磁场对黏弹性基体上变截面纳米梁振动特性的影响分析EI北大核心CSCD

针对磁场影响下的黏弹性基体上变截面纳米梁进行了动力学建模及振动特性影响分析。基于非局部欧拉梁理论、Kelvin黏弹性地基模型及麦克斯韦关系式,建立了系统的振动控制方程。通过联合传递函数法和摄动法对所建振动控制方程进行求解,得到了任意边界条件下变截面纳米梁的固有频率。在此基础上,系统地分析了非局部参数、磁场强度、松弛时间、锥度系数等对阻尼频率和阻尼比的影响情况。结果表明,所建的动力学模型在研究受磁场影响下的黏弹性基体上变截面纳米梁的振动特性问题准确有效。     

基于格林函数正交各向异性切口板自由振动特性分析

正交异性板因重量轻、承载能力强等优点而被广泛运用于工程结构。基于格林函数,结合新兴的近场动力学微分算子(peridynamic differential operator, PDDO),提出一种分析正交各向异性板自由振动特性的方法。首先,将振动控制方程中的位移函数假设为含格林函数的一阶积分形式;其次,将线性四阶偏微分方程分别在切口板的径向和周向离散成代数方程;最后,通过PDDO构造插值函数表示径向和周向非公共离散点位移,建立自由振动广义特征方程,获得正交各向异性切口板自振频率及振型,证明了该方法的准确性,并分析切口几何参数对结构振动特性的影响规律,为板壳结构设计提供支撑。     

弹性压应力波下轴向功能梯度变截面梁动力压曲稳定分析

基于微元法以及能量守恒原理,导出了轴向功能梯度变截面梁屈曲微分控制方程及应力波波前附加边界条件,研究了轴向功能梯度变截面梁屈曲与压应力波耦合动力屈曲问题。采用较为简单的数值方法,即将位移函数按Taylor级数或是Chebyshev多项式展开,从而将轴向功能梯度变截面梁屈曲问题的变系数微分控制方程转化为含参量的线性代数方程组,进而得到了含时间参量的动力屈曲问题特征方程,随后对轴向功能梯度变截面梁动力屈曲问题进行了数值研究,探讨了变截面和材料不均匀性对系统屈曲临界力参数的影响。研究表明,该数值方法具有很好的精度和收敛性。     

传递函数法在非局部弹性梁动力学分析中的应用

采用传递函数方法进行了非局部弹性梁的动力学分析。非局部弹性梁内一点的应力与梁某一区域内任意一点的应变均有关系。本文基于Eringen的非局部弹性积分型本构关系,采用幂指数型核函数,利用Laplace变换导出梁的四阶偏微分形式振动方程,通过定义状态向量,将控制方程化为一阶微分方程组,并采用传递函数方法进行了求解,针对两种边界条件给出了非局部弹性梁的固有频率和固有振型。结果表明,同阶频率下,非局部弹性梁的频率比局部梁的频率低,振型基本一致。     

磁场对黏弹性基体上变截面纳米梁振动特性的影响分析

针对磁场影响下的黏弹性基体上变截面纳米梁进行了动力学建模及振动特性影响分析。基于非局部欧拉梁理论、Kelvin黏弹性地基模型及麦克斯韦关系式,建立了系统的振动控制方程。通过联合传递函数法和摄动法对所建振动控制方程进行求解,得到了任意边界条件下变截面纳米梁的固有频率。在此基础上,系统地分析了非局部参数、磁场强度、松弛时间、锥度系数等对阻尼频率和阻尼比的影响情况。结果表明,所建的动力学模型在研究受磁场影响下的黏弹性基体上变截面纳米梁的振动特性问题准确有效。     

完全弹性支承变截面梁动力特性半解析解

基于Bernoulli-Euler梁理论对直接模态摄动方法进行改进,建立求解完全弹性支承变截面梁振动方程的半解析方法。改进摄动法(IPM)在等效等截面完全弹性支承梁的模态空间内将变截面简支、连续梁的变系数微分方程组转化为非线性代数方程组,获得完全弹性支承变截面梁动力特性的半解析解;推导弹性边界条件下系数Δkki的具体计算公式。算例分析表明,改进摄动法计算精度高、收敛速度快,可有效考虑弹性支承对结构动力特性影响;据振型的对称性给出完全弹性支承变截面对称梁动力特性的简便计算方法(SIPM);研究支座出现损伤对变截面简支梁桥自振频率影响。     

含裂纹梁自由振动分析

研究含常开裂纹矩形截面梁的自由振动问题.通过一计及裂纹对粱局部柔度影响的无质量扭簧模拟裂纹所在截面,建立起与含裂纹梁等效的力学模型;基于完整梁自由振动方程的基本解,推导出含裂纹梁的传递矩阵;以简支梁和悬臂梁为例,结合具体的边界条件,导出它们相应的频率方程.基于泰勒展开,给出求解该频率方程的一种迭代算法,能够简便地计算含裂纹梁的固有频率.     

复合材料变截面旋转薄壁悬臂梁自由振动分析

基于拉格朗日方程推导出复合材料封闭变截面旋转薄壁梁的自由振动方程。与基于哈密顿原理的动力学建模方法相比,该文所采用的方法更为简洁。此外,在薄壁梁的结构模型中还考虑除横向剪切外的扭转、拉伸和弯曲引起的翘曲,具有考虑翘曲因素多的特点。给出了两种刚度配置下的变矩形截面旋转悬臂直梁的自由振动方程简化形式及其相应的迦辽金法求解的固有频率。基于大型通用有限元软件ANSYS,计算了薄壁变截面旋转悬臂梁的固有频率,并且与迦辽金法的求解结果进行了对比。分析了复合材料的弹性耦合、铺层角度、截面变化和旋转速度对薄壁梁的自由振动的影响。     

复合材料封闭变截面薄壁梁自由振动分析

摘要：基于拉格朗日方程建立了复合材料封闭变截面薄壁梁的自由振动微分方程,给出了两种刚度配置下的变矩形截面悬臂直梁的自由振动方程简化形式及其相应的迦辽金法求解的固有频率。基于大型通用有限元软件ANSYS,计算了薄壁变截面悬臂梁的固有频率,并且与迦辽金法的求解结果进行了对比。分析了复合材料的弹性耦合,铺层角度和截面变化对薄壁梁的自由振动的影响。     

黏弹性基体中变截面挠曲电Timoshenko纳米梁振动特性研究EI北大核心CSCD

以黏弹性基体中的Timoshenko纳米梁为研究对象,综合考虑非局部效应、截面非均匀性、压电效应和挠曲电效应的影响,建立了变截面挠曲电纳米梁的自由振动控制方程,基于摄动理论给出了典型边界条件下结构自由振动控制方程的传递函数求解方法,较系统研究了非局部参数、截面非均匀性、挠曲电系数以及基体黏弹性对结构振动特性的影响规律。结果表明:增大截面锥度能减小结构固有频率对非局部效应的敏感程度,并带来结构临界阻尼系数的减小;增大非局部参数能削弱结构固有频率对截面锥度的敏感程度;增大切向挠曲电系数f_(3131)可削弱结构对横向挠曲电系数f_(3131)的敏感程度,而增大横向挠曲电系数f_(3131)却增加结构对切向挠曲电系数f_(3131)的敏感程度。相关研究成果可为挠曲电纳米梁在俘能器中的推广应用提供理论基础。     

一类变截面梁横向自由振动的精确解析解

本文研究了一类变截面梁的横向自由振动问题，半径按抛物线变化的圆形变截面梁以及高度按抛物线变化而宽度接任意次幂函数变化的矩形变截面梁是这类梁的两个典型特例。求得了其横向自由振动的精确解析解。解的形式与楔形梁完全不同，是一以幂函数表示的初等函数。本文最后给出了两个算例。     

Vibration and buckling of beam-columns subjected to non-uniform axial loads

The small-displacement free vibration of elastic Euler-Bernoulli beams subjected to non-uniform axial forces and the buckling of elastic columns are both analysed by means of various types of beam finite elements. The procedure incorporates beams and columns of varying cross-sections, such as linear tapers, inhomogeneous beams and columns, distributed axial forces, elastic end and interior restraints and point masses with linear and rotary inertias. All of these topics individually or in some combinations have been analysed by others. The purpose of this paper is to bring together under a single umbrella the various problems studied by others, and to provide the solution to one problem apparently not yet solved—the buckling and vibration of tapered columns under non-uniform axial thrust. The mass, stiffness and geometric stiffness matrices for the standard beam element are fully written out for direct incorporation into existing finite element programs. A FORTRAN subroutine for generating these matrices, and those for various higher-order beam elements, is also provided.     

Free Vibration Analysis of Generally Layered Composite Beams with Arbitrary Boundary Conditions

A hyperbolic shear deformation theory is used for the free vibration analysis of generally layered composite beams with arbitrary boundary conditions. The variationally consistent governing differential equations and boundary conditions are derived by employing Hamilton's principle. The dynamic stiffness method is applied to calculate the vibration frequencies of the laminated beams with the help of Wittrick–Williams algorithm. Examples of application of the hyperbolic shear deformation theory for the free vibration analysis of the laminated beams with a couple of different boundary conditions are presented. The present results are compared to the numerical solutions and experimental results available in the literature.     

Exact Solutions and Mode Transition for Out-of-Plane Vibrations of Nonuniform Beams with Variable Curvature

The two coupled governing differential equations for the out-of-plane vibrations of non-uniform beams with variable curvature are derived via the Hamilton's principle. These equations are expressed in terms of flexural and torsional displacements simultaneously. In this study, the analytical method is proposed. Firstly, two physical parameters are introduced to simplify the analysis. One derives the explicit relations between the flexural and the torsional displacements which can also be used to reduce the difficulty in experimental measurements. Based on the relation, the two governing characteristic differential equations with variable coefficients can be uncoupled into a sixth-order ordinary differential equation in terms of the flexural displacement only. When the material and geometric properties of the beam are in arbitrary polynomial forms, the exact solutions with regard to the outof- plane vibrations of non-uniform beams with variable curvature can be obtained by the recurrence formula. In addition, the mode transition mechanism is revealed and the influence of several parameters on the vibration of the non-uniform beam with variable curvature is explored.     

Dynamic analysis of partial-interaction composite beams

The state-space method is used to investigate the dynamic behavior of partial-interaction composite beams. The state-space formula is properly established via selecting the appropriate state variables. The characteristic equations of frequency and the corresponding modal shapes of free vibration under generalized boundary conditions are then obtained. Based on the state-space formula and the concept of symplectic inner product, a new route is proposed to prove the orthogonality of vibration modes of composite beams under generalized boundary conditions. By virtue of mode superposition method, we obtain the solution of the inhomogeneous equation for forced vibration and the dynamic response of the partial-interaction composite beams subjected to a uniformly distributed pulse load, a uniformly distributed step load or a moving constant force. Finally, some numerical examples are presented and compared with those available in the literature to validate the present method. The effect of the rigidity of shear connector on dynamic responses of a composite beam under moving constant force is discussed.     

变截面变曲率梁振型的有限元超收敛拼片恢复解和网格自适应分析

该文提出变截面变曲率梁振型的有限元后处理超收敛拼片恢复方法,建立各阶振型的超收敛解,并基于振型超收敛解进行变截面曲梁面内和面外自由振动的自适应分析。在位移型有限元后处理阶段,引入超收敛拼片恢复方法和高阶形函数插值技术,得到振型(位移)的超收敛解。利用振型超收敛解估计当前网格下振型有限元解的能量模形式下的误差,并指导网格进行自适应细分加密分析,获得优化的网格和满足预设误差限的高精度解答。数值算例表明该算法适于求解不同曲线形态、多类边界条件、变截面、变曲率形式的曲梁面内和面外自由振动连续阶频率和振型,解答精确、分析过程高效可靠。     

Vibration analyses of laminated composite beams using refined higher-order shear deformation theory

The objective of the paper is to analyze the free vibration of laminated composite beams using a refined higher-order shear deformation theory. The influences of parabolic transverse shear strain, transverse normal strain and Poisson effect are included in the present formulation. The governing differential equations of motion for coupled vibrations of laminated beams are derived using the Hamilton’s principle. In the case of simply supported composite beams, the closed-form solutions for the natural frequency of free harmonic vibration are obtained. The correctness and accuracy of the present theory are validated by comparing the present results with those previously published in the literature and ANSYS solutions.     

DQEM for free vibration analysis of Timoshenko beams on elastic foundations

 A differential quadrature element method (DQEM) based on first order shear deformation theory is developed for free vibration analysis of non-uniform beams on elastic foundations. By decomposing the system into a series of sub-domains or elements, any discontinuity in loading, geometry, material properties, and even elastic foundations can be considered conveniently. Using this method, the vibration analysis of general beam-like structures is to be studied. The governing equations of each element, natural compatibility conditions at the interface of two adjacent elements and the external boundary conditions are developed in a systematic manner, using Hamilton's principle. The present DQEM is to be implemented to Timoshenko beams resting on partially supported elastic foundations with various types of boundary conditions under the action of axial loading. The general versality, accuracy, and efficiency of the presented DQEM are demonstrated having solved different examples and compared to the exact or other numerical procedure solutions. Received: 11 October 2002/Accepted: 26 November 2002     

热载荷作用下嵌入SMA丝复合材料梁的横向自由振动

基于形状记忆合金Brinson一维热力学本构方程,采用复合材料细观力学分析方法,建立了热载荷作用下嵌入SMA丝复合材料梁的一维热弹性本构关系。其次利用Euler-Bernoulli梁的轴线可伸长几何非线性理论和自由振动理论,建立了嵌入SMA丝复合材料梁在均匀升温场内自由振动的动力学控制方程,导出了热过屈曲构形附近嵌入SMA丝复合材料梁微幅横向自由振动的模型。最后通过打靶法求解了两端固定约束条件下嵌入形状记忆合金丝复合材料梁在加热过程中的振动响应,获得了梁的前四阶固有频率在不同SMA相对体积含量时随温度变化的特征关系曲线。数值结果表明,SMA丝相变过程中的回复应力和弹性模量变化对梁在过屈曲前后的各阶固有频率均有影响,是实现梁自振频率主动控制的一种有效方法。     

Orthogonal Tapered Beam Functions in the Study of Free Vibrations for Non-uniform Isotropic Rectangular Plates

A new invented Orthogonal Tapered Beam Functions (OTBFs) have been introduced in this paper and used in accordance with the Rayleigh-Ritz method to determine the natural frequencies and mode shapes of the non-uniform rectangular isotropic plates with varying thickness in one or two directions. The generation of the OTBFs is based on the static solution of a one-dimensional beam problem subjected to constant applied load, and then extends to an orthogonal or orthonomal infinite set of admissible functions by performing the three-term recurrence scheme. A wide range of non-uniform rectangular plate whose domain is referenced by a so-called truncation factor and thickness variation is presented by the so-called taper factor is investigated in the present study in order to practice the validity and efficiency of the proposed methodology. Following the Levy approach, the fourth order differential equation governing the free vibration of non-uniform isotropic plate can be transferred into an 8th order eigenfrequency equation by inserting the OTBFs as shape functions. Three different combinations of clamped, simply-supported and free boundary conditions are imposed around the non-uniform plate and the aspect ratio which indicates the width over the length of the rectangular plate is ranging from half to two. The effects of taper factor together with the truncation factor, boundary condition and aspect ratio on the natural frequencies of free vibration are demonstrated for the first few modes by using the finite terms approximation of the proposed admissible functions. A general computer program has been implemented to solve the eigenfrequency equation, some numerical results are tabulated and comparisons of the results with those available in literature are also presented.