黏弹性三参数地基梁横向自由振动

将复模态方法推广至地基梁系统的振动分析中,研究了三参数描述的黏弹性Pasternak地基梁的横向振动特征,得到不同边界条件下的频率方程的近似解析式以及模态函数表达式。采用数值方法近似求解复模态分析得到的超越方程,并运用微分求积方法数值加以验证。通过具体算例,分析了边界条件、刚度系数以及地基黏性系数等对固有频率和模态函数的影响。研究结果表明,微分求积法的数值解与复模态的近似解析解吻合的很好。     

磁场作用下轴向运动功能梯度Timoshenko梁的振动特性

轴向运动结构的工程振动问题一直是动力学领域中的重要课题之一。为了更全面地分析工程中的振动,针对磁场作用下轴向运动功能梯度Timoshenko 梁的振动特性展开论述。基于梁的动力学方程组和相应的简支边界条件,应用复模态方法,得到不同参数时固有频率和衰减系数与轴向运动速度的对应关系。采用微分求积法分析磁场作用下前四阶固有频率和衰减系数随轴向运动速度的变化,并与复模态方法的结果进行对比验证。数据结果表明复模态方法得到的结果是精确解析解。衰减系数呈现不对称性,耦合固有频率呈现分离性。随着轴速、磁场强度和功能梯度指数的增大,梁的固有频率减小;随着支撑刚度参数的增大,梁的固有频率增大。     

黏弹性Pasternak地基梁振动的复模态分析

运用复模态分析研究了有限长黏弹性Pasternak地基梁的振动特性,将梁的振动方程写成状态方程,利用复模态的正交性解耦为常微分方程组,得出复频率和复模态及任意初始条件下外激励的响应。通过两个具体算例对比,分析了简支边界条件下的Pasternak地基梁的固有频率和模态函数的特征,并通过文中给出的复模态函数,计算了两种典型外激励作用下的动力响应。     

轴向受载粘弹性Ｔｉｍｏｓｈｅｎｋｏ梁横向自由振动

用复模态分析方法研究了在两端简支和固支边界下,轴向受载粘弹性Ｔｉｍｏｓｈｅｎｋｏ梁自由振动的固有频率、衰减系数和模态函数的特性,给出了模态函数的正交性条件。通过数值算例,讨论了长宽比、轴力和粘弹性系数对梁的固有频率、衰减系数和模态函数的影响。数值结果表明增加轴力使梁的固有频率变大、模态函数幅值变小,但衰减系数变化不明显;粘弹性系数的增大对梁的固有频率与模态函数幅值影响较小,而衰减系数明显增大。     

Winkler地基上修正Timoshenko梁振动分析

利用Bernoulli-Euler梁理论建立的弹性地基梁模型应用广泛,但其在高阶频率及深梁计算中误差较大,利用修正的Timoshenko梁理论建立新的弹性地基梁振动微分方程,由于其在Timoshenko梁的基础上考虑了剪切变形所引起的转动惯量,因而具有更好的精确度。利用ANAYS beam54梁单元进行振动模态的有限元计算,所求结果与理论基本无误差,从而验证了该理论的正确性。基于修正Timoshenko梁振动理论推导出了弹性地基梁双端自由-自由、简支-简支、简支-自由、固支-固支等多种边界条件下的频率超越方程及模态函数。分析了弹性地基梁在不同理论下不同约束条件及不同高跨比情况下的计算结果,从而论证了该理论计算弹性地基梁的适用性。分析了不同弹性地基梁理论下波速、群速度与波数的关系。得到了约束条件和梁长对振动模态及地基刚度对振动频率有重要影响等结论。     

黏弹性Pasternak地基上两端简支的Timoshenko梁横向自由振动特性解析解

地基梁的振动特性在工程领域及科学界备受关注。将黏弹性Pasternak地基与Timoshenko梁进行组合,对地基梁横向自由振动特性进行研究。首先,基于回传射线矩阵法,推导出复系数一元四次的频率方程,并对其进行求解得到Pasternak地基上两端简支的Timoshenko梁的自振频率及衰减系数的解析解;然后,根据单一局部坐标系下的边界条件推导了模态函数解析表达式,进一步根据正交归一化条件对未知参数进行求解。最后,通过具体算例验证了基于回传射线矩阵法所得的黏弹性Pasternak地基上Timoshenko梁横向自由振动特性解析解的正确性。     

Winkler地基上有限长梁非线性自由振动

基于经典Winkler地基模型及Euler-Bernoulli梁理论,考虑梁的几何非线性效应,运用Newton 第二定律建立了弹性地基上有限长梁的非线性运动方程.采用Galerkin 方法对运动方程进行一阶模态截断,进而利用多尺度法求得了该系统自由振动的一阶近似解.揭示了两端简支梁的非线性自由振动特性,分析了弹性模量、长细比及地基刚度系数等参数对系统固有频率的影响.并通过该系统的位移时程曲线,分析了阻尼对弹性地基上梁运动特性的影响.     

受初应力作用的轴向运动功能梯度梁的动力学分析

基于Euler梁模型研究了初始应力作用下轴向运动功能梯度材料梁的横向振动问题。假设材料性质沿梁的厚度方向按幂指数形式连续变化,利用Hamilton原理建立了系统的控制方程,应用复模态法求得了其固有频率和模态函数,接着分析了轴向运动速度、梯度指数、初应力大小等因素对梁的动力响应的影响。结果表明:梯度指数和轴向速度的增大都会导致固有频率降低,轴向初应力的增大则使得固有频率升高。     

含非贯穿直裂纹输流管道振动与模态功率流分析

针对含非贯穿直裂纹输流管道的振动与模态功率流进行研究，将输流管道以Euler-Bernoulli梁模型建模并据此推导其弯曲振动方程，采用断裂力学方法将裂纹模拟成无质量的转动弹簧，用波动法分析含裂纹输流管道的自由振动特性。通过计算结果与相关文献对比验证了该方法的可靠性。探讨裂纹位置、深度以及管内流速对固有频率的影响。基于模态功率流的概念进行算例分析，讨论裂纹位置、深度以及振动模态对模态功率流的影响，研究表明，裂纹处的模态功率流曲线产生突变，裂纹位置与深度和模态功率流密切相关。     

考虑质量偏心Timoshenko梁的弯-纵耦合固有振动特性研究

针对有限元法等数值方法较难处理的质量偏心梁问题,考虑质心、形心不重合情形下的弯-纵耦合效应,建立了有偏心Timoshenko梁弯-纵耦合振动的数学模型,推导了相应的特征方程。进而给出了若干偏心工况下Timoshenko梁弯-纵耦合振动的解析表达式,并探讨了偏心率和典型边界条件对纵向和弯曲振动固有频率和模态振型的影响规律。分析结果表明,固有频率随着偏心率的增大而减小,且质量偏心对纵向振动的影响较弯曲振动更为明显。     

The vibrations of pre-twisted rotating Timoshenko beams by the Rayleigh–Ritz method

A modeling method for flapwise and chordwise bending vibration analysis of rotating pre-twisted Timoshenko beams is introduced. In the present modeling method, the shear and the rotary inertia effects on the modal characteristics are correctly included based on the Timoshenko beam theory. The kinetic and potential energy expressions of this model are derived from the Rayleigh–Ritz method, using a set of hybrid deformation variables. The equations of motion of the rotating beam are derived from the kinetic and potential energy expressions introduced in the present study. The equations thus derived are transmitted into dimensionless forms in which main dimensionless parameters are identified. The effects of dimensionless parameters such as the hub radius ratio, slenderness ration, etc. on the natural frequencies and modal characteristics of rotating pre-twisted beams are successfully examined through numerical studies. Finally the resonance frequency of the rotating beam is evaluated.     

经典边界条件黏弹性Pasternak地基上Bernoulli-Euler梁横向自振特性分析

自振特性在结构的动力分析中具有重要的意义。将回传射线矩阵法(MRRM)推广到地基梁自振特性的研究中,通过节点力平衡和位移协调方程及对偶局部坐标系下单元相位关系,建立两端简支、两端自由、两端固支、简支-自由、简支-固支及固支-自由这六种边界条件下黏弹性Pasternak地基上的Bernoulli-Euler梁的回传射线矩阵,进而得到其频率方程。根据单一局部坐标系下的边界条件,推导出模态函数解析表达式,进一步根据正交归一化条件求解模态函数表达式中的未知参数。通过具体算例验证了回传射线矩阵法求解的正确性,并对不同边界条件下的自振频率、衰减系数及模态函数进行了分析。为黏弹性地基梁的振动特性研究提供理论基础。     

Viscoelastic Timoshenko beam theory

The concept of elastic Timoshenko shear coefficients is used as a guide for linear viscoelastic Euler-Bernoulli beams subjected to simultaneous bending and twisting. It is shown that the corresponding Timoshenko viscoelastic functions now depend not only on material properties and geometry as they do in elasticity, but also additionally on stresses and their time histories. Possible viscoelastic definitions are formulated and evaluated. In general, the viscoelastic relations are sufficiently complicated so that the elastic-viscoelastic correspondence principle (analogy) cannot be applied. This is particularly true for, but not limited to, elastic shear coefficients which are Poisson ratio dependent. Expressions for equivalent viscoelastic Timoshenko shear functions must, therefore, be derived de novo on a case by case basis, taking in to account specific relaxation moduli, stresses, temperatures and their time histories. Thus the elastic simplicity and generality is lost and hence rendering the use of viscoelastic Timoshenko shear functions as highly impractical. Consequently, it is necessary to directly solve the coupled viscoelastic beam governing relations for bending and twisting deflections by using appropriate solution protocols as discussed herein.     

On the response of a timoshenko beam under initial stress to a moving load

When an axial compressive force is present, the wavelength of the propagating free waves in a beam rapidly decreases. The conventional Euler-Bernoulli beam equations are often not adequate for determining dynamic behavior of the moving load on a beam supported on an elastic foundation when initial axial stress is present. Equations derived by Sun for the Timoshenko beam with initial axial stress (based on Trefftz's theory), form the basis of this investigation. Analytical solutions are presented for deformations of the beam both with and without damping. Expressions of the critical velocity as a function of initial axial stress and foundation modulus parameters, are obtained for the Timoshenko beam. Critical velocities of the Timoshenko beam, with and without axial stress, are compared with that obtained using Euler-Bernoulli beam formulation. Some significant agreements and disagreements in the behaviors of the two systems are described.     

Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

Structural elements supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass system and Bernoulli-Euler multi-span beams carrying multiple spring-mass systems are plenty, but on Timoshenko multi-span beams carrying multiple spring-mass systems is fewer. This paper aims at determining the natural frequencies and mode shapes of a Timoshenko multi-span beam. The model allows to analyse the influence of the shear effect and spring-mass systems on the dynamic behaviour of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The natural frequencies of Timoshenko multi-span beam calculated by using secant method for non-trivial solution are compared with the natural frequencies of multi-span beam calculated by using Bernoulli-Euler Beam Theory (EBT) in literature; the mode shapes are presented in graphs.     

Vibration of nonclassical shear beams with Winkler-Pasternak-type restraint

Transverse vibration of the shear beams containing rotary inertia and with a two-parameter elastic foundation is studied. Using asymptotic analysis of Timoshenko beam theory, we derive explicit characteristic equations of the nonclassical shear beams with Winkler-Pasternak elastic restraint and with both ends linked to translational and rotational springs. The condition of the nonclassical shear beams reducing to the classical ones is found. Natural frequencies of the nonclassical modes are evaluated for free- and pinned-elastically restrained shear beams with or without bracing. The influences of elastic restraint stiffness and rotary inertia on the natural frequencies are discussed. Some extreme cases can be recovered from the present. The obtained results are helpful in the design of a tall frame building.