非保守弹性动力学初值问题两类变量的广义变分原理

Generalized quasi-variational principles with two kinds of variables of initial value problemin non-conservative elasto-dynamics

非保守系统广义变分原理的研究涵盖了许多学科,是一个相当重要的研究领域.按照广义力和广义位移之间的对应关系,将弹性动力学的动态平衡方程和几何方程分别卷乘上相应的虚量,然后积分、代数相加.考虑到体积力和面积力均为伴生力,建立了非保守系统初值问题卷积型两类变量的广义拟变分原理.应用第一类卷积型两类变量广义拟余能原理研究了一个典型的非保守动力学系统初值问题的动态特性,并给出同时求解该系统的内力和变形两类变量的计算方法.理论和计算都表明,将非保守系统卷积型两类变量广义拟变分原理和计算方法退化到保守系统,可得到保守系统卷积型两类变量广义变分原理和相应的计算方法.

It＇s important to research the generalized variational principles in non-conservative systems. According to the corresponding relations between generalized forces and generalized displacements, the basic equations of non-conservative elasto-dynamics were convoluted by corresponding virtual quantities, integrated and then added algebraically. In view of the character of the accompanying body forces and surface forces, convolutional generalized quasi-variational principles with two kinds of variables of initial value problem were established in non-conservative elasto-dynamics. Applying the first kind of convolutional generalized quasi-variational principle with two kinds of variables, we studied the dynamical properties of the initial value problem of typical non-conservative elasto dynamics, and gave a calculation method for solving two kinds of variables simultaneously： the internal force and the displacement. It was shown that convolutional generalized variational principles of the initial value problem in a conservative system could be obtained by degenerating convolutional generalized quasi variational principles of the initial value prob lem in a non-conservative system to a conservative system.