双特征参数法与最优模态法在弹性直杆动力屈曲问题中解的一致性

采用求解最优模态的方法,分别对弹性压应力波作用下受载端夹支和简支两种边界条件直杆的动力屈曲问题进行了探讨,研究中所设的屈曲模态不仅满足边界条件,而且满足文献所得的波前附加约束条件。研究发现屈曲模态中放大最快的模态所对应的临界力参数和惯性项的指数参数与双特征参数法所得的结果是一致的,即用双特征参数法求解所得屈曲模态就是最优模态。另外,计算表明,最低阶动力屈曲载荷远高于静力屈曲载荷,确定动力屈曲载荷时应计及横向惯性。     

轴向冲击载荷下圆柱壳的塑性动力屈曲

对于轴向冲击载荷下圆柱壳的轴对称塑性动力屈曲问题。将临界应力和屈曲惯性项指数参数作为双特征参数求解．由相邻平衡准则导出失稳控制方程、边界条件和波阵面上的连续条件．由失稳瞬间的能量转换和守恒准则，导出波阵面上的一个屈曲变形约束方程．由此得出定量求解2个特征参数和动力屈曲模态的完备定解条件．关于屈曲应力和屈曲波数的理论计算结果与已有实验吻合良好．     

直杆塑性动力屈曲的能量准则和特征参数解

提出弹塑性应力波作用下直杆动力屈曲的定量求解方法，将临界应力和惯性指数作为一对特征参数求解．由相平衡邻位形准则得出屈曲控制方程和边界条件，由所导出的能量转换和守恒准则得出压缩波阵面上的附加约束方程，由此得出了问题的完备定解条件，从而提出了求解直杆塑性动力屈曲的特征参数方法。     

基于双特征参数解的直杆弹性动力后屈曲研究

利用差分方法求解动力后屈曲非线性方程解，研究了弹性直杆的2类轴向碰撞屈曲问题．将双特征参数解得出的含有小幅值参数的初始动力屈曲模态作为非线性后屈曲解的初始条件．理论计算的结果与文献中的实验数据达到了很好的一致，由此验证了双特征参数方法的正确性．研究结果还揭示了碰撞过程中屈曲变形扩展和发展的机理，以及轴向应力波和屈曲变形的相互作用规律．     

弹性压应力波下直杆分又动力失稳特征值有限元分析

运用有限元特征值分析方法对弹性压应力波作用下直杆分叉动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了直杆动力失稳时的有限元特征方程，把弹性直杆的动力失稳问题归结为特征值问题。通过引入直杆动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。     

弹性压应力波下直杆分叉动力失稳特征值有限元分析

运用有限元特征值分析方法对弹性压应力波作用下直杆分叉动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了直杆动力失稳时的有限元特征方程,把弹性直杆的动力失稳问题归结为特征值问题。通过引入直杆动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。     

两种边界条件直杆的撞击屈曲及其应力波效应

在对Bernoulli-Euler梁运动方程定性分析的基础上,利用非零解的条件,直接展开含双参数的特征行列式得到了两端固定和一端铰支一端固定直杆动力屈曲临界载荷和相应的屈曲模态;证明了b<-α4/4时,模态方程的解不代表杆的动力屈曲。进一步,讨论了杆-杆类直杆动力屈曲过程中的应力波效应,其理论预测结果和相应的撞击实验结果显示出相当好的一致性。     

轴力和水压作用下深水输液管道湿模态振动特性分析

采用Love-Timoshenko理论和Helmholtz方程建立了轴力和水压作用下原油-管道-海水耦合模型,计算得到了深水输液管道壳振动周向模态的固有频率。通过文献对比,验证了该计算结果的准确性。通过不同工况管道固有频率对比,发现湿模态分析具有不可替代性,原油、海水的存在会降低管道壳振动固有频率,但不会影响管道弹性失稳的临界压力,原油恒定流速的影响可以忽略不计。通过耦合模型参数影响分析,发现边界条件和长径比对高周向模态频率影响较小,而对低周向模态频率影响较大,特别是基频。轴向拉力会小幅降低管道固有频率,进而小幅降低管道弹性失稳临界压力。水压会大幅降低管道固有频率,甚至引发结构失稳。因此,在深水输液管道湿模态周向振动特性分析中轴力和水压作用应加以重视。     

轴向碰撞弹性直杆动力后屈曲有限元分析

利用显式动力学有限元方法对弹性直杆的动力后屈曲进行了分析;模拟了弹性直杆轴向碰撞动力屈曲的变形及发展过程。分析中将碰撞杆视为无初始缺陷的理想直杆,将弹性直杆动力屈曲双特征参数的解答作为非线性动力后屈曲求解的初始条件,实现了对无缺陷理想直杆的动力后屈曲分析。计算结果与文献中的实验数据获得了很好的一致。计算结果同时也揭示了直杆动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

轴向时变冲击载荷作用下直杆弹性动力屈曲研究

基于应力波理论,用半解析半数值方法对轴向时变冲击载荷作用下的直杆进行研究,给出了一种利用压应力波前附加约束条件求解轴向时变载荷作用下直杆弹性动力屈曲问题的方法。以三角脉冲载荷作用下的直杆为例,对其临界屈曲长度、初始屈曲模态和动力特征参数进行了求解,探讨了脉冲载荷峰值和载荷持续时间对临界屈曲长度和屈曲模态的影响。总结了三角脉冲载荷作用下直杆弹性动力屈曲的规律,并与阶跃载荷作用下的情况进行对比分析,结果与之前文献研究结果吻合良好。     

Dynamic stability analysis of functionally graded higher-order shear deformable microshells based on the modified couple stress elasticity theory

Size-dependent dynamic stability response of higher-order shear deformable cylindrical microshells made of functionally graded materials (FGMs) and subjected to simply supported end supports is investigated. Material properties of the microshells vary in the thickness direction according to the Mori–Tanaka scheme. The modified couple stress elasticity theory in conjunction with the classical higher-order shear deformation shell theory is utilized to develop non-classical shell model containing additional internal length scale parameter to interpret size effect. The differential equations of motion and boundary conditions are derived by using Hamilton’s principle. The governing equations are then written in the form of Mathieu–Hill equations and then Bolotin’s method is employed to determine the instability regions. Selected numerical results are given to indicate the influences of internal length scale parameter, material property gradient index, static load factor and axial wave number on the dynamic stability behavior of FGM microshells. It is found that the width of the instability region for an FGM microshell increases with the decrease of the value of dimensionless length scale parameter. Moreover, it is shown that the classical shell model has an overestimated prediction for the width of instability region corresponding to the FGM microshells especially with lower values of material property gradient index.     

封闭薄膜屋盖的风致气动力失稳分析

根据大挠度薄壳的无矩理论,建立了薄膜屋盖的控制方程.采用势流理论并结合空气动力学中的薄翼型理论推导了作用于封闭式薄膜屋盖表面的气动力,从而建立风与薄膜屋盖的动力耦合作用控制方程.分别得到了二维和三维薄膜屋盖模型的无量纲特征方程,并利用单模态法求解屋盖的临界发散失稳风速和双模态法求解屋盖的临界颤振失稳风速.通过二维模型和三维模型的结果分析和对比,得到了屋盖气动力失稳的临界风速及其相应的规律.     

闭口薄壁截面圆弧拱空间动力稳定性分析

通过能量法和Hamilton原理,建立径向均布周期荷载作用下闭口薄壁截面圆弧拱动力稳定偏微分方程,利用Galerkin方法将其转化为2阶常微分Mathieu-Hill型参数振动方程,求得周期解所包围的动力不稳定区域,探讨了闭口截面圆弧拱发生空间参数振动的动力稳定性问题,分析了恒载系数、圆弧半径以及圆心角等参数对空间动力不稳定区域的影响,为工程结构动力设计提供参考依据。     

Postbuckling and free vibrations of composite beams

An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse deformations of a composite laminated beam accounting for the midplane stretching are derived. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single nonlinear fourth-order partial–integral–differential equation governing the transverse deformations. We find out that the governing equation for the postbuckling of symmetric or asymmetric composite beams has the same form as that of beams made of an isotropic material. Composite beams with fixed–fixed, fixed–hinged, and hinged–hinged boundary conditions are considered. A closed-form solution for the postbuckling deformation is obtained as a function of the applied axial load, which is beyond the critical buckling load. To study the vibrations that take place in the vicinity of a buckled equilibrium position, we exactly solved the linear vibration problem around the first buckled configuration. Solving the resulting eigen-value problem results in the natural frequencies and their associated mode shapes. Both the static response represented by the postbuckling analysis and the dynamic response represented by the free vibration analysis in the postbuckling domain strongly depend on the lay-up of the laminate. Variations of the beam’s midspan rise and the fundamental natural frequency of the postbuckling domain vibrations with the applied axial load are presented for a variety of lay-up laminates. The ratio of the axial stiffness to the bending stiffness was found to be a crucial parameter in the analysis. This control parameter, through the selection of the appropriate lay-up, can be manipulated to help design and optimize the static and dynamic behavior of composite beams.     

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。     

Mechanism of buckling development in elastic bars subjected to axial impact

By use of the finite difference method, the non-linear equations governing the elastic dynamic post-buckling deformations are solved for two types of impact buckling problems for straight bars. The initial dynamic buckling mode with a small amplitude parameter, given by the twin-characteristic-parameter solution, is used as the initial condition of the non-linear post-buckling solution. Particular attention is paid to the mechanism of growth and spread of buckling deformation in the bar and the interaction between the axial stress wave and the buckling deformation in the process of impact. It is found that the initial buckling deflection with one half-wave, occurring near the impacted end, spreads forward and develops into the higher mode as the axial stress wave propagates in the bar. The theoretical results are in good agreement with the experimental results reported in the literatures.