轴向运动粘弹性夹层梁的横向振动

研究了小扰度下轴向匀速运动粘弹性夹层梁的振动模态和固有频率.基于Kelvin粘弹性本构方程,建立了轴向运动粘弹性夹层梁横向振动控制方程.分别采用Galerkin截断和复模态分析方法,研究两端简支的粘弹性夹层梁的固有频率和模态函数,讨论了轴向运动速度、夹心层与约束层厚度比、初始轴力等参数对夹层梁固有频率、临界速度及稳定性的影响.     

复模态分析超临界轴向运动梁横向非线性振动

近似解析研究了简支边界条件下超临界轴向运动梁横向非线性自由振动的固有频率和模态函数.采用复模态方法处理控制方程,一个积分偏微分方程.将Galerkin截断思想用于近似处理线性化方程,一个含空间依赖系数的常微分方程.给出了不同截断项数对固有频率的影响.基于8项截断,讨论了系统参数对模态函数的影响.     

分析两端扭转弹簧约束下简支输流管道的动力特性

研究了两端受扭转弹簧约束的简支输流管道的固有频率特性和静态失稳临界流速.根据梁模型横向弯曲振动模态函数,由端部支承和约束边界条件得到了其模态函数的一般表达式.根据动力方程的特征方程,具体分析了约束弹性刚度、流体压强、流速和管截面轴向力等参数对管道固有频率特性和静态失稳临界流速的影响.数值分析表明,约束弹性刚度的增大使管道的固有频率和失稳临界流速明显提高;流体流速、压强和管截面受到的轴向压力的增加使管道的固有频率和失稳临界流速降低.当管道的固有频率和失稳临界流速较低时,可以通过增加端部约束的方法来提高.     

轴向运动复合材料薄壁梁的横向振动分析

研究可轴向运动复合材料薄壁梁的动力学特性.基于VAM（变分渐进法）复合材料薄壁梁理论,采用Euler Bernoulli梁模型并根据Hamilton原理来建立复合材料薄壁梁的动力学方程.应用假设模态法对薄壁梁进行自由振动分析,通过比较研究验证了该建模方法的正确性,并分析了几何参数和物理参数对薄壁梁固有频率的影响.推导了轴向运动复合材料薄壁梁的横向振动方程,借助四阶Runge-Kutta法进行数值计算,研究了不同纤维铺层方式和不同匀速度大小对可轴向运动复合材料薄壁梁横向振动末端位移响应的影响.     

带边角裂纹悬臂Mindlin 板的振动特性研究

本文基于Mindlin板理论,应用Ritz法研究带边角裂纹Mindlin板的振动特性,分析了不同裂纹参数如裂纹位置,裂纹长度,裂纹角度对悬臂Mindlin板的固有频率和模态的影响.利用Ritz法求解固有频率和模态函数,本文构造了一个特殊的模态函数,其模态函数由两部分构成,一部分是用梁函数组合法得到的无裂纹理想完整矩形板的振型,另一部分是利用裂纹尖端奇异性理论,构造描述裂纹附近位移和转角不连续的角函数.通过高精度的数值计算软件Maple得出结果,并与有限元软件ANSYS分析的结果进行对比,验证本文计算结果的准确性.     

基于欧拉 伯努利梁和铁木辛柯梁理论的功能梯度材料模量测定

为测定功能梯度材料的弹性模量和剪切模量,引入梁理论并将梁沿长度方向离散,建立单元平衡方程后可得到弹性模量和剪切模量分布;假设弹性模量为沿长度方向的线性函数或指数函数,用有限元软件仿真计算功能梯度材料梁单元节点处的挠度和转角,然后用插值法构造变形特征函数,并计算得出弹性模量和剪切模量,且计算值与理论值的误差较小.计算结果还表明,采用铁木辛柯梁理论不仅可以得到弹性模量,还可以计算剪切模量,且弹性模量计算结果比用欧拉-伯努利梁计算结果更接近真实值,但铁木辛柯梁理论中需测定转角,对测定过程的要求会更加严格。     

热环境中超临界黏弹性输流管道自由振动分析

基于Euler-Bernoulli梁模型,本文研究了热环境中输流管道在超临界范围内流固耦合自由振动特性.考虑温度增量以及初始轴向拉力作用,在两端简支边界条件下,利用广义Hamilton原理建立输流管道横向振动偏微分-积分控制方程.通过解析方法得到输流管道非平凡静平衡位形及临界流速精确表达式,与微分求积单元法(DQEM)数值结果吻合较好.基于复模态法,结合伽辽金(Galerkin)法离散系统偏微分-积分控制方程,得到热环境下超临界输流管道的模态函数和固有频率.结果表明,温度增量越大,临界流速越小,此时的管道越容易屈曲,但相同流速下超临界管道固有频率越大;初始拉力越大,临界流速越大,相同流速下超临界固有频率越小.该研究可以为热环境中超临界状态下的管道系统振动设计提供理论指导.     

运动车辆梁模型的横向振动频率及模态

将运动车辆的车身模型化为Eder-Bernoulli梁,车轮模型化为梁两端边界处的弹性不等的弹簧,形成半车模型.通过复模态分析法研究平滑路面上移动车体的横向振动特性,给出车体横向振动的频率方程以及模态的表达式,通过数值方法求解系统固有频率以及模态函数.并通过数值算例研究车辆运行速度、车体刚度、轮胎弹性系数对车体横向振动...     

杆在固有振动中的对偶关系

本文研究线弹性均质材料杆的固有振动对偶问题,即两种杆在怎样的截面变化和齐次边界下具有相同固有频率.首先,通过纵向位移和内力的对偶描述,给出两种杆异截面对偶的截面变化条件和边界条件,并将其分类为固定-固定杆与自由-自由杆对偶,固定-自由杆与自由-固定杆对偶等.上述对偶杆具有相同固有频率,而两者的位移振型互为位置坐标的导数.其次,限定两种对偶杆的截面变化相同,给出杆的截面积函数表达式.此时,固定-固定杆与自由-自由杆构成同截面对偶,而固定-自由杆和自由-固定杆的同截面对偶彼此为镜像;等截面杆也具有上述对偶性质.最后,将上述研究推广到材料性质沿轴向变化的变截面杆固有振动对偶问题.文中所有结论均适用于圆轴在齐次边界条件下的扭转固有振动对偶问题.     

变截面粘弹性旋转梁非线性参数振动研究

研究了变截面粘弹性旋转梁的非线性参数振动.基于Kelvin-Voigt粘弹性本构关系,考虑几何非线性建立了变截面粘弹性旋转梁的非线性振动方程,用Galerkin法将其转化为常微分方程.运用多重尺度法得到其幅频响应.用数值方法讨论了转速和轮毂半径对梁固有频率和幅频响应的影响.研究表明:不稳定域随轮毂半径、转速的增大而增大,随锥度的增大而减小.     

Torsional vibrations of composite bars of variable cross-section by BEM

In this paper a boundary element method is developed for the nonuniform torsional vibration problem of doubly symmetric composite bars of arbitrary variable cross-section. The composite bar consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli and are firmly bonded together. The beam is subjected to an arbitrarily distributed dynamic twisting moment, while its edges are restrained by the most general linear torsional boundary conditions. A distributed mass model system is employed which leads to the formulation of three boundary value problems with respect to the variable along the beam angle of twist and to the primary and secondary warping functions. These problems are solved employing a pure BEM approach that is only boundary discretization is used. Both free and forced torsional vibrations are considered and numerical examples are presented to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. The discrepancy in the analysis of a thin-walled cross-section composite beam employing the BEM after calculating the torsion and warping constants adopting the thin tube theory demonstrates the importance of the proposed procedure even in thin-walled beams, since it approximates better the torsion and warping constants and takes also into account the warping of the walls of the cross-section.     

Dynamic stiffness formulation and free vibration analysis of a spinning composite beam

The dynamic stiffness matrix of a spinning composite beam is developed and then used to investigate its free vibration characteristics. Of particular interest in this study is the inclusion of the bending–torsion coupling effect that arises from the ply orientation and stacking sequence in laminated fibrous composites. The theory is particularly intended for thin-walled composite beams and does not include the effects of shear deformation and rotatory inertia. Hamilton’s principle is used to derive the governing differential equations, which are solved for harmonic oscillation. Exact expressions for the bending displacement, bending rotation, twist, bending moment, shear force and torque at any cross-section of the beam, are also obtained in explicit analytical form. The dynamic stiffness matrix, which relates the amplitudes of loads to those of responses at the end of the spinning beam in free vibration is then derived by imposing the boundary conditions. This enables natural frequency calculation of a spinning composite beam at various spinning speeds to be made by applying the Wittrick–Williams algorithm to the resulting dynamic stiffness matrix. The spinning speed at which the fundamental natural frequency tends to zero is the critical speed, which is established for a composite shaft that has been taken from the literature as an example. The results are discussed and some are compared with published ones. The paper concludes with some remarks.     

Nonuniform torsion of multi-material composite bars by the boundary element method

In this paper a boundary element method is developed for the nonuniform torsion of arbitrary constant cross-section multi-material composite bars. The materials have different elasticity and shear moduli and are firmly bonded together. The bar is subjected to an arbitrarily concentrated or distributed twisting moment while its edges are restrained by the most general linear torsional boundary conditions. Since warping is prevented, beside the Saint-Venant torsional shear stresses, the warping normal stresses are also computed. Two boundary value problems with respect to the variable along the beam angle of twist and to the warping function with respect to the shear center are formulated and solved employing a BEM approach. Both the warping and the torsion constants are computed by employing an effective Gaussian integration over domains of arbitrary shape. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The contribution of the normal stresses due to restrained warping is investigated.     

Effect of boundary conditions on natural frequencies for rotating composite cylindrical shells with orthogonal stiffeners

The effect of the boundary conditions on the natural frequencies for rotating composite cylindrical shells with the orthogonal stiffeners is investigated using Love’s shell theory and the discrete stiffener theory. The frequency equation is derived using the Rayleigh–Ritz procedure based on the energy method. The considered boundary conditions are four sets, namely: (1) clamped–clamped; (2) clamped–simply supported; (3) clamped–sliding; and (4) clamped–free. The beam modal function is used for the axial vibration mode and the trigonometric functions are used for the circumferential vibration mode. The composite shells are stiffened with uniform intervals and the stiffeners have the same material. By comparison with the previously published analytical results for the rotating composite shell without stiffeners and the orthogonally stiffened isotropic cylindrical shells, it is shown that natural frequencies can be determined with adequate precision.     

三阶剪切变形板的振动特性研究

对于中厚板或层合板而言,横向剪切变形的影响是显著的,采用三阶剪切变形理论比采用经典薄板理论和一阶剪切变形理论能更好的满足精度的要求,而且能更好地描述板的剪切变形和剪应力沿厚度方向的分布情况.本文用解析的方法研究了简支、自由和固定三种边界条件的任意组合下三阶剪切变形板的自由振动问题.首先应用哈密顿原理建立自由振动方程,再通过引入中间变量使得原来耦合的自由振动方程得到解耦和简化,基于分离变量法,利用边界条件得到基函数的表达式,利用Rayleigh-Ritz法,求得三阶剪切变形板在任意边界条件下的固有频率和振型.本文得到的结果可以为厚板在工程中的应用提供理论依据,具有较高的工程实际应用价值.     

LSFD method for accurate vibration modes and modal stress-resultants of freely vibrating plates that model VLFS

The Ritz method and some finite element formulations fail to furnish accurate modal stress-resultants for vibrating plates with free edges, even though the natural frequencies and mode shapes are accurately obtained. For example, by using the Ritz method, it was found that the modal twisting moments and shear forces violate the natural boundary conditions and that they contain erroneous “oscillations”. This paper presents the least squares finite difference (LSFD) method for solving the freely vibrating plate problem. It will be shown herein that the modal stress-resultants obtained by the LSFD method satisfy the natural boundary conditions at the free edges without any oscillations.     

Boundary perturbation method applied to optimal plastic design of beams under concentrated moment and distributed loadings

The paper applies the boundary perturbation method (BPM) to optimal plastic design under bending with considerable shear effects. This method uses expansion of stress components and of the unknown boundary into power series of a small parameter. In the present paper the small parameter α represents the effects of shear. The shape is described by a power series resulting from boundary conditions. The loading of the cantilever beam consists of a concentrated moment and distributed loading regarded as a perturbing factor. The material of the beam is perfectly plastic, subject to the Huber–Mises–Hencky yield condition. The beam is in the plane stress state.     

Macro-element analysis of skewed and triangular orthotropic thin plates with beam boundaries

A generalized macro-flexibility analysis of stiffened orthotropic skewed and triangular thin plates with beam stiffened boundaries subjected to bending and stretching is presented. The proposed method accounts for minimized number of elements in a domain, i.e. the element size is independent of the final results. This is accomplished by satisfying the equilibrium and compatibility conditions along the nodal lines interconnecting contiguous elements. The solution form and shape functions of element shapes are a combination of Fourier series and polynomials with undetermined coefficients. To obtain a solution of a general domain, the orthotropic triangular and parallelogram macro-plate elements with edge beams, satisfying moment and shear equilibrium conditions along nodal lines, were assembled and analyzed by utilizing compatibility of deflection and slope. The results from the proposed methodology were compared to the ones from the finite element method. Also, the convergence was checked by increasing the number of harmonics. The study indicates that good convergence is observed within the first four harmonics.     

Solution of non-uniform torsion of bars by an integral equation method

In this paper, a boundary element method (BEM) is developed for the non-uniform torsion of simply or multiply connected cylindrical bars of arbitrary cross-section. The bar is subjected to an arbitrarily distributed twisting moment while its edges are restrained by the most general linear torsional boundary conditions. Since warping is prevented, besides the Saint-Venant torsional shear stresses, the warping normal stresses are also computed. Two boundary value problems with respect to the variable along the beam angle of twist and to the warping function are formulated and solved employing a BEM approach. Both the warping and the torsion constants are computed by employing an effective Gaussian integration over the domains of arbitrary shape. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The contribution of the normal stresses due to a restrained warping is investigated, by numerical examples, with great practical interest.