无拉力弹性半空间地基上预应力四边自由中厚板的动力响应

基于Reissner-Mindlin一阶剪切变形板理论,讨论在预加面内机械荷载和温度场作用下,无拉力弹性半空间地基上四边自由中厚板在动荷载作用下的动力特性。把地基看作三维弹性半空间体,考虑地基变形衰减,用一组数学上完备的二元多项式作为位形函数,采用pb-2 Rayleigh-Rizt法求得四边自由中厚板的动力响应,并讨论了初应力对板的动挠度和动弯矩的影响。     

用弹性力学方法研究横观各向同性四边简支矩形平板的自由振动问题

本文用横观各向同性体的弹性力学方程,分析了四边简支横观各向同性矩形板的自由振动问题。平板自振频率的特征方程可以分解成三个因子的乘积,它分别对应于厚度剪切振动、反对称振动和对称振动。通过数值算例,考察了非各向同性对自振频率的影响,并同经典理论、Mindlin修正理论作了比较。计算表明,板的面内和横向杨氏模量之比,对高阶自振频率有较大的影响,而一般的修正理论都不能得到这个结论。     

单向线性分布温度场中两对边简支矩形板横向自振频率的渐近解法

本文研究单向线性分布温度场中两对边简文短形板的横向自振特性，给出了一种既能保证一定精度、计算又很简单的自振频率的渐近解法，可定量得到线性分布温度对自振频率的近似影响规律。最后，以四边简支矩形板为例，给出了自振频率一级近似的具体计算公式，并与已有结果进行比较。     

褶皱发展对平面张拉薄膜屈曲后动力特性的影响

剪切位移荷载作用下,平面张拉薄膜经历缺陷、临界褶皱和宏观褶皱3种状态。该文依次分别对处于3种状态的薄膜进行自振特性分析,并明确了3种状态的划分原则。计入平面张拉薄膜的微小抗弯刚度,采用ANSYS/LS-DYNA中显式-隐式连续求解的方法对屈曲后薄膜的动力特性进行分析。依据忽略面外变形的理想模型自振特性分析结果,把平面张拉薄膜的振型划分为贯通振型和间断振型,贯通振型又划分为纵向贯通振型和横向贯通振型。研究结果表明:薄膜处于缺陷状态时,面外变形对薄膜自振特性的影响可以完全忽略,受主应力分布的影响,低阶振型中纵向贯通振型更易于出现,纵向贯通振型的波峰或波谷数量随着频率阶数的递增而规律递增。临界褶皱状态,薄膜的各阶频率均随剪切位移的增加而出现大幅波动,面外变形对薄膜振型的影响逐渐增大,横向贯通振型消失,纵向贯通振型的递增规律逐渐破坏;宏观褶皱状态,薄膜的各阶频率趋于稳定,其主应力分布及振型受面外变形的影响显著。     

单向面内约束混凝土双向板火灾试验及承载力分析

为研究混凝土板在面内约束作用下的火灾行为,对1块面内约束混凝土双向板进行了恒载-升温条件下的火灾试验,获得了试验板沿板厚的温度场分布、钢筋温度、板挠度和平面外变形以及板角约束力等规律。基于EC2和ASCE两本构模型,采用五种理论对四块不同面内约束作用下试验板的极限承载力进行对比分析。结果表明:单向面内约束作用时,试验板板顶出现沿约束力方向的平行裂缝;与挠度相比,板在垂直约束力方向的平面内膨胀变形较大且不可忽略;面内约束作用和破坏准则对火灾下混凝土双向板极限承载力有重要影响。     

四边简支FGM矩形板非线性振动中的内共振

基于Reddy高阶剪切变形板理论、Galerkin法与Hamilton原理,在同时考虑几何非线性、材料物性参数随温度变化且材料组分沿厚度方向按幂律分布的情况下,通过理论推导建立起四边简支功能梯度材料矩形板受面内与横向简谐载荷共同作用下的非线性运动控制微分方程;在此基础上建立了受热载荷作用下的具有二阶模态的非线性运动控制微分方程。分析了面内静态载荷对于给定参数下系统不同内共振的影响,发现随着面内静态载荷的不同系统会出现1:1、1:2 与1:3的内共振关系。计算结果发现由于不同内共振关系对应的面内静态载荷不同,不同内共振关系下所求得的一阶频率大小各不相同,所对应的瞬态响应也会不同。     

考虑温度和剪切变形的改进型波形钢腹板组合箱梁动力特性研究

为了精确分析温度效应和剪切变形效应对改进型波形钢腹板组合箱梁自振特性的影响,提出一种考虑温度效应和剪切变形效应的改进型波形钢腹板组合箱梁自振特性分析方法。综合考虑温度、剪切变形和波形钢腹板刚度修正的影响,运用应力等效原则推导出改进型波形钢腹板组合箱梁的自振频率解析公式;利用实桥ANSYS有限元分析结果和试验实测结果对自振频率解析公式的正确性进行了验证;分析了温度等效轴向偏心力变化、弹性模量变化、剪切变形效应、不同高跨比和不同宽跨比下温度效应对该桥型自振频率的影响。结果表明：温度效应对改进型波形钢腹板组合箱梁的基频影响较大,计算该桥型的基频时需要考虑温度效应的影响;波形钢腹板的剪切变形效应对该桥型自振频率的影响较为显著,从第4阶自振频率开始剪切变形的影响已超过50%;不同高跨比下温度效应对基频的影响较大,且随着高跨比的增大呈线性急剧增大;不同宽跨比下温度效应对自振频率的影响较小,可以忽略不计。研究成果可为改进型波形钢腹板组合箱梁的自振频率计算和分析提供参考依据。     

单向面内约束混凝土双向板抗火性能试验研究及数值分析

为了分析简支板受到单向面内约束作用下的火灾行为,对两块足尺混凝土双向板进行了面内荷载和竖向荷载共同作用下的火灾试验。研究了双向板在受火过程中沿板厚混凝土温度场分布规律、钢筋温度、板平面内外变形以及板角平面外约束力变化规律,并与相关试验进行对比。在此基础上,基于EC2和ASCE本构模型,编程对试验板温度场、变形行为和力学机理进行了数值分析。结果表明:当板受到单向面内约束作用时,其裂缝模式及变形规律与四边简支板明显不同,且易出现完整性破坏;板角裂缝分布情况对板角约束力有重要影响;本构模型对火灾下约束板的力学机理影响较大。     

FGM中厚圆板轴对称自由振动的打靶法求解

研究了由陶瓷和金属两种材料组成的功能梯度材料(FGM)中厚圆板的自由振动问题。基于考虑横向剪切变形中厚板的几何方程、物理方程及平衡方程,建立了以中面转角和横向位移为基本未知量的功能梯度中厚圆板轴对称自由振动问题的控制方程;假定功能梯度中厚圆板的材料性质方向按照幂函数连续变化规律;采用打靶法数值求解所得非线性两点边值问题出,获得了多种边界下功能梯度中厚圆板的无量纲自然频率以及振动模态。讨论了材料梯度指数、板的厚度以及边界条件对自然频率的影响。     

单桩基础海上风机横向自振频率求解及参数敏感性分析EI北大核心CSCD

梁理论的合理选择对风机横向自振频率的求解意义重大。以往提出的海上风机自振频率计算方法都基于某一种梁理论,且缺乏各参数的敏感性分析。为了对比不同梁理论对风机自振频率求解的影响,采用回传射线矩阵法,分别基于Bernoulli-Euler梁、经典Timoshenko梁和修正Timoshenko梁理论,提出海上风机横向自振频率计算方法,通过实测数据验证了该方法的准确性,并综合对比各参数的敏感性。研究结果表明:Bernoulli-Euler梁理论未考虑剪切变形与转动惯量,自振频率计算结果略大于Timoshenko梁理论;剪切变形引起的转动惯量可以忽略不计,修正Timoshenko梁理论与经典Timoshenko梁理论计算结果一致,但物理意义更加清晰;基频对塔筒结构参数的敏感性最高,其次是连接段与桩基;基频对塔筒高度的敏感性最高,对海床高度与叶轮机舱组件质量的敏感性较高,壁厚变化对基频的影响不显著。     

Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses

In this paper, the effect of non-ideal boundary conditions and initial stresses on the vibration of laminated plates on Pasternak foundation is studied. The plate has simply supported boundary conditions and is assumed that one of the edges of the plate allows a small non-zero deflection and moment. The initial stresses are due to in-plane loads. The vibration problem is solved analytically using the Lindstedt–Poincare perturbation technique. So the frequencies and mode shapes of the plate with non-ideal boundary condition is extracted by considering the Pasternak foundation and in-plane stresses. The results of finite element simulation, using ANSYS software, are presented and compared with the analytical solution. The effect of various parameters like stiffness of foundation, boundary conditions and in-plane stresses on the vibration of the plate is discussed. Dependency of non-ideal boundary conditions on the aspect ratio of the plate for changing the frequencies of vibrations is presented. The relation between the shear modulus of elastic foundation and the frequencies of the plate is investigated.     

Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory

This paper proposes a new higher-order shear deformation theory for buckling and free vibration analysis of isotropic and functionally graded (FG) sandwich beams. The present theory accounts a new hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Lagrange's equations. Analytical solutions are presented for the isotropic and FG sandwich beams with various boundary conditions. Numerical results for natural frequencies and critical buckling loads obtained using the present theory are compared with those obtained using the higher and first-order shear deformation beam theories. Effects of the boundary conditions, power-law index, span-to-depth ratio and skin-core-skin thickness ratios on the critical buckling loads and natural frequencies of the FG beams are discussed.     

Stability and vibration analyses of carbon nanotube-reinforced composite beams with elastic boundary conditions: Chebyshev collocation method

This article aims to investigate stability and vibration behavior of carbon nanotube-reinforced composite beams supported by classical and nonclassical boundary conditions. To include significant effects of shear deformation and rotary inertia, Timoshenko beam theory is used to formulate the coupled equations of motion governing buckling and vibration analyses of the beams. An effective mathematical technique, namely Chebyshev collocation method, is employed to solve the coupled equations of motion for determining critical buckling loads and natural frequencies of the beams with different boundary conditions. The accuracy and reliability of the proposed mathematical models are verified numerically by comparing with the existing results in the literature for the cases of classical boundary conditions. New results of critical buckling loads and natural frequencies of the beams with nonclassical boundary conditions including translational and rotational springs are presented and discussed in detail associated with many important parametric studies.     

Nonlinear dynamic response and vibration of imperfect shear deformable functionally graded plates subjected to blast and thermal loads

Based on Reddy's higher-order shear deformation plate theory, this article presents an analysis of the nonlinear dynamic response and vibration of imperfect functionally graded material (FGM) thick plates subjected to blast and thermal loads resting on elastic foundations. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical results for the dynamic response and vibration of the FGM plates with two cases of boundary conditions are obtained by the Galerkin method and fourth-order Runge–Kutta method. The results show the effects of geometrical parameters, material properties, imperfections, temperature increment, elastic foundations, and boundary conditions on the nonlinear dynamic response and vibration of FGM plates.     

On refined computational models of composite laminates

Finite element models of the continuum-based theories and two-dimensional plate/shell theories used in the analysis of composite laminates are reviewed. The classical and shear deformation theories up to the third-order are presented in a single theory. Results of linear and non-linear bending, natural vibration and stability of composite laminates are presented for various boundary conditions and lamination schemes. Computational modelling issues related to composite laminates, such as locking, symmetry considerations, boundary conditions, and geometric non-linearity effects on displacements, buckling loads and frequencies are discussed. It is shown that the use of quarter plate models can introduce significant errors into the solution of certain laminates, the non-linear effects are important even at small ratio of the transverse deflection to the thickness of antisymmetric laminates with pinned edges, and that the conventional eigenvalue approach for the determination of buckling loads of composite laminates can be overly conservative.     

Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments

Size-dependent forced vibration behavior of functionally graded (FG) nanobeams subjected to an in-plane hygro-thermal loading and lateral concentrated and uniform dynamic loads is investigated via a higher-order refined beam theory, which captures shear deformation influences needless of any shear correction factor. The nanobeam is in contact with a three-parameter Kerr foundation consisting of upper and lower spring layers as well as a shear layer. Hygro-thermo-elastic material properties of the nanobeam are described via power-law distribution considering exact position of the neutral axis. Through nonlocal elasticity theory of Eringen and Hamilton's principle, the governing equations of higher-order FG nanobeams on Kerr foundation under dynamic loading are derived. These equations are solved for simply-supported and clamped-clamped boundary conditions. A detailed parametric study is performed to show the importance of moisture concentration rise, temperature rise, material composition, nonlocality, Kerr foundation parameters, and boundary conditions on forced vibration characteristics and resonance frequencies of FG nanobeams. As a consequence, Kerr foundation parameters lead to a significant delay in the occurrence of resonance frequencies.     

用Fourier边界展开的方法研究具有曲线边界的厚板的自由振动

应用Fourier边界展开的方法研究具有曲线边界的厚板的自由振动问题。主要是应用一次剪切变形理论研究实心厚板的自由振动特性。首先，在极坐标系里表示出任意具有曲线边界厚板的边界条件，导出所需公式。其次，用Fourier边界展开的方法分析问题，并作相应的阶次截断，得到固有频率方程。这里，就可数值求得无因次的固有频率。由于使用的解精确满足板振动的微分方程，此方法能给出高精度的结果，而计算量小、分析过程较简单且编程也较容易。     

A nth-order meshless generalization of Reddy’s third-order shear deformation theory for the free vibration on laminated composite plates

In this paper, a nth-order shear deformation theory is proposed to analyze the free vibration of laminated composite plates. The present nth-order shear deformation theory satisfies the zero transverse shear stress boundary conditions on the top and bottom surface of the plate. Reddy’s third-order theory can be considered as a special case of present nth-order theory (n = 3). Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, material properties are computed by present nth-order theory and a meshless radial point collocation method based on the thin plate spline radial basis function. The results are compared with available published results which demonstrate the accuracy and efficiency of present nth-order theory.     

不同边界条件下波纹夹芯板的自由振动特性

波纹夹芯板作为一种特殊的复合材料结构,边界条件对其振动特性有重要影响。根据不同剪切方式下的剪切变形理论和基尔霍夫经典板理论(CLPT),利用Hamilton原理建立波纹夹芯板的动力学方程。其中,波纹芯层等效成各向异性均质体。根据四边简支、四边固支、对边简支和固支、一边固支三边简支的边界条件,推导出位移形式的偏微分动力学方程。求解得到波纹夹芯板在不同边界条件下自由振动的固有频率,与有限元仿真结果进行对比,验证了理论结果的正确性。在此基础上,基于指数剪切变形理论(ESDT),分析了不同边界条件下波纹夹芯板的基频随材料参数和结构几何参数的变化规律。结果表明,材料和几何参数对不同边界条件下波纹夹芯板的振动特性有重要影响。相关研究结果将对波纹夹芯板在工程应用中的减振设计及优化分析提供一定的理论依据。      

Nonlinear vibration and dynamic response of shear deformable laminated plates in hygrothermal environments

This paper deals with hygrothermal effects on the nonlinear vibration and dynamic response of shear deformable laminated plates. The temperature field considered is assumed to be a uniform distribution over the plate surface and through the plate thickness. The material properties of the composite are affected by the variation of temperature and moisture, and based on a micro-mechanical model. The formulations are based on higher-order shear deformation plate theory and general von Kármán-type equation of motion, which includes hygrothermal effects. The equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies and dynamic responses of shear deformable antisymmetric angle-ply and unsymmetric cross-ply laminated plates. The numerical illustrations concern the nonlinear vibration and dynamic response of the shear deformable laminated plates under different sets of hygrothermal environmental conditions. Effects of temperature rise, the degree of moisture concentration, and fiber volume fraction on natural frequencies, nonlinear to linear frequency ratios and dynamic responses are studied.