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

【摘要】：隨著科技的發(fā)展和實際的需求,航天器的長機械臂、太空發(fā)動機的曲軸系等眾多的輕質(zhì)柔性、高速運動的多體系統(tǒng)被應用到各個領域。當這些機構(gòu)工作時,系統(tǒng)的大范圍剛性運動將會與柔體變形運動產(chǎn)生強烈的耦合效應。研究表明,基于小變形、小轉(zhuǎn)動假設的傳統(tǒng)柔性多體系統(tǒng)建模方法已經(jīng)不能得出這些問題的精確解。絕對節(jié)點坐標方法的出現(xiàn)可以很好地解決此類問題。近年來,該方法已成為柔性多體動力學中一個非�；钴S的研究領域。 本文基于絕對節(jié)點坐標法建立了一維Euler梁和平面Rayleigh梁單元模型。在全局坐標系下定義了兩模型的單元節(jié)點坐標,采用全局絕對斜率矢量代替?zhèn)鹘y(tǒng)有限元方法中的轉(zhuǎn)動坐標矢量來描述梁單元的運動�；趲缀畏蔷�性理論,運用虛功原理和拉格朗日運動方程等推導出大變形、大旋轉(zhuǎn)柔性Euler梁和Rayleigh梁的動力學運動方程。該動力學微分代數(shù)方程具有質(zhì)量矩陣為常數(shù)陣、科氏力和離心力項均為零等優(yōu)良特點。研究證明,絕對節(jié)點坐標法即使在大轉(zhuǎn)動、大變形情況下也可以精確的建模,同時還大大降低了動力學方程的非線性度。 本文采用變步長Runge-Kutta法對Euler梁模型的動力學運動方程進行求解,研究了該柔性梁模型大范圍旋轉(zhuǎn)運動下的動力學特性,并通過能量守恒定律去驗證了Euler柔性梁單元模型的正確性。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的動力學特性。然后,使用轉(zhuǎn)換矩陣將絕對坐標系下的位移和速度轉(zhuǎn)化為隨體坐標系下的變形和變形速度,研究比較了隨體坐標系下各種情況的Euler梁的動力學特性,并給出相應的柔性Euler梁端點和中間節(jié)點處絕對坐標系下的相平面圖。作為比較,文中還計算了分布質(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動的理論解和自由端在絕對坐標系下的相平面圖,并與本文的柔性Euler梁模型下的計算結(jié)果進行對比。最后,本文還研究了計及剪切效應的平面Rayleigh梁模型的仿真計算,對其進行動力學分析,并相應地與Euler梁進行了比較研究。
[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.
【學位授予單位】：大連理工大學
【學位級別】：碩士
【學位授予年份】：2011
【分類號】：TH113

【參考文獻】

相關期刊論文 前7條

1 ;Nonlinear formulation for flexible multibody system with large deformation[J];Acta Mechanica Sinica;2007年01期

2 劉錦陽;李彬;陸?zhàn)?;計及熱應變的空間曲梁的剛-柔耦合動力學[J];固體力學學報;2007年01期

3 田強;張云清;陳立平;覃剛;;柔性多體系統(tǒng)動力學絕對節(jié)點坐標方法研究進展[J];力學進展;2010年02期

4 李彬,劉錦陽;大變形柔性梁系統(tǒng)的絕對坐標方法[J];上海交通大學學報;2005年05期

5 沈凌杰;劉錦陽;余征躍;;柔性梁斜碰撞問題的非線性動力學建模和實驗研究[J];力學季刊;2006年04期

6 田強;張云清;陳立平;覃剛;;基于增廣拉格朗日方法的多柔體動力學研究[J];系統(tǒng)仿真學報;2009年24期

7 劉錦陽;崔麟;;熱載荷作用下大變形柔性梁剛?cè)狁詈蟿恿W分析[J];振動工程學報;2009年01期

相關博士學位論文 前1條

1 田強;基于絕對節(jié)點坐標方法的柔性多體系統(tǒng)動力學研究與應用[D];華中科技大學;2009年

，

本文編號：1971404