Non-linear interactions in imperfect beams at veering

Non-linear interactions in a hinged-hinged uniform moderately curved beam with a torsional spring at one end are investigated. The two-mode interaction is a one-to-one autoparametric resonance activated in the vicinity of veering of the frequencies of the lowest two modes and results from the non-linear stretching of the beam centerline. The excitation is a base acceleration that is involved in a primary resonance with either the first mode only or with both modes. The ensuing non-linear responses and their stability are studied by computing force- and frequency-response curves via bifurcation analysis tools. Both the sensitivity of the internal resonance detuning—the gap between the veering frequencies—and the linear modal structure are investigated by varying the rise of the beam half-sinusoidal rest configuration and the torsional spring constant. The internal and external resonance detunings are varied accordingly to construct the non-linear system response curves. The beam mixed-mode response is shown to undergo several bifurcations, including Hopf and homoclinic bifurcations, along with the phenomenon of frequency island generation and mode localization.     

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.     

简支梁振台的理论解及位移测试

利用由机械振动理论推导出的等截面简支梁的理论解,推导出了带集中质量的简支梁振动台的理论解,并通过分析动态条件下简支梁的位移与应变之间的关系,证明了:在动态条件下梁的位移与应变之间存在很好的正比关系。利用梁的位移与应变之间正比关系,如果在梁上适当位置粘贴应变片,通过测试应变就能准确地测得梁的动态位移。本文通过实例证明了该方法确实可行,理论解与实测结果非常吻合。这为简支梁的动态测试提供了有效而简便的方法。     

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。     

STATIC STUDY OF CANTILEVER BEAM STICTION UNDER ELECTROSTATIC FORCE INFLUENCE

I. INTRODUCTION For capacitor-like microelectromechanical systems (MEMS) structure[1??6], the voltage betweenthe structure and substrate causes attractive force. The sources of the voltage can be an arti?ciallymounted device[2 , 7??9] or the temporar…     

剪切弯曲下短深梁位移数值计算精度的研究

分析了短深梁位移的基本解，评述了有限元解法中关于高次分布力简化为节点力的问题。使用虚功原理和位移线性插值推导了满足二次分布力作用的精确节点力分配公式。通过矩形截面悬臂梁自由终端受集中载荷的算例，阐明了提高短深梁位移计算精度的途径。     

梁板结构埋入压电片的深度和厚度优化研究

根据梁的弯曲变形理论，以及压电材料的压电效应，对压电复合材料梁结构的应变和应力状态进行了分析。推导了压电材料埋入梁结构时其埋入深度和压电材料本身厚度的优化目标函数。根据优化目标函数，绘制出了在给定的基体材料和压电材料弹性模量比之下，压电材料的驱动力矩随埋入深度和压电材料厚度变化的三维曲面和等高线图，直观地表示出了埋入型压电材料智能结构获得最佳驱动力矩的配置方案。同时也分析了结构和压电材料两者的弹性模量之比对其结果的影响。结果表明，压电材料对于结构的作动力矩与其埋入基体材料的深度、本身厚度以及基体材料和压电材料的弹性模量之比都有着密切的联系。同时将结果也推广到了压电板结构，此时压电材料和基体材料的泊松比时其结果也有一定的影响。     

刚柔耦合建模理论的实验验证

传统的混合坐标建模理论是零次近似方法，对刚柔耦合问题的描述存在缺陷，研究以一个由中心刚体，柔性梁及末端质量组成的刚柔耦合系统对象，建立了精确的一次近似的刚柔耦合动力学方程，在该模型中计及了结构阻尼及风阻的影响，利用单轴气浮台动力学实验平台，通过与实验数据的比较，说明了传统零次近似方法在某些条件下已不能下确描述柔性的刚性正确性和可靠性。     

Elastic impact on finite Timoshenko beam

In this paper the analytical solutions of the impact of a particle on Timoshenko beams with four kinds of different boundary conditions are obtained according to Navier's idea, which is further developed. The initial values of the impact forces are exactly determined by the momentum conservation law. The propagation of the longitudinal and transverse waves along the beam, especially, the effects of boundary conditions on the characteristics of the reflected waves, are investigated in detail. Some results are compared with those by MSC/NASTRAN.     

中柱失效工况下单层组合框架受力理论分析

基于已有试验，本文提出了轴向弹簧和转动弹簧约束的组合框架简化计算模型，推导了在集中荷载作用下刚性、半刚性连接平面组合梁双跨钢框架移除中柱后的荷载-跨中挠度曲线计算公式，考虑了压拱效应和连接刚度的影响，将公式计算结果与试验结果进行对比证明了推导过程和计算公式的可靠性．在对比结果的基础上，根据已有试验和模拟结果对已有悬索阶段的计算公式进行修正，修正后的公式与试验结果吻合较好．