基于内流动力学的海洋输油柔性立管鲁棒边界控制

海洋输油柔性立管的振动是引起立管疲劳破坏的主要原因,对其研究边界控制是消除振动疲劳、减少断裂的有效方法.本文引入内流动力学,完善了立管原始无穷维分布参数模型,更好地表达了柔性立管的动力学响应.为抑制柔性立管在内外流激励下的振动奠下基础,本文用Lyapunov直接法对柔性立管系统的稳定性和状态一致有界性进行了证明,设计了边界控制器调节柔性立管的振动,其中控制器使用了符号函数来消除不确定性环境扰动对振动控制效果的影响,提高了系统的鲁棒性.仿真实验表明本文所设计的控制算法有效地减少了柔性立管的振动偏移量.     

Forced vibration analysis of piezoelectric quartz plates in resonance

Quartz is a widely used piezoelectric material and quartz resonators are the primary components in many industrial applications due to the piezoelectric effect. To have a thorough understanding on the vibration characteristics of quartz plates, the experimental measurement of resonant frequencies and mode shapes is indispensable. In this paper, two experimental techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), which are, respectively, full-field and point-wise displacement measurement methods, are used to obtain the out-of-plane vibration characteristics of AT-Cut quartz in real time. The resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time from AF-ESPI method. However, only the resonant frequencies of the out-of-plane vibration modes are determined by the LDV. The cantilever and completely free quartz plates are used in this study and the experimental results are verified by the finite element method (FEM) analysis. The cantilever quartz plates are excited from applying voltage and acoustic waves. Furthermore, three designs of electrode for a quartz plate with free-boundary condition are studied. Excellent agreement between the measured data from the optical method and the numerical results predicted by FEM are found for both resonant frequencies and mode shapes.     

混流式水轮发电机组主轴系统振动特性分析

针对混流式水轮发电机组振动现象严重影响水电站安全运行的问题,应用ANSYS建立主轴系统的有限元模型,分析主轴系统固有频率及振型变化的特点,研究主轴系统的振动特性,并分析主轴系统在激励影响下发生共振的可能性及其振型.研究结果表明,主轴系统在多种外激励作用下,除了产生强迫振动外,还可产生主共振、分数共振等复杂的振动现象.研究结果对进一步研究主轴系统动态特性有一定的参考价值.     

磁浮交通轨排耦合自激振动分析及自适应控制方法

本文针对中低速磁浮交通的轨排自激振动问题, 首先建立了包括轨枕、导轨在内的多跨磁浮轨排动力学模型, 通过理论方法分析轨排的模态振型、频率等关键参数. 其次, 建立了包含一体化电磁铁的悬浮模块的动力学模型, 并与轨排模型结合建立轨排 ? 悬浮模块耦合模型, 分析了耦合系统失稳发生自激振动的原因. 提出了一种带辨识器的自适应振动控制方法, 能够实时辨识轨排的主要动力学参数, 并由此产生自适应振动控制律.相比现有的轨排振动控制方法, 该方法具有更好的稳定性和环境适应性.     

The transformation of the modal equations into the force equations

For discrete, linear elastic systems in free vibration, the existing methods of problem solution employ as input values, the system mass coefficients and either its stiffness or influence coefficients. The output values for these methods are, the system natural frequencies, and corresponding member displacements, which are its mode shapes. By transforming the modal equations into the problem force equations, using the same input values, the output values become the system natural frequencies and the corresponding member forces. Since stresses are most easily calculated from forces, the force equations appear to be ideally suited for engineering design.     

Natural frequencies and mode shapes of thin-walled members

An analytical procedure to estimate both the natural frequencies and mode shapes of thin-walled members is presented using the transfer matrix method. The transfer matrix is derived from the differential equations of the plate panel of thin-walled members. The proposed method gives exact natural frequencies and mode shapes of thin-walled members. Thus the vibration phenomenon of such members can be clarified exactly. Some numerical examples are presented to illustrate the accuracy and efficiency of the proposed method.     

A study on the free vibration of the joined cylindrical–spherical shell structures

The free vibration characteristics of the joined spherical–cylindrical shell with various boundary conditions are investigated. The boundary conditions considered herein are free–free, simply supported–free and clamped–free for the joined cylindrical–spherical shell structures. The Flügge shell theory and Rayleigh’s energy method are applied in order to analyze the free vibration characteristics of the joined shell structure and individual shell components. In the modal test, the I-DEAS test module is used to calculate mode shapes and natural frequencies of the joined shell structure. The natural frequencies and mode shapes are calculated numerically and they are compared with those of the FEM and modal test to confirm the reliability of the analytical solution. The effects of the shallowness of the spherical shell and length of the cylindrical shell to the free vibrational behavior of joined shell structure are investigated.     

Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory

In the present study, nonlinear free and forced vibration of Euler–Bernoulli nanobeam with attached nanoparticle at the free end is investigated based on nonlocal elasticity theory. The effects of the different nonlocal parameters (γ) and mass ratios (α) as well as effects of fixed-free boundary conditions on the vibrations are determined. To obtain the equation of motion of the system, the Hamilton’s principle is employed. The stretching of neutral axis which introduces cubic nonlinearity is included into the equation for deriving nonlinear equation. And also effects of damping and forcing are included into the equations. The approximate solutions of the equations are derived by using the multiple scale method. Fundamental frequencies, frequency shift and mode shapes for the linear problem are estimated for a nonlocal Euler–Bernoulli nanobeam with an attached nanoparticle and graphically represented the frequency shift and mode shapes. Nonlinear frequencies are derived depending on amplitude and phase modulation. Frequency–response curves are drawn for different nonlocal parameters and different modes.

     

Mode coupling in the vibration response of asymmetric buildings

Coupling of the lateral and torsional modes in the vibration response of asymmetric buildings is treated using simple three-dimensional computer models. This study will be useful in predicting the torsional coupling in the earthquake response of the building. The computer models are based on energy methods and assume that each floor is a rigid diaphragm with three degrees of freedom (two lateral and one rotational) and can analyse buildings which are unsymmetrical in plan and/or elevation. To treat various types of asymmetry, buildings which are square, rectangular and L-shaped in plan are considered. In these buildings, the position of the core is varied to obtain different degrees of asymmetry and the consequent coupling of the modes of vibration. Numerical examples are presented where the natural periods of vibration and associated mode shapes are obtained for different degrees of asymmetry. The mode shapes demonstrate the torsional coupling inherent in asymmetric buildings. The relationship between the coupled mode shapes obtained in the free vibration analysis and the anticipated dynamic response is discussed.     

Vibration analysis of composite plate wing

Vibration characteristics, including natural frequencies and mode shapes for various shaped composite wings, are evaluated using finite elements based on the shear deformable theory. The present analysis gives the influence of the sweep angle, the fiber orientation, the aspect ratio, and the taper ratio of a composite wing on the vibration properties. Natural frequencies have been obtained for a composite wing which has symmetric stacking sequences of laminates. Frequency closeness phenomena of different modes can be observed for the negative fiber angles. The present analysis uses eight-node quadrilateral elements which provide very accurate results.     

Design for frequency by the integrated force method

The integrated force method of analysis is extended to calculate frequencies of structures, using the hitherto unexplored concept of “force mode shapes” as the prime variables in vibration analysis. Utilizing the concept of force mode shapes, a direct design method is developed to design structures subjected to frequency constraints. Merits and limitations of the method are examined.A computer programme GIFT is developed for the analysis and frequency limited design of structures. The design part of the program GIFT is limited to discrete structures like spring-mass systems, trusses and beams. Several analysis and design examples (solved using the programme GIFT) are included to illustrate the versatility of the method.     

A system for the dynamic characterization of microstructures

This paper describes a fully automated measurement system designed to evaluate the dynamic characteristics of micromechanical structures (millimeter dimensions). To validate the system, vibration measurements have been carried on two structures-a micromachined silicon cantilever and bridge-and the results are presented. Out-of-plane measurements show that for the cantilever, both the mode shapes and resonant frequencies agree with beam theory predictions. However, for the bridge structure, tension due to boron doping causes a change from beam-like behavior and a more complex model is required. Mode-shapes natural frequencies and modal damping are determined from data obtained by vibrating the structures using a piezoelectric mounting system and deriving the transfer function between the piezodrive voltage and beam vibrational velocity     

Free vibration analysis of mindlin plates with parabolically varying thickness

The free transverse vibration characteristics of rectangular plates, including the effect of transverse shear deformation and rotary inertia, are presented. A method based on the variational procedure in conjunction with the finite difference technique is used to determine the natural frequencies and mode shapes. The convergence characteristics of the present method are studied by varying the thickness parameter and running a comparison with the classical thin plate solutions. The effects of the thickness parameter and taper thickness ratio on the vibration characteristics are studied. The predictions are presented for the simply supported and clamped plates and they are compared with existing solutions based on the thin plate theory.     

An innovative eigenvalue problem solver for free vibration of Euler–Bernoulli beam by using the Adomian decomposition method

This paper deals with free vibration problems of Euler–Bernoulli beam under various supporting conditions. The technique we have used is based on applying the Adomian decomposition method (ADM) to our vibration problems. Doing some simple mathematical operations on the method, we can obtain ith natural frequencies and mode shapes one at a time. The computed results agree well with those analytical and numerical results given in the literature. These results indicate that the present analysis is accurate, and provides a unified and systematic procedure which is simple and more straightforward than the other modal analysis.     

Free vibration analysis of circular cylindrical shells

Determination of the vibrational characteristics of circular cylindrical shells often requires significant computational effort. This paper presents the results of a comprehensive, computer based, numerical investigation of the free vibration of circular cylindrical shells. An analytical procedure which accurately predicts the natural frequencies and radial mode shapes (corresponding to axial wave number and circumferential wave number both equal to one) for a wide range of circular cylindrical shells is developed. The procedure is applicable to shells either with or without a top closure. Several numerical examples are presented which illustrate application of the procedure and verify its accuracy.     

压电谐振驱动三足机器人的平面运动

设计并实现了一类利用压电陶瓷片作动,由三条曲梁足支撑的振动驱动机器人.建立了在一条足共振驱动下机器人水平运动的动力学方程,数值计算解释了摩擦作用下的运动机理,寻找到异性摩擦对运动方向、速度的影响和压电激励频率与运动速度间的关系.通过建立圆弧曲梁控制方程求解圆弧型足面内振动的固有频率及振型,设计了三组不同频率的圆弧曲梁足参数,实验制作了机器人模型,利用压电控制三足间振动的共振切换,实现了预想的三个方向的运动以达到平面运动的效果,实验测量了机器人的运动速度与理论计算吻合得较好.     

A compact method for computing the eigenvalues and eigenvectors of plane frames

Two Fortran computer programs are presented which calculate the eigenvalues and eigenvectors of rigidly jointed plane frames. The eigenvalues are natural frequencies and critical load factors in vibration and buckling problems, respectively, while the eigenvectors are the corresponding mode shapes. The theory is based on the stiffness method of analysis and uses classical (exact) member equations together with an algorithm which ensures that the required eigenvalues are found with certainty. The corresponding eigenvectors are then retrieved by a simple technique which offers improved accuracy over more established methods. The programming style is specifically aimed towards minicomputer application and this is illustrated by annotated listings of the programs, each of which contains just over two hundred Fortran statements. The use of the programs as ‘black boxes’ is fully explained with illustrative examples.     

A dynamic stiffness element for free vibration analysis of composite beams and its application to aircraft wings

The dynamic stiffness matrix of a composite beam that exhibits both geometric and material coupling between bending and torsional motions is developed and subsequently used to investigate its free vibration characteristics. The formulation is based on Hamilton’s principle leading to the governing differential equations of motion in free vibration, which are solved in closed analytical form for harmonic oscillation. By applying the boundary conditions the frequency dependent dynamic stiffness matrix that relates the amplitudes of loads to those of responses is then derived. Finally the Wittrick-Williams algorithm is applied to the resulting dynamic stiffness matrix to compute the natural frequencies and mode shapes of an illustrative example. The results are discussed and some conclusions are drawn. The theory can be applied for modal analysis of high aspect ratio composite wings and can be further extended to aeroelastic studies.     

变截面舵面结构全场瞬态变形测量及振动特性分析

搭建了一套全场非接触应变测量系统,对变截面舵面结构受随机载荷激励作用下的变形及振动特性进行实验研究。实验以2A12铝合金材料制成的变截面舵面结构为试验对象,采用高分辨率的相机记录舵面结构全场清晰的散斑图像,然后利用三维数字图像相关方法对其结构表面的连续变形进行直接测量,同时利用傅里叶变换对采集到的散斑图像进行振动特性分析,获得变截面舵面结构的模态频率和模态振型。为验证非接触测量得到的振动特性结果的准确性,用小质量加速度传感器得到的振动响应信号进行对比。试验结果表明,在0~500Hz的测试频段内,三维数字图像相关方法辨识变截面舵面结构前三阶模态参数与加速度传感器测量结果非常吻合,前三阶固有频率误差在2%以内,阻尼比误差在6%以内,前二阶模态振型均为弯曲模式,第三阶模态振型为弯曲扭转耦合模式,验证了三维数字图像相关的全场振动测量技术的有效性,为高温环境及非线性变截面舵面结构非接触振动测试提供依据。     

An exact solution for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends

In this paper, a new exact solution based on the classical shell theory (CST) for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends is proposed. The present exact solution can be summed up in the following steps: Firstly, the displacement functions are constructed by the governing differential equations with the exact closed form solutions; Then, the artificial spring technology is introduced to simulate the general boundary conditions of the two end edges of shell; Thirdly, the equation for natural frequencies is obtained by means of the method of reverberation-ray matrix (MRRM); Lastly, the vibration results are presented by the modified golden section search (MGSS) algorithm. By comparing the present method with published papers, the accuracy of present method is verified. On the basis of that, some new exact nature frequencies and mode shapes of the cross-ply laminated composite cylindrical shells with various classical boundary conditions and elastic restraints are performed and they can be served as the benchmark data for the future.