两端固定超临界轴向运动梁横向平衡位形与振动

研究了超临界速度下,两端固定的轴向运动梁静平衡位形及其分岔,以及横向非线性振动前两阶的固有频率.在超临界范围,轴向运动梁的静平衡位形由直线和对称曲线组成.基于轴向运动梁横向振动的非线性积分-偏微分控制方程,给出了固定边界条件下非平凡静平衡位形的解析表达式,讨论了梁的物理参数对轴向运动临界速度的影响.对于非平凡静平衡位形,经坐标变换,建立超临界轴向运动梁连续陀螺系统的标准控制方程.结合有限差分法以及离散傅立叶变换研究了超临界状态下梁横向振动的前两阶固有频率.并将数值结果与局部线性化后的Galerkin截断结果相比较.     

轴压作用下自由-自由运动梁振动特性研究

针对轴向压力作用下的两端自由运动梁的振动问题,根据Timoshenko梁理论和Hamilton原理建立了梁的横向振动控制方程,通过解析法和微分求积法(DQM)求解了梁的振动特性,分析了轴向压力和运动效应以及轴向力导数和运动加速度对梁固有特性的影响,并对临界载荷、临界速度等的影响因素进行了比较研究。结果表明:轴向压力和运动效应都使得固有频率降低,压力和运动速度的特定组合会导致超临界现象和耦合模态颤振的出现;压力导数和加速度效应都会使得梁的基础频率产生不稳定性;梁的临界载荷随着运动速度增大而变小,临界速度随轴向压力增大而降低。     

中间约束轴向运动梁横向非线性振动

聚焦于中间弹性约束对轴向运动梁横向非线性振动的影响。应用哈密顿原理,建立带有中间弹簧支撑的轴向运动梁的动力学控制方程。通过Galerkin截断方法数值计算了简支边界梯型截面轴向运动梁的固有频率,并数值计算得到梁的稳态响应。着重讨论了中间约束弹簧的刚度、系统的轴向运动速度、不同Galerkin截断阶数对系统固有频率、非线性受迫振动稳态响应的影响。研究发现,中间约束弹簧显著改变轴向运动梁的横向振动特性,而且轴向运动的速度能够改变中间弹簧对系统横向振动的影响。     

基于微分求积法的轴向运动板横向振动分析

研究受面内载荷轴向运动薄板横向振动的运动微分方程,采用微分求积法计算四边简支轴向运动薄板的固有频率和临界速度。分析轴向运动速度、板材料刚度及长宽比对板横向振动固有频率及临界速度的影响。结果发现,随着轴向速度增大,各阶固有频率减小;随着刚度的增大,各阶固有频率增大;当长宽比较小时,轴向运动板可以用梁模型分析。     

黏弹性轴向运动变张力梁非线性动力学

在黏弹性轴向运动梁横向参数振动的非线性动力学行为研究中,首次计入因速度变化引起的、沿梁的径向变化的、轴向变张力的影响。给出描述变张力轴向运动梁横向非线性振动的偏微分—积分控制方程。基于微分求积法给出轴向运动梁横向非线性参数振动的数值解,通过观察梁中点的位移、速度随时间变化的历程,识别轴向运动系统的非线性动力学行为。同时,通过从数值解中提取的相图、Poincaré映射图和频谱分析,考察轴向运动梁横向振动的分岔与混沌特性,揭示了工程应用中的非线性轴向运动系统的混沌动力学行为。     

轴向运动黏弹性夹层板的多模态耦合横向振动

基于薄板小挠度理论和Kelvin-Voigt黏弹性本构方程, 建立了轴向运动黏弹性夹层板横向振动控制方程, 研究了其横向振动特性。采用一阶和二阶Galerkin截断得到夹层板横向振动的特征方程, 讨论了两种夹心层所占总厚度比率下轴向运动速度对其横向振动特性的影响。研究表明: 在未超过临界速度前, 无论一阶还是二阶截断, 在定性描述系统特征上二者相同, 但一阶截断不适合描述轴向运动速度超过临界速度的情形; 对四边简支黏弹性夹层板, 临界速度和发生耦合模态颤振的速度随着夹心层比率的减少逐渐增大。     

考虑非局部效应的纳米梁非线性振动

以弹性理论为基础,建立考虑非局部效应和轴向非线性伸长的两端固支纳米梁物理模型,推导出其动力学方程,计算得到考虑非局部效应和轴向非线性纳米梁的固有频率,研究了考虑非局部效应的纳米梁主谐波共振响应。数值结果表明,非局部效应对两端固支纳米梁固有频率和幅频关系均有影响。     

热冲击作用下轴向运动梁的振动特性研究

研究了两端简支不可移、轴向运动梁在热冲击作用下的横向振动特性,根据Timoshenko梁理论和Hamilton原理建立了梁的横向振动控制方程,采用微分求积法求解了梁的横向振动问题,分析了热冲击和轴向运动效应对梁固有特性的影响。研究发现:热冲击引起的梁的等效热轴力、热弯矩和弹性模量变化三因素中,热轴力对梁固有频率的影响起主导作用,材料的弹性模量变化和热弯矩起次要作用;当热冲击载荷大于或等于梁的临界压力时,达到梁的第一阶失稳模态;热冲击和轴向运动效应都会降低梁的固有频率,它们的联合作用会导致模态之间的耦合现象,使梁更易达到失稳状态。     

固定边界超临界轴向运动梁平面振动频率

通过数值方法研究超临界速度下,两端固定边界的轴向运动梁平面耦合非线性振动固有频率。发展有限差分法,确定在超临界范围轴向运动梁的径向与横向耦合平面内非平凡静平衡位形。基于非平凡静平衡位形,经坐标变换,建立超临界轴向运动梁连续陀螺系统的标准控制方程。运用高阶Galerkin截断,研究超临界运动状态下梁平面振动的固有频率;并研究Galerkin截断阶数对计算结果的影响。     

超临界轴向运动Timoshenko梁横向受迫振动EI北大核心CSCD

研究外部激励作用下,超临界轴向运动Timoshenko梁横向非线性振动的稳态响应。通过对非零平衡位形的坐标变换,从轴向运动Timoshenko梁的横向振动控制方程推导得到超临界速度下受横向外部激励的陀螺系统标准控制方程。运用Galerkin截断法数值研究超临界下轴向运动Timoshenko梁的稳态周期幅频响应关系,并通过与超临界速度下轴向运动Euler-Bernoulli梁的稳态幅频响应曲线进行对比,研究Euler-Bernoulli梁理论的适用范围。     

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。     

Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle

This study presents an analytical method for the forced vibration of an elastically connected double-carbon nanotube system (DCNTS) carrying a moving nanoparticle based on the nonlocal elasticity theory. The two nanotubes are identical and are connected with each other continuously by elastic springs. The problem is also solved numerically by using the Galerkin method and the time integration method of Newmark to establish the reliability of the analytical method. Two sets of critical velocity exist for DCNTS. The closed-form solutions for the dynamic deflections of the two nanotubes are derived for these two sets of critical velocity for the first time in this study. The influences of the nonlocal parameter, aspect ratio, velocity of the moving nanoparticle and the elastic layer between the nanotubes on the dynamic responses are discussed. The study shows that the dynamic behavior of the double-carbon nanotube system is greatly influenced by the nonlocal effects. The dynamic deflections predicted by the classical theory are always smaller than those predicted by the nonlocal theory due to the nonlocal effects. Thus, the classical beam models are not suitable in modeling carbon nanotubes with small aspect ratio, and nonlocal effects should be taken into account. Furthermore, the velocity of the nanoparticle and the stiffness of the elastic layer have significant effects on the dynamic behavior of DCNTS.     

热冲击下轴向运动FGM梁的自由振动分析

基于Timoshenko梁理论研究两端夹紧、一端夹紧一端简支、两端简支三种不同边界条件下的轴向运动功能梯度材料(FGM)梁在热冲击载荷作用下的自由振动响应。利用Hamilton原理推导热冲击下轴向运动FGM梁的自由振动控制微分方程,并采用分离变量法求解一维热传导方程。通过微分求积法(DQM)在梁的长度方向进行离散,将原方程转化为四阶广义特征值问题,求解FGM梁自由振动的无量纲固有频率并进行特性分析。考虑了不同热冲击载荷,不同梯度指数和不同轴向运动无量纲速度对FGM梁自振频率的影响。结果表明:热冲击载荷越大,对降低FGM梁的固有频率的效果越明显;在轴向运动速度和热流输入不改变的情况下,逐渐增大材料梯度指数会使FGM梁的固有频率随之减小;FGM梁对热冲击短时间内有减缓作用,相对于均匀材料一阶失稳所需时间更长,受到热冲击的FGM梁在轴向运动时也更快达到失稳状态。     

Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes

Summary Vibration and buckling of in-plane loaded simply supported double-walled carbon nanotubes were investigated using the nonlocal Timoshenko-beam theory. The influence of in-plane loads on the natural frequencies was determined. The results show that while the natural frequencies decrease with increasing compressive in-plane loads, an increase in frequencies is observed for tension type of in-plane loads. Effects of in-plane loads are more pronounced for lower modes, and some mode changes are observed at critical in-plane loads. A comparison of nonlocal elasticity solutions with local elasticity solutions indicates that the nonlocal effects should be considered for higher modes of vibration of double-walled carbon nanotubes.     

Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory

In this study, the free vibration behavior of circular graphene sheet under in-plane pre-load is studied. By using the nonlocal elasticity theory and Kirchhoff plate theory, the governing equation is derived for single-layered graphene sheets (SLGSs). The closed-form solution for frequency vibration of circular graphene sheets under in-plane pre-load has been obtained and nonlocal parameter appears into arguments of Bessel functions. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, pre-load, mode number and boundary conditions on natural frequencies are investigated. The results are shown that at smaller radius of circular nanoplate, the effect of in-plane pre-loads is more importance.     

Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory

A single-elastic beam model has been developed to analyze the thermal vibration of single-walled carbon nanotubes (SWCNT) based on thermal elasticity mechanics, and nonlocal elasticity theory. The nonlocal elasticity takes into account the effect of small size into the formulation. Further, the SWCNT is assumed to be embedded in an elastic medium. A Winkler-type elastic foundation is employed to model the interaction of the SWCNT and the surrounding elastic medium. Differential quadrature method is being utilized and numerical solutions for thermal-vibration response of SWCNT is obtained. Influence of nonlocal small scale effects, temperature change, Winkler constant and vibration modes of the CNT on the frequency are investigated. The present study shows that for low temperature changes, the difference between local frequency and nonlocal frequency is comparatively high. With embedded CNT, for soft elastic medium and larger scale coefficients (e₀a) the nonlocal frequencies are comparatively lower. The nonlocal model-frequencies are always found smaller than the local model-frequencies at all temperature changes considered.     

Vibration analysis of parabolic shear-deformable piezoelectrically actuated nanoscale beams incorporating thermal effects

Thermoelectric-mechanical vibration behavior of functionally graded piezoelectric (FGP) nanobeams is first investigated in this article, based on the nonlocal theory and third-order parabolic beam theory by presenting a Navier-type solution. Electro-thermo-mechanical properties of a nanobeam are supposed to change continuously throughout the thickness based on the power-law model. To capture the small-size effects, Eringen's nonlocal elasticity theory is adopted. Using Hamilton's principle, the nonlocal governing equations for the third-order, shear deformable, piezoelectric, FG nanobeams are obtained and they are solved applying an analytical solution. By presenting some numerical results, it is demonstrated that the suggested model presents accurate frequency results of FGP nanobeams. The influences of several parameters, including external electric voltage, power-law exponent, nonlocal parameter, and mode number on the natural frequencies of the size-dependent FGP nanobeams are discussed in detail. The results should be relevant to the design and application of the piezoelectric nanodevices.     

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。