含脱层损伤复合材料层合梁的冲击动力屈曲

针对含初始缺陷和脱层损伤的复合材料层合梁的轴向冲击动力屈曲问题进行了分析。基于Hamilton原理导出了考虑初始缺陷、轴向和横向惯性、横向剪切变形以及转动惯性影响时含脱层损伤复合材料梁的非线性动力屈曲控制方程;基于B-R准则,采用有限差分方法求解了受轴向冲击载荷作用下含脱层损伤复合材料梁的动力屈曲问题;讨论了冲击速度、初始几何缺陷、铺层角度以及脱层长度等因素对复合材料层合梁动力屈曲的影响。     

静力预加载环向加筋圆柱壳的轴向流-固冲击屈曲

将初缺陷放大准则应用于静力预加载环向加筋圆柱壳结构受轴向流-固冲击加载作用时的几何非线性动力屈曲研究中。运用Galerkin方法推导出壳体-肋骨系统的动力屈曲控制方程,并且采用Runge-Kutta法进行数值求解。着重分析了静力预加载荷对结构屈曲性态及抗轴向冲击能力的影响。     

两参数轴向冲击载荷作用下圆柱壳弹塑性动力屈曲

研究圆柱壳在两参数轴向冲击载荷下的弹塑性动力屈曲问题，基本控制方程由弹塑性连续介质中关于加速度的最小原理获得，本构关系采用增量理论。研究表明：屈曲过程可划分为两相，两相之间由临界时间ｔ表征，并分别讨论了应力波对屈曲的影响，压缩波与弯曲波的相互作用及几何尺寸，材料参数，初始缺陷，载荷峰值及持续时间等诸多因素与动力屈曲的关系。     

冲击载荷作用下矩形薄板的弹性动力屈曲

为了研究冲击载荷作用下考虑应力波效应弹性矩形薄板的动力屈曲,根据动力屈曲发生瞬间的能量转换和守恒准则,导出板的屈曲控制方程和波阵面上的补充约束条件,真实的屈曲位移应同时满足控制方程和波阵面上的附加约束条件。满足上述条件,建立了该问题的完整数值解法,对屈曲过程中冲击载荷、屈曲模态和临界屈曲长度之间的关系进行研究,定量计算了横向惯性效应对提高薄板动力屈曲临界应力的贡献。研究表明:板的厚宽比一定时,临界屈曲长度随冲击载荷的增大而减小;由于屈曲时的横向惯性效应,应力波作用下薄板一阶临界力参数是相应边界板的静力失稳临界力参数的1.5倍;随着边界约束逐渐减弱,板临界力参数逐渐减小,动力特征参数逐渐增大。     

基于裂纹扭转弹簧模型的Timoshenko裂纹梁动力特性分析

忽略裂纹对梁剪切变形的影响,基于开裂纹的等效扭转弹簧模型,建立了Timoshenko裂纹梁动力弯曲的控制方程,得到了一种新的裂纹梁动力弯曲控制方程的求解方法,得出了具有任意条裂纹Timoshenko梁自振模态的统一显式表达式。数值分析了简支、悬臂、两端固支Timoshenko裂纹梁的自振频率和振动模态,考察了裂纹数目和裂纹深度等因素对裂纹梁动力特性的影响。结果表明:随着裂纹数目和深度的增加,裂纹梁的自振频率减小,且当裂纹较深时,裂纹深度对自振频率的影响显著;裂纹梁的挠度模态曲线和转角模态曲线在裂纹处分别呈现尖点和跳跃现象,且尖点效应和转角跳跃随裂纹深度的增加而愈加明显。另外,当裂纹处的弯矩为零时,裂纹对梁的自振频率和振动模态没有影响。这些结果可对梁的安全性评估及裂纹损伤检测提供理论指导。     

Hamilton体系下功能梯度梁的热冲击动力屈曲分析

在Hamilton体系下,基于Euler梁理论研究了功能梯度材料梁受热冲击载荷作用时的动力屈曲问题;将非均匀功能梯度复合材料的物性参数假设为厚度坐标的幂函数形式,采用Laplace变换法和幂级数法解析求得热冲击下功能梯度梁内的动态温度场:首先将功能梯度梁的屈曲问题归结为辛空间中系统的零本征值问题,梁的屈曲载荷与屈曲模态分别对应于Hamilton体系下的辛本征值和本征解问题,由分叉条件求得屈曲模态和屈曲热轴力,根据屈曲热轴力求解临界屈曲升温载荷。给出了热冲击载荷作用下一类非均匀梯度材料梁屈曲特性的辛方法研究过程,讨论了材料的梯度特性、结构几何参数和热冲击载荷参数对临界温度的影响。     

爆炸冲击下复合材料层合扁球壳的动力屈曲

研究计及横向剪切的复合材料层合扁球壳在爆炸冲击载荷作用下的非线性轴对称动力屈曲问题。通过在复合材料层合扁球壳非线性稳定性的基本方程中增加横向转动惯量项并引入R.H.Cole理论的爆炸冲击力,得到爆炸冲击下复合材料层合扁球壳的动力控制方程,应用Galerkin方法得到用顶点挠度表达的爆炸冲击动力响应方程,并采用Runge-Kutta方法进行数值求解,采用Budiansky-Roth准则确定冲击屈曲的临界载荷,讨论了壳体几何尺寸对复合材料层合扁球壳冲击屈曲的影响;数值算例表明,此方法是可行的。     

含脱层损伤复合材料层合梁冲击动力响应实验研究

对纤维增强复合材料层合梁在受轴向冲击时的动力响应问题进行了实验研究。实验以单向玻璃纤维布和环氧树脂材料制作试件,在层间预埋薄铜箔模拟脱层损伤。采用激光测速仪测量子弹速度,动态应变仪和TDS420A数字示波器记录应变时程曲线进行动力响应分析。实验结果表明铺层角度是决定材料性能的主要原因,脱层损伤的存在及大小对动力响应和发生动力屈曲有重要影响。此外,初始缺陷的影响也是不可忽视的重要因素。     

横向载荷作用下轴向运动梁的屈曲失稳以及非线性振动特性

梁的轴向运动会诱发其产生横向振动并可能导致屈曲失稳，对结构的安全性和可靠性产生重大的影响。本文重点研究了横向载荷作用下轴向运动梁的屈曲失稳及横向非线性振动特性。基于Hamilton变分原理，建立了横向载荷作用下轴向运动梁的动力学方程，获得了梁的后屈曲构型。使用截断Galerkin法，将控制方程改写成Duffing方程的形式。用同伦分析方法确定载荷作用下轴向运动梁的非线性受迫振动的封闭形式的表达式。结果表明，后屈曲构型对轴向速度和初始轴向应力有明显的依赖性。通过同伦分析法得出非线性基频的显式表达式，获得了初始轴向力会影响非线性频率随初始振幅和轴向速度的线性关系。另外，轴向外激励的方向也会改变系统固有频率。     

初曲矩形薄板的非线性动力屈曲研究

对两参数冲击载荷面内压缩作用下初曲矩形薄板的非线性动力屈曲问题进行了理论研究。首先采用双重余弦函数的组合确定了面内冲击矩形薄板的艾雷应力函数和中面力的分布；其次根据伽辽金法求得了初曲矩形薄板非线性动力屈曲问题的控制方程，基于巴拿赫压缩映象原理，采用逐次逼近方法求解了该控制方程。最后，应用本文发展的理论，给出了面内两参数冲击载荷作用下初曲矩形薄板动力屈曲响应的计算实例，计算结果与已有的实验结果较吻合     

Dynamic bifurcation and sensitivity analysis of non-linear non-planar vibrations of geometrically imperfect cantilevered beams

The non-linear non-planar dynamic responses of a near-square cantilevered (a special case of inextensional beams) geometrically imperfect (i.e., slightly curved) and perfect beam under harmonic primary resonant base excitation with a one-to-one internal resonance is investigated. The sensitivity of limit-cycles predicted by the perfect beam model to small geometric imperfections is analyzed and the importance of taking into account the small geometric imperfections is investigated. This was carried out by assuming two different geometric imperfection shapes, fixing the corresponding frequency detuning parameters and continuation of sample limit-cycles versus the imperfection parameter. The branches of periodic responses for perfect and imperfect (i.e. small geometric imperfection) beams are determined and compared. It is shown that branches of periodic solutions associated with similar limit-cycles of the imperfect and perfect beams have a frequency shift with respect to each other and may undergo different bifurcations which results in different dynamic responses. Furthermore, the imperfect beam model predicts more dynamic attractors than the perfect one. Also, it is shown that depending on the magnitude of geometric imperfection, some of the attractors predicted by the perfect beam model may collapse. Ignoring the small geometric imperfections and applying the perfect beam model is shown to contribute to erroneous results.     

The unilateral contact buckling problem of continuous beams in the presence of initial geometric imperfections: An analytical approach based on the theory of elastic stability

An analytical method for the treatment of the elastic buckling problem of continuous beams with intermediate unilateral constraints is presented, which is based on the fundamental theory of elastic stability. The study focuses on the unilateral contact buckling problem of beams in the presence of initial geometric imperfections. The mathematical Euler approach, based on the fundamental solution of the boundary value problem of the buckling of continuous beams, is appropriately modified in order to take into account the unilateral contact conditions. Furthermore, in order the obtained analytical solutions to be applicable for practical design cases, the actual strength of the cross-section of the beam under combined compression and bending is considered. The implementation of the proposed method is demonstrated through a characteristic example.     

Non-linear stability analysis of imperfect thin-walled composite beams

The static non-linear behavior of thin-walled composite beams is analyzed considering the effect of initial imperfections. A simple approach is used for determining the influence of imperfection on the buckling, prebuckling and postbuckling behavior of thin-walled composite beams. The fundamental and secondary equilibrium paths of perfect and imperfect systems corresponding to a major imperfection are analyzed for the case where the perfect system has a stable symmetric bifurcation point. A geometrically non-linear theory is formulated in the context of large displacements and rotations, through the adoption of a shear deformable displacement field. An initial displacement, either in vertical or horizontal plane, is considered in presence of initial geometric imperfection. Ritz's method is applied in order to discretize the non-linear differential system and the resultant algebraic equations are solved by means of an incremental Newton-Rapshon method. The numerical results are presented for a simply supported beam subjected to axial or lateral load. It is shown in the examples that a major imperfection reduces the load-carrying capacity of thin-walled beams. The influence of this effect is analyzed for different fiber orientation angle of a symmetric balanced lamination. In addition, the postbuckling response obtained with the present beam model is compared with the results obtained with a shell finite element model (Abaqus).     

复合材料层合梁的屈曲

本文在铁摩辛柯梁理论基础上,利用迭合刚度方法及Hamilton原理建立了层合梁屈曲问题控制方程,并用此控制方程求解了在具体边界条件下层合梁的屈曲问题,得出了无论在什么边界条件下层合梁的最小屈曲载荷不会大于等效剪切刚度系数C的结论.     

Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation

This paper investigates the nonlinear flexural dynamic behavior of a clamped Timoshenko beam made of functionally graded materials (FGMs) with an open edge crack under an axial parametric excitation which is a combination of a static compressive force and a harmonic excitation force. Theoretical formulations are based on Timoshenko shear deformable beam theory, von Karman type geometric nonlinearity, and rotational spring model. Hamilton’s principle is used to derive the nonlinear partial differential equations which are transformed into nonlinear ordinary differential equation by using the Least Squares method and Galerkin technique. The nonlinear natural frequencies, steady state response, and excitation frequency-amplitude response curves are obtained by employing the Runge–Kutta method and multiple scale method, respectively. A parametric study is conducted to study the effects of material property distribution, crack depth, crack location, excitation frequency, and slenderness ratio on the nonlinear dynamic characteristics of parametrically excited, cracked FGM Timoshenko beams.     

Nonlinear dynamic stability analysis of Euler–Bernoulli beam–columns with damping effects under thermal environment

In this study, a unified nonlinear dynamic buckling analysis for Euler–Bernoulli beam–columns subjected to constant loading rates is proposed with the incorporation of mercurial damping effects under thermal environment. Two generalized methods are developed which are competent to incorporate various beam geometries, material properties, boundary conditions, compression rates, and especially, the damping and thermal effects. The Galerkin–Force method is developed by implementing Galerkin method into force equilibrium equations. Then for solving differential equations, different buckled shape functions were introduced into force equilibrium equations in nonlinear dynamic buckling analysis. On the other hand, regarding the developed energy method, the governing partial differential equation for dynamic buckling of beams is also derived by meticulously implementing Hamilton’s principles into Lagrange’s equations. Consequently, the dynamic buckling analysis with damping effects under thermal environment can be adequately formulated as ordinary differential equations. The validity and accuracy of the results obtained by the two proposed methods are rigorously verified by the finite element method. Furthermore, comprehensive investigations on the structural dynamic buckling behavior in the presence of damping effects under thermal environment are conducted.     

Dynamic buckling of a 2-DOF imperfect system with symmetric imperfections

Non-linear dynamic buckling of a two-degree-of freedom (2-DOF) imperfect planar system with symmetric imperfections under a step load of infinite duration (autonomous system) is thoroughly discussed using energy and geometric considerations. This system under the same load applied statically exhibits (prior to limit point) an unstable symmetric bifurcation lying on the non-linear primary equilibrium path. With the aid of the total energy-balance equation of the system and the particular geometry (due to symmetric imperfections) of the plane curve corresponding to the zero level total potential energy “surface” exact dynamic buckling loads are obtained without solving the non-linear initial-value problem. The efficiency and the reliability of the technique proposed herein is demonstrated with the aid of various dynamic buckling analyses which are compared with numerical simulation using the Verner-Runge-Kutta scheme, the accuracy of which is checked via the energy-balance equation.     

A Motion Amplifier Using an Axially Driven Buckling Beam: II. Modeling and Analysis

In this paper, the nonlinear behavior of a motion amplifier used to obtain large rotations from small linear displacements produced by a piezoelectric stack is studied. The motion amplifier uses elastic (buckling) and dynamic instabilities of an axially driven buckling beam. Since the amplifier is driving a large rotary inertia at the pinned end and the operational frequency is low compared to the resonant frequencies of the beam, the mass of the buckling beam and the dynamics of the PZT stack are neglected and the system is modeled as a single-degree-of-freedom, nonlinear system. The beam simply behaves as a nonlinear rotational spring having a prescribed displacement on the input end and a moment produced by the inertial mass acting on the output end. The moment applied to the mass is then a function of the beam end displacement and the mass rotation. The system can, thus, be modeled simply as a base-excited, spring–mass oscillator. Results of the response for an ideal beam using this reduced-order model agree with the experimental data to a high degree. Inclusion of loading and geometric imperfections show that the response is not particularly sensitive to these imperfections. Parameter studies for the ideal buckling beam amplifier were conducted to provide guidance for improving the design of the motion amplifier and finding the optimal operating conditions for different applications. An erratum to this article can be found at