Transverse vibration analysis for piezoceramic rectangular plates using Ritz's method with equivalent constants.

The transverse vibration of piezoceramic rectangular thin plates is investigated theoretically and experimentally using the Ritz's method incorporated with the defined equivalent constants. The equivalent constants are derived by comparing the characteristic equations of transverse resonant frequencies between isotropic and piezoceramic disks. By replacing the Poisson's ratio and flexural rigidity with the equivalent constants, the well-known Ritz's method can be used to investigate the transverse vibration of piezoceramic rectangular plates. Two different types of boundary conditions-clamped-free-free-free (CFFF) and clamped-free-clamped-free (CFCF)-are analyzed in this paper. For the experimental measurement, two optical techniques-amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV)-are used to validate the analytical results. Both the transverse vibration modes and resonant frequencies of piezoceramic rectangular plates are obtained by the AF-ESPI method. Numerical calculations using the finite-element method (FEM) are performed, and the results are compared with the theoretical analysis and experimental measurements. Excellent agreements are obtained for results of both resonant frequencies and mode shapes. According to the theoretical calculations with different equivalent Poisson's ratios, resonant frequency variations versus aspect ratios ranging from 0.1 to 10 also are discussed for the first several modes in the work.     

Vibration analysis for piezoceramic rectangular plates using Ritz's method with equivalent constants

The transverse vibration of piezoceramic rectangular thin plates is investigated theoretically and experimentally using the Ritz's method incorporated with the defined equivalent constants. The equivalent constants are derived by comparing the characteristic equations of transverse resonant frequencies between isotropic and piezoceramic disks. By replacing the Poisson's ratio and flexural rigidity with the equivalent constants, the well-known Ritz's method can be used to investigate the transverse vibration of piezoceramic rectangular plates. Two different types of boundary conditions - clamped-free-free-free (CFFF) and clamped-free-clamped-free (CFCF) - are analyzed in this paper. For the experimental measurement, two optical techniques - amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV) - are used to validate the analytical results. Both the transverse vibration modes and resonant frequencies of piezoceramic rectangular plates are obtained by the AF-ESPI method. Numerical calculations using the finite-element method (FEM) are performed, and the results are compared with the theoretical analysis and experimental measurements. Excellent agreements are obtained for results of both resonant frequencies and mode shapes. According to the theoretical calculations with different equivalent Poisson's ratios, resonant frequency variations versus aspect ratios ranging from 0.1 to 10 also are discussed for the first several modes in the work.     

Theoretical analysis and experimental measurement for resonant vibration of piezoceramic circular plates

Based on the electroelastic theory for piezoelectric plates, the vibration characteristics of piezoceramic disks with free-boundary conditions are investigated in this work by theoretical analysis, numerical simulation, and experimental measurement. The resonance of thin piezoceramic disks is classified into three types of vibration modes: transverse, tangential, and radial extensional modes. All of these modes are investigated in detail. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), are used to validate the theoretical analysis. Because the clear fringe patterns are shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Good quality of the interferometric fringe patterns for both the transverse and extensional vibration mode shapes are demonstrated. The resonant frequencies of the piezoceramic disk also are measured by the conventional impedance analysis. Both theoretical and experimental results indicate that the transverse and tangential vibration modes cannot be measured by the impedance analysis, and only the resonant frequencies of extensional vibration modes can be obtained. Numerical calculations based on the finite element method also are performed, and the results are compared with the theoretical analysis and experimental measurements. It is shown that the finite element method (FEM) calculations and the experimental results agree fairly well for the resonant frequencies and mode shapes. The resonant frequencies and mode shapes predicted by theoretical analysis and calculated by finite element method are in good agreement, and the difference of resonant frequencies for both results with the thickness-to-diameter (h/D) ratios, ranging from 0.01 to 0.1, are presented.     

Measurement of displacement and vibration by using the oblique ray method

An optical system that can measure vibrations and displacements is developed by using the oblique ray method. By employing a single convex lens that plays both roles of sending and receiving the beams that are reflected by the target surface, the optical measurement system became compact and reliable. A position-sensitive detector is used to measure the position change of the beam spot on the target surface. The resolution of the optical system can be controlled by changing the optical magnitude of the objective lens and is designed to be less than 0.1 microm for the developed system.     

Free vibration analysis of the piezoceramic bimorph with theoretical and experimental investigation

This paper investigates the vibration characteristics of an asymmetric, three-layered piezoceramic circular bimorph under traction-free boundary conditions by applying the electroelasticity and Kirchhoff plate theory. The asymmetric, three-layered bimorph consists of an isotropic shim layer and two piezoceramic layers of equal thickness and same polarization. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), are used to validate the theoretical analysis. The resonant frequencies of the piezoceramic bimorph also are measured by an impedance analyzer. Both theoretical and experimental results indicate that the transverse vibration modes cannot be measured by impedance analysis, and only resonant frequencies of extensional vibration modes are present. However, transverse vibration modes of the piezoceramic bimorph can be obtained by the AF-ESPI and LDV measurements. The numerical calculations also are obtained using the finite-element method (FEM), and the results agree comparatively well with the theoretical analysis and experimental measurements. According to the theoretical calculation, the variations in resonant frequencies and effective coupling factors versus the various layer-thickness ratios also are investigated in this work.     

用薄层法分析高架轨道交通引发的环境振动

薄层法是分析和模拟弹性波在层状介质中传播的一种半解析半数值方法。将由车辆一桥梁动力分析程序算得的高架轨道支架动反力作为支架的激振荷载。在支架上激振荷载作用下，利用薄层法计算位于上海典型场地上的高架轨道线路承台群桩基础周围地基的频率响应函数。根据频率响应函数和激振荷载可算得高架轨道线路周围场地的加速度响应及振级。分别采用单支架模型和多支架模型计算高架轨道交通引发的环境振动。振级计算结果与实测回归公式的比较表明，多支架模型中相邻基础的影响不大，实用时可采用单支架模型进行计算。本文提出的高架轨道交通环境振动分析模型可以应用于高架轨道交通引发环境振动的分析和预测。     

多层次等效的Mori-Tanaka法预测含空腔点阵增强芯层的等效弹性模量

提出了兼具力学和声学性能的夹层吸声复合材料-含空腔点阵增强夹芯结构;为了预测含空腔点阵增强结构芯层的等效弹性模量,建立了包含空腔、点阵增强柱和泡沫基体的三相复合材料的细观力学多层次等效数理模型,结合点阵增强柱和空腔周期性分布的特点建立代表性体积单元,利用Mori-Tanaka方法进行两次单相夹杂等效处理,获取了含空腔点阵增强芯层等效弹性模量的解析解,与试验数据和细观力学有限元法结果对比均吻合较好。采用有限元软件ANSYS建立了含空腔点阵增强夹芯结构的实际模型和等效模型,并将芯层等效模量解析结果作为等效模型芯层的材料参数,计算弯曲变形和固有频率并进行对比分析,弯曲变形位移和中低频固有频率的相对误差不超过2%,满足工程精度要求。进一步利用该等效方法,分别探讨了点阵增强柱和空腔体积比对芯层等效弹性模量的影响规律。结果表明,上述方法能较准确地预测含空腔点阵增强结构芯层的等效弹性模量,且数理模型清晰,公式简单,计算快速。     

随机振动对波导缝隙阵天线增益影响的等效算法研究

波导缝隙阵天线具有结构紧凑、质量轻、性能好等优点,常被用于机载或弹载雷达等多种设备。随机振动是雷达工作时的主要载荷形式,振动引起的天线变形会对天线增益产生一定影响。目前用传统方法计算随机振动对天线增益影响的过程非常复杂,且计算量很大,为此提出一种利用位移响应的均方根来计算随机振动对天线增益影响的等效方法。假设随机振动是满足均值为零的正态分布的随机过程,利用各个节点的完全相关性可生成多组样本,首先利用传统方法和等效方法分别计算得到随机振动下天线增益的均方根,然后利用泰勒展开式推导等效方法的适用条件,最后以宽边波导缝隙阵天线为例,通过数值仿真和实验验证等效方法的有效性。研究表明:等效方法误差小于0.1dB,该方法在满足一定条件时,能够快速计算随机振动对天线增益的影响。该等效算法可大大提高计算效率、节约计算时间,同时计算结果具有重要工程意义,为天线设计人员提供参考。     

Experimental and numerical investigations for the free vibration of cantilever trapezoidal plates

Abstract

Based on the advantages of non‐contact and full field measurement, the optical technique called amplitude‐fluctuation electronic speckle pattern interferometry (AFESPI) with an out‐of‐plane setup is employed to investigate the free vibration of cantilever trapezoidal plates with various taper ratios and sweep‐back angles. Twenty different plate configurations are analyzed, including triangular and trapezoidal plates, and the first seven vibration modes of each plate are measured. The AF‐ESPI method is very convenient for measuring vibrating objects because no contact is required in contrast to classical modal analysis using accelerometers. Based on the fact that clear fringe patterns will appear only in resonance, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present technique. Numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Excellent agreements are obtained for both results of resonant frequencies and mode shapes. The influences of taper ratios and sweep‐back angles on the vibration behavior of cantilever trapezoidal plates are also demonstrated in terms of the dimensionless frequency parameter.     

Time analysis of structural concrete elements using the equivalent displacement method

This paper presents a modelling technique referred to as the equivalent displacement method (EDM) which describes the behaviour in time of structural concrete elements, such as reinforced concrete beams and composite beams with full shear interaction, accounting for time effects, such as creep, of the concrete component. The time-dependent behaviour of the concrete is modelled using the algebraic representations, such as the age-adjusted effective modulus method (AEMM), while the steel joist and reinforcement are assumed to behave in a linear-elastic fashion. The main advantage of the EDM method is that it requires only one analysis to obtain the deformation state of the structural system at one step in time based on the AEMM methods, instead of the two required by available modelling techniques (i. e. one performed at timet ₀ and one performed one step in timet). The EDM method is then applied to the analysis of structural concrete elements using the stiffness analysis and the results obtained based on this modelling technique are validated against other modelling methods. The advantages of using the EDM method in design applications are also illustrated.

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Résumé Cet article présente une méthode appelée méthode de déplacement équivalent (EDM), qui décrit le comportement temporel des éléments de béton, par example les poutres en béton armé et les poutres mixtes à interaction complète, tenant compte des effets temporaux, tel que le fluage du béton. Le comportement temporel du béton est modelé par représentation algébrique, tel que la méthode age ajusté du module effectif (AEMM), tandis que la poutre d'acier et les renforts sont supposés linéaire et élastique. L'avantage majeur de la méthode EDM est qu'elle n'exige qu'une seule analyse pour obtenir l'état de déformation du système à un point temporel (méthode EDM), au lieu des deux points exigés par les méthodes courantes, en temps t₀ et l'autre à t. La méthode EDM est ensuite appliquée à l'analyse des éléments structurels en béton, utilisant l'analyse de raideur, et les résultats obtenus par cette méthode sont vérifiés par d'autres méthodes. Les avantages de l'utilisation de la méthode EDM dans les applications du dessein sont aussi illustrés.

     

The growth of non-stoichiometric apatites using the constant composition method

The kinetics of the crystal growth of calcium-deficient hydroxyapatites with different stoichiometry (Ca₅-(HPO₄)(PO₄)₃-(OH)₁-) have been investigated at 37°C using the constant composition method. The growth was performed in solutions supersaturated only with respect to Ca₅(PO₄)₃(OH) (HAp) by inoculating with well-characterized seed crystals. The stoichiometry of the grown apatites was consistent with values of 00.185. The deviation from HAp stoichiometry of the growing apatite increased with increasing supersaturation degree (S). The constant composition method also provides relevant information about the solubility behaviour of the growing phase with a definite composition. From the decrease of the normalized growth rate j with decreasing S, an estimate could be made of the composition of the solution for which the growth ceases. The determined solubility product of the grown apatite (4.28×10^-54 M⁹) was higher than the value obtained by the equilibration of the seed material. The results were interpreted on the basis of differences in crystal lattice perfection.This paper was accepted for publication after the 1995 Conference of the European Society of Biomaterials, Oporto, Portugal, 10–13 September.     

基于有限差分法的水平旋转梁的自由振动解析

在水平旋转梁模型的基础上,利用哈密尔顿原理建立了动力学微分方程。在悬臂梁边界条件下,运用二阶中心差分原理对欧拉梁进行有限差分离散,推导出系统模型的自由振动差分方程。运用MATLAB振动工具箱和一般阻尼振动理论对其进行了编程运算,得到了不同转速下水平梁的无量纲固有频率。相关文献的结果比对验证了有限差分方法的有效性,然后对旋转梁的自由振动特性进行了扩展分析和结果的优化处理。另外,对固支梁和自由梁的自由振动也进行了解析。     

The investigation of three-dimensional vibration for piezoelectric rectangular parallelepipeds using the AF-ESPI method

Electronic speckle pattern interferometry (ESPI) is a powerful tool for the full-field measurement of a deformed body. In this paper, a three-dimensional vibrating block that couples the out-of-plane and in-plane motions is investigated using the amplitude-fluctuation ESPI (AF-ESPI). This method demonstrates the advantages of combining high processing speed, such as in the subtraction method, with high fringe sensitivity, such as in the time-averaged method. The optical system for AF-ESPI is then employed to analyze the volume vibration of piezoelectric material for a rectangular parallelepiped configuration. Based on the fact that fringe patterns measured by the AF-ESPI method appear as a clear picture only at the resonant frequency, both the natural frequencies and the out-of-plane and in-plane vibration mode shapes are successfully obtained in this study. Finally, the impedance analysis as well as the finite element method (FEM) with three-dimensional model are also conducted to compare with the result obtained by AF-ESPI. It is shown that the numerical calculation and the experimental result agree fairly well for both the resonant frequency and the mode shape in three-dimensional configurations     

Prediction of the dynamic equivalent stiffness for a rubber bushing using the finite element method and empirical modeling

International Journal of Mechanics and Materials in Design - A hybrid method using an approximation that is based on the finite element analysis and empirical modeling is proposed to analyze the...     

Calibration of vibration pickups by the reciprocity method

Summary The above calibration method provides absolute values of vibration transducers' sensitivity at higher frequencies by means of simpler methods, but with the same accuracy as equipments which set the required values of vibrations by vibrating plates of a complex design.The disadvantages of this method consist of repeated mechanical reconnection of the tested transducers, which lowers the accuracy of calibration. The author of this article together with S. D. Margolin have developed a switching technique which replaces mechanical reconnection of vibration transducers by electrical switching, thus speeding up the calibration and raising the accuracy of measurements [7].     

基于统计能量法的隔声瓦减振性能仿真研究

在水下结构表面敷设隔声去耦材料是应用最广泛也是非常有效的一种提高舰船隐身性能的方法。基于统计能量法开展了隔声瓦对复杂锥柱结构水下振动的影响研究,讨论了隔声瓦敷设方式对复杂锥柱结构水下振动的影响,分析了阻尼损失系数对隔声瓦减振效果的影响。研究表明,隔声瓦敷设方式、阻尼损失系数对隔声瓦减振效果有较大影响:当隔声瓦敷设在结构振动主导传递途径上时,其对传递途径下游结构的振动抑制效果较为明显,而对于振源及传递途径上游结构振动的影响较小;隔声瓦减振效果随敷设密度的增大而增加,随阻尼损失系数的增大而有所降低。