为14 mm板中的A0模式兰姆波具有等效性.进一步研究了激励频率、激励脉冲周数、传播距离对轨底垂直振动模态导波传播的影响,设计了导波斜探头,选择合适的参数在钢轨轨底激励出垂直振动模态导波并检测出了轨底的人工缺陷.本文的研究结果为线路钢轨轨底的导波检测技术奠定了一定的基础.     

基于应力波传播机理的混凝土无损检测研究综述

混凝土结构在基础设施中应用广泛,但环境与荷载导致材料和结构的老化损伤问题,势必影响材料性能及耐久性和结构完整性及安全性．构建有效的混凝土材料性能评估和结构损伤识别体系是当前研究热点．现有研究因对应力波传播机理不深入理解、损伤定位定量模型理想化、损伤形式简化等问题仍存在局限性．因此,开发普适全面、稳定可靠的无损检测系统,对在建或既有混凝土结构服役状况进行长期、实时跟踪,具有重要学术意义和工程应用价值．本文结合混凝土无损检测领域的国内外研究现状及进展,从智能压电材料振动机理研究、混凝土无损检测方法发展、基于应力波的无损检测研究进展这三个逻辑层面,即按照研究手段到研究方法再到具体研究方案的顺序,循序渐进地对混凝土材料性能评估和结构损伤识别的研究进行了成果总结和方法提炼;基于此进一步概述了该领域所存在的瓶颈问题、研究重难点,最后提出了针对这些局限性的混凝土无损检测研究展望．