理论力学双语教学第十六章虚位移原理.ppt

1 1 代入(a)式，得： Substitution into equation (a) results in 1 Because is independent on , we get 由于 是彼此独立的，所以： 1 由此解得： So we obtain 1 But Solution 2 解法二： Firstly, keep ? constant, but let ? change by a variation . Then we obtain a set of virtual displacements of the system as show in the diagram. 先使? 保持不变，而使 ? 获得变分 ，得到系统的一组虚位移，如图所示。 1 代入上式，得 Substitution into the equation above results in 1 But Keep ? constant, but let ? choux of . Then we have another set of virtual displacements of the system as shown in the. 再使? 保持不变，而使? 获得变分 ，得到系统的另一组虚位移，如图所示。 diagram 1 代入上式后，得： Substitution into the equation above gives 1 [Example 3] This is a multispan statically determinate a beam. Determine the reaction forces on the hinged support B. 例3 多跨静定梁，求支座B处反力。 1 解：将支座B 除去，代入相应的约束反力 。 Solution Relieve the hinged support B, substitute the corresponding reaction force of the constraint . 1 Hence, 1 1 [Example 4] A sliding sleeve D is slipping on the rod AB and drives the rod CD sliding vertical. If ?=0o, the spring is at its largest length, the stiffness of the spring is 5(kN/m). Determine the moment M acting on the rod AB when the system is in equilibrium at a certain angle ?. 例4 滑套D套在光滑直杆AB上，并带动杆CD在铅直滑道上滑动。已知?=0o时，弹簧等于原长，弹簧刚度系数为5(kN/m)，求在任意位置（ ? 角）平衡时，加在AB杆上的力偶矩M ？ 1 解：这是一个已知系统平衡，求作用于系统上主动力之间关系的问题。将弹簧力计入主动力，系统简化为理想约束系统，故可以用虚位移原理求解。 Solution The problem is to determine the relationships among the positive forces acting on the system when it is in equilibrium. The spring force can be treated as a positive force, and the constraints are ideal ones. Therefore, the problem can be solved by the theorem of virtual displacements. 1 Select the system to consist of the rods AB, CD and select the sliding sleeve D as the object to be investigated. 选择AB杆、CD杆和滑套D的系统为研究对象。 1 由虚位移原理，得： From the theorem of virtual displacements, we have 1 Steps and key points in solving the equilibrium problem of a system of parti