梁板壳的几何大变形--从近似的非线性理论到有限变形理论

对梁板壳的线性理论、近似几何非线性理论与有限变形理论作了比较,介绍了有限转动理论,指出了应用有限变形理论求解梁板壳的大变形问题的高效率、高精度的巨大优越性。     

轴向移动系统的参数振动问题研究进展

对近二十年来轴向移动系统(移动弦，移动梁和移动带等)的参数振动研究进展进行了详细的评述，特别关注了轴向张紧力和移动速度随时间改变时轴向移动系统的参数振动特性和稳定性等问题。文章首先讨论了所研究问题的控制方程。然后详细说明了目前研究中人们较为关注的几个重点问题，如参数激励的形式，求解方法和所研究的问题等。接着在其后的两节中，分别评述了在张紧力和移动速度随时间变化时，轴向移动弦和轴向移动梁的振动问题近年来的研究进展，详细、深入讨论了模型的类型、张紧力和轴向移动速度随时间变化的形式以及在研究中使用的解题方法和系统的振动特性(振动响应、固有频率和动态稳定性)等；最后给出了在此领域今后研究中应关注的问题。     

Principal parametric and three-to-one internal resonances of flexible beams undergoing a large linear motion

A set of nonlinear differential equations is established by using Kane‘s method for the planar oscillation of flexible beams undergoing a large linear motion. In the case of a simply supported slender beam under certain average acceleration of base, the second natural frequency of the beam may approximate the tripled first one so that the condition of 3 : 1 internal resonance of the beam holds true. The method of multiple scales is used to solve directly the nonlinear differential equations and to derive a set of nonlinear modulation equations for the principal parametric resonance of the first mode combined with 3 : 1 internal resonance between the first two modes. Then, the modulation equations are numerically solved to obtain the steady-state response and the stability condition of the beam. The abundant nonlinear dynamic behaviors, such as various types of local bifurcations and chaos that do not appear for linear models, can be observed in the case studies. For a Hopf bifurcation,the 4-dimensional modulation equations are reduced onto the central manifold and the type of Hopf bifurcation is determined. As usual, a limit cycle may undergo a series of period-doubling bifurcations and become a chaotic oscillation at last.     

带套筒构件埋地燃气管道绝缘接头的密封性研究

本文对直径为100mm带套筒构件埋地燃气管道绝缘接头的强度进行了计算和实验分析研究.计算研究中根据在符合实际工程下确定带套筒构件埋地燃气管道绝缘接头密封部位的应力和位移,以及对管道密封性能的影响;实验研究中根据对直径为100mm带套筒构件埋地燃气管道绝缘接头进行符合实际工况的试验,测量绝缘接头密封部位的应力和位移,以及密封圈的受损程度.对计算和实验结果进行分析比较,确定带套筒构件埋地燃气管道绝缘接头在装配中的最小预紧力,分析在不同因素作用下管道绝缘接头的安全性,并为其它直径类型带套管构件埋地燃气管道绝缘接头的设计提供可靠的依据.     

复合纤维增强混凝土阻尼测试装置开发与试验研究

纤维与聚合物的掺入可以明显改善混凝土材料的阻尼性能。本文首先给出了正弦交变激励下粘弹性材料三点弯曲梁阻尼特性关系,其次首次自主开发了大尺寸材料的阻尼性能测试装置,然后利用开发的装置在频率(0.5~2.0Hz)条件下测定了6种不同配比复合纤维增强阻尼混凝土的损耗因子与储存模量,最后对纤维的阻尼增强机理进行了初步探讨。试验结果表明:复合纤维增强阻尼混凝土与素混凝土相比,提高了混凝土的损耗因子80%~200%。主要原因是聚合物分子在外力作用下的内耗增加了普通混凝土的阻尼能力,而纤维的阻尼增强机理在于纤维的掺入增加了纤维与水泥基材的界面摩擦力。     

不连续岩石梁的失稳解析

本文根据不连续岩石梁的物理力学特性提出了无拉力岩石梁的力学解析模型。根据Ｆｒｅｅｂｏｄｙ法及Ｃａｓｔｉｇｌｉａｎｏ定量导出了不连续梁各物理量的求解方程式。进而采用挠度增量δｍａｘ＾ｉ＋１＝δｍａｘ＾ｉ＋Δδ↑－的逐次解析方法，求解了不连续梁的失稳问题，得出了与Ｆ．Ｄ．Ｗｒｉｇｈｔ的试验值相吻合的结果。探讨了不连续岩石梁在不同荷载条件下的失稳特性。     

Existence of positive solutions for a general nonlinear eigenvalue problem

Let Ω R n be a bounded domain, H = L 2 (Ω), L : D(L) H → H be an unbounded linear operator, f ∈ C(■× R, R) and λ∈ R. The paper is concerned with the existence of positive solutions for the following nonlinear eigenvalue problem Lu = λf (x, u), u ∈ D(L), which is the general form of nonlinear eigenvalue problems for differential equations. We obtain the global structure of positive solutions, then we apply the results to some nonlinear eigenvalue problems for a second-order ordinary differential equation and a fourth-order beam equation, respectively. The discussion is based on the fixed point index theory in cones.     

热荷载作用下Timoshenko功能梯度夹层梁的静态响应

在精确考虑轴线伸长和一阶横向剪切变形的基础上建立了Timoshenko功能梯度夹层梁在热载荷作用下的几何非线性控制方程.采用打靶法数值求解所得强非线性边值问题,获得了两端固支功能梯度夹层梁在横向非均匀升温作用下的静态热过屈曲和热弯曲变形数值解.分析了功能梯度材料参数变化、不同表层厚度和升温参数对夹层梁弯曲变形、拉-弯耦...     

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.     

轴向变速粘弹性Rayleigh梁参数共振稳定性

运用近似解析方法和数值方法研究轴向变速运动黏弹性Rayleigh梁的次谐波共振和组合共振的稳定性区域。基于变分原理,考虑梁断面旋转惯性的影响,推导轴向速度有周期波动的微变形梁横向振动的数学模型;采用多尺度方法建立前两阶次谐波共振和组合共振范围内的参数振动的可解性条件;进而确定梁两端简支边界条件下,因共振而产生的失稳区域;通过微分求积方法求解表征细长Rayleigh梁横向振动的运动微分方程。数值算例分析了黏弹性系数和扭转系数对梁振动失稳区域的影响,将数值仿真结果与近似解析方法的结论进行比较。算例表明:近似解析解的精度较高,第一、第二阶主共振的最大误差分别为3.206%、4.213%。