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。     

功能梯度材料梁在后屈曲构型附近的自由振动

基于轴线可伸长杆的几何非线性理论,建立了由陶瓷和金属两种材料组成的功能梯度(FGM)梁在轴向载荷作用下后屈曲横向自由振动的精确模型,采用打靶法数值求解了一端可移简支一端固定的功能梯度梁在后屈曲附近的小振幅自由振动,获得了线性振动的响应,给出了不同梯度指标下FGM梁前三阶固有频率与载荷之间的特征关系曲线.数值结果表明,屈曲前各阶频率随轴向力的增加而降低,而屈曲后轴向力对各阶频率影响不同     

轴向受压中间支承梁的横向振动和稳定性

研究了一端固支且自由端轴向受压具有中间支承梁的横向振动和稳定性。利用边界条件推导了此种梁频率方程及分段振型函数的解析表达式。根据频率方程讨论了中间支承位置变化对梁固有频率的影响。应用Ritz-Galerkin截断方法,采用梁的前四阶振型对梁的运动微分方程进行离散化处理,讨论了梁在各个中间支承位置处的失稳形式。发现了在梁上存在一个特殊的中间支承位置ξl,当中间支承位置ξbξl时,随着压力p从零开始增加,梁先发生颤振失稳,当中间支承位置ξbξl时,则梁先发生发散失稳,而在中间支承位置ξl处,梁由颤振失稳跳跃到发散失稳。     

轴向运动梁在轴向载荷作用下的动力学特性研究

研究了轴向运动Timoshenko梁在轴向载荷作用下的振动特性。首先通过考虑轴向拉压载荷作用,根据Timoshenko梁理论和Hamilton原理建立了梁的横向振动控制微分方程,推导了简支-简支边界条件下的梁的无量纲频率随轴向载荷的变化关系,采用新的无量纲化形式消除了无载荷作用下控制方程的奇异性。通过微分求积法进行数值求解并对结果进行验证,分析结果表明:无载荷作用下,长细比越大,越易达到失稳状态;在相同运动速度下,受压状态时比受拉状态下更易达到失稳;临界速度随着轴向载荷的绝对值的增大而减小。通过研究探索了影响临界速度和临界载荷的因素以及两者的关系,对于轴向受载运动系统设计具有一定指导意义。     

湿-热-机-弹耦合FGM梁的稳定性及振动特性

研究了初始轴向机械载荷作用下Winkler-Pasternak弹性地基上功能梯度材料（FGM）梁在湿-热环境中的稳定性及振动特性。假设温度和湿度沿梁厚度方向稳态分布,材料的物性依赖于温度且按Voigt混合幂律模型连续分布。首先,基于一种扩展的n阶广义梁理论,应用Hamilton原理,统一建立了以轴向位移、弯曲变形项挠度及剪切变形项挠度为基本未知函数FGM梁的屈曲及自由振动方程,采用Navier解法获得了FGM简支梁静动态响应的精确解。其次,通过算例验证并给出了该广义梁理论阶次n的理想取值,丰富梁理论的同时,可供验证或改进其他各种剪切变形梁理论。最后,着重探讨了3种湿-热分布下湿度与温度增加、初始轴向机械载荷、跨厚比、地基刚度、梯度指标等诸多参数对FGM梁稳定性和振动特性的影响。     

非均匀热载荷作用下功能梯度梁的非线性静态响应

由于功能梯度材料结构沿厚度方向的非均匀材料特性,使得夹紧和简支条件的功能梯度梁有着相当不同的行为特征。该文给出了热载荷作用下,功能梯度梁非线性静态响应的精确解。基于非线性经典梁理论和物理中面的概念导出了功能梯度梁的非线性控制方程。将两个方程化简为一个四阶积分-微分方程。对于两端夹紧的功能梯度梁,其方程和相应的边界条件构成微分特征值问题;但对于两端简支的功能梯度梁,由于非齐次边界条件,将不会得到一个特征值问题。导致了夹紧与简支的功能梯度梁有着完全不同的行为特征。直接求解该积分-微分方程,得到了梁过屈曲和弯曲变形的闭合形式解。利用这个解可以分析梁的屈曲、过屈曲和非线性弯曲等非线性变形现象。最后,利用数值结果研究了材料梯度性质和热载荷对功能梯度梁非线性静态响应的影响。     

湿-热-机耦合作用下多孔功能梯度梁的振动及屈曲特性

采用一种拓展的n阶广义梁理论（GBT）,研究了轴向机械载荷作用下多孔功能梯度材料（FGM）梁在湿热环境中的振动及屈曲特性。考虑了材料的物性随温度变化,湿-热沿梁厚按三种不同类型分布,采用含孔隙率的修正Voigt混合率模型描述多孔功能梯度梁的材料属性,在宏-细观力学模型框架下应用Hamilton原理统一建立了系统的自由振动及屈曲方程,采用Navier法求解FGM简支梁的静动态响应。通过算例验证并讨论了GBT阶数n的理想取值,可用于丰富梁理论。探讨了湿热效应、湿-热-机耦合、孔隙率、材料梯度指标、跨厚比对FGM梁振动及屈曲特性的影响。结果表明:湿-热加剧降低了FGM梁的频率和临界载荷,且不同类型的湿热分布对其减小程度有显著差异;随着孔隙率增大,梁结构的整体刚度虽有所弱化,但在湿热环境中频率反而增大,稳定性增强;湿-热效应对多孔FGM细长梁频率和稳定性影响十分显著,但对短粗梁的影响比较有限。      

功能梯度Levinson梁自由振动响应的均匀化和经典化表示

在两端简支边界条件下,给出了Levinson高阶剪切变形理论下功能梯度材料(FGM)梁的固有频率与参考均匀Euler-Bernoulli(E-B)梁的固有频率之间的解析转换关系。假设FGM梁的材料性质沿着梁的高度任意连续变化,通过分析FGM Levinson梁和均匀E-B梁的自由振动控制方程以及边界条件在数学上的相似性,推导出了用参考均匀E-B梁的固有频率表示的FGM Levinson梁的固有频率的解析式;从而,将复杂的耦合微分方程边值问题的求解简化为一些与梁的材料非均匀特性及几何特性有关的系数的计算问题。从而实现了Levinson剪切变形理论下FGM梁的振动响应的经典化和均匀化表示,可为工程应用提供便利。     

移动质量作用下轴向运动悬臂梁振动特性分析

将弹炮发射系统简化为移动质量作用下的轴向运动悬臂梁系统,推导了轴向运动梁的振动方程,采用修正的Galerkin法离散求解该偏微分方程,得到以模态坐标表示的二阶时变常微分方程组,通过Newmark-β法对方程组进行了求解。计算结果表明,移动质量载荷主要使梁的一阶模态受到激励,移动质量的大小和运动速度对悬臂梁的振动响应影响较大,在移动质量作用下梁的伸缩运动都处于不稳定状态;在移动质量脱离悬臂梁后,梁的轴向收缩运动使得梁的瞬时振动频率不断减小,振动位移逐渐衰减,而振动速度逐渐增大,梁的运动处于不稳定状态,伸展时梁的自由振动规律相反。     

材料属性温度相关变厚度FGM圆板自由振动DQM求解

基于一阶剪切理论和哈密顿原理,研究了功能梯度材料(FGM)变厚度圆板在热环境中的自由振动问题。假设材料性质沿厚度幂指数连续变化且材料属性与温度相关,推导了问题的运动微分方程。用微分求积法(DQM)计算了变厚度FGM圆板横向振动的无量纲频率,并与各向同性等厚度圆板的固有频率进行了比较。讨论不同均匀和非均匀温度场、材料梯度变化、厚度系数变化以及不同边界条件对FGM圆板固有频率的影响。     

Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory

Investigated herein is the free vibration characteristics of microbeams made of functionally graded materials (FGMs) based on the strain gradient Timoshenko beam theory. The material properties of the functionally graded beams are assumed to be graded in the thickness direction according to the Mori–Tanaka scheme. Using Hamilton’s principle, the equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of FGM microbeams including size effect. A detailed parametric study is performed to indicate the influences of beam thickness, dimensionless length scale parameter, and slenderness ratio on the natural frequencies of FGM microbeams. Moreover, a comparison between the various beam models on the basis of the classical theory (CT), modified couple stress theory (MCST), and strain gradient theory (SGT) is presented for different values of material property gradient index. It is observed that the value of gradient index play an important role in the vibrational response of the microbeams of lower slenderness ratios. It is further observed that by increasing the length-to-thickness ratio of the microbeam, the value of dimensionless natural frequency tends to decrease for all amounts of the gradient index.     

Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory

Investigated herein is the free vibration characteristics of microbeams made of functionally graded materials (FGMs) based on the strain gradient Timoshenko beam theory. The material properties of the functionally graded beams are assumed to be graded in the thickness direction according to the Mori–Tanaka scheme. Using Hamilton’s principle, the equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of FGM microbeams including size effect. A detailed parametric study is performed to indicate the influences of beam thickness, dimensionless length scale parameter, and slenderness ratio on the natural frequencies of FGM microbeams. Moreover, a comparison between the various beam models on the basis of the classical theory (CT), modified couple stress theory (MCST), and strain gradient theory (SGT) is presented for different values of material property gradient index. It is observed that the value of gradient index play an important role in the vibrational response of the microbeams of lower slenderness ratios. It is further observed that by increasing the length-to-thickness ratio of the microbeam, the value of dimensionless natural frequency tends to decrease for all amounts of the gradient index.     

Free vibration analysis of pre-twisted rotating FGM beams

The natural frequencies of vibration of a rotating pre-twisted functionally graded cantilever beam are investigated. Rotating cantilever beam with pre-twist made of a functionally gradient material (FGM) consisting of metal and ceramic is considered for the study. The material properties of the FGM beam symmetrically vary continuously in thickness direction from core at mid section to the outer surfaces according to a power-law form. Equations of motion for free vibration are derived using Lagrange’s equation and the natural frequencies are determined using Rayleigh–Ritz method. The effect of parameters such as the pre-twist angle, power law index, hub radius and rotational speed on the natural frequencies of rotating functionally graded pre-twisted cantilever beams are examined through numerical studies and comparison is made with the numerical results obtained using other methods reported in literature. The effect of coupling between chordwise and flapwise bending modes on the natural frequencies has also been investigated.     

轴向运动功能梯度Timoshenko梁稳定性分析

由Hamilton原理建立轴向运动功能梯度Timoshenko梁运动微分方程组,通过引入新未知函数,将方程组化为该函数的四阶偏微分方程。用WDQ法获得简支FGM Timoshenko梁特征方程及复频率与轴向运动速度变化关系。分析梁随轴向运动速度变化的失稳形式,并与均质材料梁进行比较。分析梯度指标、梁长高比对FGM Timoshenko梁动力稳定性影响。     

温度影响下Winkler-Pasternak弹性地基上多孔FGM矩形板的自由振动分析

基于经典薄板理论和Hamilton原理研究温度影响下Winkler-Pasternak弹性地基上多孔功能梯度材料(FGM)矩形板的自由振动特性。采用Voigt混合幂率模型和孔隙任意分布模型来表征多孔FGM矩形板的材料属性,并考虑多孔FGM矩形板内部均匀温升和材料具有温度依赖特性;应用物理中面推导弹性地基上多孔FGM矩形板自由振动的控制微分方程并进行无量纲化;采用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,引入典型的六种边界在MATLAB统一编程且保证计算精度一致,经过迭代收敛,求解出无量纲固有频率;通过算例研究了边界条件、梯度指数、升温、孔隙率、长宽比、边厚比、无量纲弹性刚度系数和无量纲剪切刚度系数对多孔FGM矩形板振动特性的影响。     

A parametric study on thermo-mechanical vibration of axially functionally graded material pipe conveying fluid

In this article, we study the thermo-elastic vibration of axially functionally graded material (FGM) pipe conveying fluid considering temperature changes. The governing equation based on Euler–Bernoulli beam theory is solved by differential quadrature method. The FGM properties are defined by the property ratios and the volume fraction functions. Power volume fraction function and exponent volume fraction function are compared. We also use sigmoid volume fraction functions so that the exclusive influence of function distribution can be isolated from that of total material proportions. The property ratios’ effects of elasticity and thermo-elasticity gradient are also discussed. Based on the numerical results of first-order dimensionless frequencies and critical flow velocities, concerning thermo-elasticity gradient can theoretically change the stability of the pipe. And the influences of the pure distribution on the first-order critical flow velocities are much smaller than that of the varying total proportions of the component materials. These conclusions will hopefully be used as reference for FGM pipe designing and fabricating.

     

Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory

This article proposes a higher-order shear deformation beam theory for free vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in a thermal environment. The temperature-dependent material properties of functionally graded carbon nanotube-reinforced composite beams are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture. The governing equations and boundary conditions are derived by using Hamilton's principle, and the Navier solution procedure is used to achieve the natural frequencies of the sandwich beam in a thermal environment. A parametric study is led to carry out the effects of carbon nanotube volume fractions, slenderness ratio, and core-to-face sheet thickness ratio on free vibration behavior of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets. Numerical results are also presented in order to compare the behavior of sandwich beams including uniformly distributed carbon nanotube-reinforced composite face sheets to those including functionally graded carbon nanotube-reinforced composite face sheets.     

轴向运动功能梯度悬臂梁动力学分析

针对轴向运动悬臂梁振动会影响系统的安全性、稳定性问题,对功能梯度悬臂梁振动特性进行分析,利用广义哈密尔顿原理及假设模态法导出系统动力学方程。结果表明,功能梯度悬臂梁的横向位移与轴向位移耦合,功能梯度材料在厚度方向按体积分数函数呈指数变化,且梁自由端有集中质量块。并讨论材料指数及末端集中质量大小对振动影响,分析梁在伸展、收缩时的运动特性。所得结论可为类似结构的动力学分析、设计提供依据。