本文選題：Euler梁 + Rayleigh梁��； 參考：《大連理工大學(xué)》2011年碩士論文

【摘要】：隨著科技的發(fā)展和實(shí)際的需求,航天器的長(zhǎng)機(jī)械臂、太空發(fā)動(dòng)機(jī)的曲軸系等眾多的輕質(zhì)柔性、高速運(yùn)動(dòng)的多體系統(tǒng)被應(yīng)用到各個(gè)領(lǐng)域。當(dāng)這些機(jī)構(gòu)工作時(shí),系統(tǒng)的大范圍剛性運(yùn)動(dòng)將會(huì)與柔體變形運(yùn)動(dòng)產(chǎn)生強(qiáng)烈的耦合效應(yīng)。研究表明,基于小變形、小轉(zhuǎn)動(dòng)假設(shè)的傳統(tǒng)柔性多體系統(tǒng)建模方法已經(jīng)不能得出這些問(wèn)題的精確解。絕對(duì)節(jié)點(diǎn)坐標(biāo)方法的出現(xiàn)可以很好地解決此類(lèi)問(wèn)題。近年來(lái),該方法已成為柔性多體動(dòng)力學(xué)中一個(gè)非常活躍的研究領(lǐng)域。 本文基于絕對(duì)節(jié)點(diǎn)坐標(biāo)法建立了一維Euler梁和平面Rayleigh梁?jiǎn)卧Ｐ�。在全局坐�?biāo)系下定義了兩模型的單元節(jié)點(diǎn)坐標(biāo),采用全局絕對(duì)斜率矢量代替?zhèn)鹘y(tǒng)有限元方法中的轉(zhuǎn)動(dòng)坐標(biāo)矢量來(lái)描述梁?jiǎn)卧倪\(yùn)動(dòng)�；趲缀畏蔷�性理論,運(yùn)用虛功原理和拉格朗日運(yùn)動(dòng)方程等推導(dǎo)出大變形、大旋轉(zhuǎn)柔性Euler梁和Rayleigh梁的動(dòng)力學(xué)運(yùn)動(dòng)方程。該動(dòng)力學(xué)微分代數(shù)方程具有質(zhì)量矩陣為常數(shù)陣、科氏力和離心力項(xiàng)均為零等優(yōu)良特點(diǎn)。研究證明,絕對(duì)節(jié)點(diǎn)坐標(biāo)法即使在大轉(zhuǎn)動(dòng)、大變形情況下也可以精確的建模,同時(shí)還大大降低了動(dòng)力學(xué)方程的非線性度。 本文采用變步長(zhǎng)Runge-Kutta法對(duì)Euler梁模型的動(dòng)力學(xué)運(yùn)動(dòng)方程進(jìn)行求解,研究了該柔性梁模型大范圍旋轉(zhuǎn)運(yùn)動(dòng)下的動(dòng)力學(xué)特性,并通過(guò)能量守恒定律去驗(yàn)證了Euler柔性梁?jiǎn)卧Ｐ偷恼_性。隨后,分別分析比較了不同彈性模量和單元數(shù)目下的Euler梁模型的位形圖以及相應(yīng)的動(dòng)力學(xué)特性。然后,使用轉(zhuǎn)換矩陣將絕對(duì)坐標(biāo)系下的位移和速度轉(zhuǎn)化為隨體坐標(biāo)系下的變形和變形速度,研究比較了隨體坐標(biāo)系下各種情況的Euler梁的動(dòng)力學(xué)特性,并給出相應(yīng)的柔性Euler梁端點(diǎn)和中間節(jié)點(diǎn)處絕對(duì)坐標(biāo)系下的相平面圖。作為比較,文中還計(jì)算了分布質(zhì)量的剛性單擺僅在自身重力作用下自水平位置做自由下落運(yùn)動(dòng)的理論解和自由端在絕對(duì)坐標(biāo)系下的相平面圖,并與本文的柔性Euler梁模型下的計(jì)算結(jié)果進(jìn)行對(duì)比。最后,本文還研究了計(jì)及剪切效應(yīng)的平面Rayleigh梁模型的仿真計(jì)算,對(duì)其進(jìn)行動(dòng)力學(xué)分析,并相應(yīng)地與Euler梁進(jìn)行了比較研究。
[Abstract]:With the development of science and technology and the actual demand, the long manipulator of spacecraft, the crankshaft system of space engine, and so on, many light flexible and high-speed multi-body systems have been applied to various fields. When these mechanisms work, the large range of rigid motion of the system will have a strong coupling effect with the deformation of flexible body. The research shows that the traditional modeling method of flexible multi-body system based on small deformation and small rotation assumption can not get the exact solution of these problems. The emergence of absolute node coordinate method can solve this kind of problem well. In recent years, this method has become a very active research field in flexible multibody dynamics. In this paper, one dimensional Euler beam and plane Rayleigh beam element model are established based on the absolute node coordinate method. The element node coordinates of the two models are defined in the global coordinate system. The global absolute slope vector is used to replace the rotational coordinate vector in the traditional finite element method to describe the motion of the beam element. Based on the theory of geometric nonlinearity, the dynamic equations of motion of large deformation, large rotating flexible Euler beams and Rayleigh beams are derived by using the principle of virtual work and Lagrange equation of motion. The differential algebraic equation is characterized by constant mass matrix and zero Coriolis force and centrifugal force. It is proved that the absolute nodal coordinate method can be used to model the dynamic equations accurately even in the case of large rotation and large deformation. At the same time, the nonlinear degree of the dynamic equations is greatly reduced. In this paper, the variable step Runge-Kutta method is used to solve the dynamic equations of the Euler beam model, and the dynamic characteristics of the flexible beam model under the large-scale rotation motion are studied. The correctness of the Euler flexible beam element model is verified by the conservation law of energy. Then, the configuration diagram of the Euler beam model with different elastic modulus and the number of elements are analyzed and compared respectively, and the corresponding dynamic characteristics are compared. Then, the displacement and velocity in the absolute coordinate system are transformed into the deformation and deformation velocities in the body coordinate system by using the transformation matrix, and the dynamic characteristics of the Euler beam under various conditions in the accompanying body coordinate system are studied and compared. The phase plane diagram in the absolute coordinate system between the end point and the middle node of the flexible Euler beam is given. For comparison, the theoretical solution of the free falling motion of a rigid pendulum with distributed mass only under its own gravity is calculated, and the phase plane diagram of the free end in absolute coordinate system is also calculated. The results are compared with the calculated results under the flexible Euler beam model in this paper. Finally, the simulation calculation of the plane Rayleigh beam model with shear effect is studied, and the dynamic analysis is carried out, and the results are compared with that of the Euler beam.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2011
【分類(lèi)號(hào)】：TH113

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