Vibration analysis of shape-optimized rotating cantilever beams

The shape optimization of rotating beams is carried out in order to minimize the vibrations. The objective is the maximization of the fundamental frequency with constraints on the beam mass and static tip deflections. The finite-element method (FEM) is used to model the rotating beam and sequential quadratic programming (SQP) is used for the optimization. The effects of beam frequency maximi-zation and hub–beam frequency maximization on the optimized shapes and the dynamic characteristics of these shapes are studied. The beam shapes are optimized for different speeds. The natural frequencies and time responses of these optimized shapes are studied using numerical simulation. Based on the numerical study, suggestions for formulating an appropriate optimization problem in a given context are made.     

磁致伸缩层合悬臂梁式作动器的振动分析

为了分析磁致伸缩薄膜型层合悬臂梁式作动器的振动问题,应用磁致伸缩材料的非线性本构关系,由哈密尔顿原理导出了双层悬臂梁的振动微分方程。采用分离变量方法和常微分方程组的解析解法对磁致伸缩薄膜型层合悬臂梁的自由振动和受迫振动进行了理论分析。数值算例表明本文计算结果与有限元结果吻合较好,从而佐证了本文理论模型和求解方法的正确性,并讨论了几何参数、材料参数对层合梁固有频率的影响。还分析了在周期输入磁场激励下悬臂梁的挠度响应,且挠度响应呈现出倍频效应的动态特性。      

Vibration analysis of orthotropic cantilever cylindrical shells with axial thickness variation

A semi-analytical finite element method is used to determine the free vibration characteristics of thin orthotropic cantilever circular cylindrical shells. Love's first approximation shell theory is used for the formulation. The effect of the variation of thickness along the axial direction on natural frequencies, especially on the lowest frequency, has been studied with a constraint on the total mass of the shell for a particular length to middle surface radius ratio. Studies have been conducted for different degrees of orthotropy and various values of length to radius ratio.     

Vibration analysis of sandwich plates with lattice truss core

An effective methodology is developed to investigate the vibration of the sandwich plate with pyramidal lattice core. Equation of motion of lattice sandwich plate is established by Hamilton's principle. Displacement fields are expressed with a simple method, and the natural frequencies of the lattice sandwich plate are conveniently calculated. The correctness of the analytical method is verified by comparing the present results with published literatures. The effects of structural and material parameters on the vibration characteristics of lattice sandwich plate are analyzed. The present method will be useful for vibration analysis and design of lattice sandwich plates.     

Vibration analysis of variable stiffness laminated composite sandwich plates

Abstract

This paper presents the free vibration analysis of a variable stiffness laminated composite sandwich plates. The fiber orientation angle of the face sheets (Skin) is assumed to vary linearly with the x-axis. The problem formulation is based on the higher-order shear deformation plate theory HDST C⁰ coupled with p-version of finite element method. The elements of the stiffness and mass matrices are calculated analytically. The sandwich plate is presented with a uniform mesh of four p-elements and the convergence properties are achieved by increasing the degree p of the hierarchical shape functions. A calculation program is developed to determine the fundamental frequencies for different physical and mechanical parameters such as plate thickness, core to face sheets thickness ratio, orientation angle of curvilinear fibers and boundary conditions. The results obtained show a good agreement with the available solutions in the literature. New comparison study of vibration response of laminated sandwich plate between the straight and curvilinear fibers is presented.     

Vibration analysis of orthotropic rectangular plates on elastic foundations

The vibration responses of orthotropic plates on nonlinear elastic foundations are numerically modeled using the differential quadrature method. The differential quadrature technique is utilized to transform partial differential equations into a discrete eigenvalue problem. Numerical results and those from literature closely correspond to each other. Numerical results demonstrate that elastically restrained stiffness, plate aspect ratio and foundation stiffness significantly impact the dynamic behavior of orthotropic plates.     

Vibration analysis of a rotating flexible shaft–disk system

Free vibrations of a spinning disk–shaft system are analysed using the finite-element method. The spinning disk is described by the Kirchhoff plate theory. The shaft is modelled by a rotating beam. Using Lagrange’s principle and including the rigid-body translation and tilting motion, equations of motion of the spinning flexible disk and shaft are derived consistently to satisfying the geometric compatibility conditions on the internal boundaries among the substructures. The finite-element method is then used to discretize the derived governing equations. The method is applied to the shaft–disk spinning system. The sensitivity to the running speed as well as the effect of both disk flexibility and boundary condition on the natural frequencies of the spinning system are numerically investigated.     

Nonlocal nonlinear bending and free vibration analysis of a rotating laminated nano cantilever beam

In this article, we present the nonlocal, nonlinear finite element formulations for the case of nonuniform rotating laminated nano cantilever beams using the Timoshenko beam theory. The surface stress effects are also taken into consideration. Nonlocal stress resultants are obtained by employing Eringen’s nonlocal differential model. Geometric nonlinearity is taken into account by using the Green Lagrange strain tensor. Numerical solutions of nonlinear bending and free vibration are presented. Parametric studies have been carried out to understand the effect of nonlocal parameter and surface stresses on bending and vibration behavior of cantilever beams. Also, the effects of angular velocity and hub radius on the vibration behavior of the cantilever beam are studied.     

On buckling of crosswise rigid elastic cantilever plates

Summary The classical two-dimensional equations for the buckling of thin elastic anisotropic plates are reduced, on the basis of an assumption of crosswise rigidity, to a system of one-dimensional equations. The reduction pre-supposes that the crosswise dimension of the plate is small compared to it's spanwise dimension and leads, effectively, to a system of beam buckling equations which automatically associates a warping stiffness effect with the classical beam bending and twisting stiffness effects. In the event that inertia load terms are to be considered the system is of the eight order with respect to the spanwise space coordinate. In the absence of such load terms the system can be reduced to the sixth order, with further reductions possible for suitably specialized load conditions.     

Flapwise bending vibration of rotating plates

Linear equations of motion for the flapwise bending vibration analysis of rotating plates are derived in the present work. The equations of motion are transformed into dimensionless forms in which three dimensionless parameters are identified. The effects of the dimensionless parameters on the characteristics of the flapwise bending vibration of rotating plates are investigated. The accuracy of the present modelling method is verified through comparing its numerical results to those obtained by an existing method in the related literature. Eigenvalue loci crossing and eigenvalue loci veering phenomena are observed and discussed. The variations of mode shapes associated with the phenomena are also exhibited. Copyright © 2002 John Wiley & Sons, Ltd.     

Vibration of pretwisted cantilever trapezoidal symmetric laminates

Summary A first known investigation on the vibratory characteristics of pretwisted composite symmetric laminates with trapezoidal planform is presented. A governing eigenvalue equation is derived based on the Ritz minimization procedure. This formulation shows that bending and stretching effects of these symmetric laminates are coupled by the presence of twisting curvature. For the solution method, a set of orthogonally generated shape functions is employed to approximate the transverse and in-plane displacements. These functions are generated through a proposed recurrence formula. During the orthogonalization process, a basic function is introduced to ensure the satisfaction of the essential boundary conditions. This proposed method is applied to determine the vibration response of the titled problem. The effects of angles of twist and laminated layers upon the vibration frequencies are examined. Convergence tests for selected examples are presented in which the accuracy of the results is established. It has been found that an increase in the angle of twist also strengthens the torsional stiffness of the laminated plates and therefore results in higher twisting frequencies. The present solutions, where possible, are verified by comparison with data of simplified examples that are available in the literature.     

Vibration analysis of symmetric laminated composite plates with attached mass

In this study, vibration of symmetrically laminated composite plates with attached mass is studied. The Ritz method with algebraic polynomial displacement field is used. The plates with at least two adjacent free edges are considered in the formulations. The effect of various parameters (number of layers, ratio of attached mass to the plate mass, position of attached mass, fiber orientation) upon the frequencies and mode shapes is investigated. It is found that attachment of a mass has important effects on the vibration characteristics of composite laminated plates.     

Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs

Three experimental techniques are used in this study to access the resonant characteristics of piezoceramic bimorphs in parallel and series connections. These experimental methods, including the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), laser Doppler vibrometer-dynamic signal analyzer (LDV-DSA), and impedance analysis, are based on the measurement of full-field displacement, point-wise displacement, and electric impedance, respectively. Because the clear fringe patterns will be shown only at resonant frequencies, both the resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time by the AF-ESPI method. LDV-DSA is used to determine the resonant frequencies of the vibration mode for out-of-plane motion. The impedance analysis is used to measure the resonant and antiresonant frequencies for in-plane motion. Although the out-of-plane mode is the dominant motion of piezoceramic bimorphs, it is found in this study that the amount of displacement for the in-plane motion in parallel connection is large enough to be measured by AF-ESPI and impedance. It is interesting to note that resonant frequencies of the specimen in parallel connection for the out-of-plane motion determined by LDV-DSA are the same as that for the in-plane motion obtained by impedance. Furthermore, both in-plane and out-of-plane mode shapes for the specimen in parallel connection are obtained in the same resonant frequency from the AF-ESPI method. It is concluded in this study that the particle motions of piezoceramic bimorphs for parallel connection in resonance are essentially three-dimensional. However, it is found that only out-of-plane vibration modes can be excited for the specimen in series connection. Numerical computations based on the finite-element method are presented, and the theoretical predicted results are compared with the experimental measurements. Good agreements between the experimental measured data and numerical calculated results are found for resonant frequencies and mode shapes of the piezoceramic bimorph.     

旋转机械非平稳振动信号的时频分析比较

信号分析与处理是机械故障监测与诊断中故障提取的常用方法,传统的振动故障分析方法难以满足频率随时间变化的非平稳信号的要求,联合时频分析是非平稳信号比较有力的分析工具。以转子实验台的典型振动故障信号为研究对象,分析研究了几种时频分析方法如STFT、Wigner-Ville分布、小波变换和Hilbert-Huang变换。对比结果表明:STFT和Wigner-Ville分布的时频分辨率是矛盾的,易出交叉项或使信号变得微弱;小波分解会出现多余信号;Hilbert-Huang变换的时频分析能够直观检测信号中的微弱奇异成分,清楚给出时频分布情况,为旋转机械状态监测和故障诊断提供了新的手段。     

移动质量作用下轴向运动悬臂梁振动特性分析

将弹炮发射系统简化为移动质量作用下的轴向运动悬臂梁系统,推导了轴向运动梁的振动方程,采用修正的Galerkin法离散求解该偏微分方程,得到以模态坐标表示的二阶时变常微分方程组,通过Newmark-β法对方程组进行了求解。计算结果表明,移动质量载荷主要使梁的一阶模态受到激励,移动质量的大小和运动速度对悬臂梁的振动响应影响较大,在移动质量作用下梁的伸缩运动都处于不稳定状态;在移动质量脱离悬臂梁后,梁的轴向收缩运动使得梁的瞬时振动频率不断减小,振动位移逐渐衰减,而振动速度逐渐增大,梁的运动处于不稳定状态,伸展时梁的自由振动规律相反。     

含圆周非贯穿裂纹悬臂管道的振动分析与裂纹识别

摘 要：根据线性断裂力学理论和应变能释放原理,推导了含圆周非贯穿裂纹管道在轴力、剪力和弯矩等荷载作用下的局部柔度系数方程,利用适应性Simpson方法编写了数值积分程序进行局部柔度系数求解,建立了含裂纹管道的二维有限元模型进行含裂纹悬臂管道的振动特性分析,应用等值线图原理进行了悬臂管道的裂纹识别。研究结果表明：本文裂纹模型克服了当前裂纹模型仅针对特定的荷载模式或非空心截面的缺陷,基于等值线图法能有效识别含裂纹悬臂管道的裂纹位置、深度。     

基于Bessel和Meijer-G函数的楔形和锥形悬臂梁振动分析

基于欧拉-伯努利梁理论,利用Lagrange法建立了楔形和锥形截面梁在外激作用下的非线性微分方程.提出了一种基于Bessel函数和Meijer-G函数线性组合的无需迭代及近似截断的振型函数,且该振型函数不依赖于楔形和锥形变截面梁的弯曲振动的运动方程是否为标准的Bessel形式,该方法能快速求解线性基频和模态函数.随后将...     

含非贯穿直裂纹管道的振动特性分析

摘 要：根据线性断裂力学理论和应变能释放原理,推导了管道在轴力、剪力和弯矩等荷载作用下由非贯穿直裂纹引入的附加局部柔度,利用适应性Simpson数值积分编写了局部柔度计算程序,克服了当前方法仅针对特定的荷载模式或非空心截面的缺陷,通过与Naniwadekar等人试验结果进行对比验证本文局部柔度系数的合理性。建立了裂纹管结构的有限元模型,对悬臂裂纹管和简支裂纹管的自由振动特性进行了分析。研究结果表明：裂纹位置、裂纹深度对裂纹管类结构的自振频率影响明显。     

厚度不连续悬臂梁板的自由振动分析

将厚度不连续梁板视为层合板, 分别应用Hamilton 正则方程半解析法建立每一层的线性方程。考虑到每两层连接界面上应力和位移的连续性, 联立各层的方程得到整个结构的特征方程, 其主要的优越性表现为: 控制方程不限制不连续梁板的厚度, 并能适合处理厚度不对称且不连续的层合板。本文中的方法可修改或扩展用来分析加筋压电材料层合板或带有压电材料传感器和驱动器块的板壳等问题。