含阻尼非保守分析力学的拟变分原理

Quasi-Variational Principles on Non-Conservative Analytical Mechanics with Damping

明确了含阻尼非保守分析力学问题的控制方程,按照广义力和广义位移之间的对应关系,将各控制方程乘以相应的虚量,积分并代数相加,考虑到系统的非保守特性,进而建立了非保守分析力学问题的拟变分原理和广义拟变分原理.应用拟Hamilton原理研究了具有阻尼的二自由度非保守动力系统的算例.

With the basic equation on non-conservative analytical mechanics with damping settled, according to the corresponding relations between generalized forces and generalized displacements, the basic equations are multiplied by corresponding virtual quantities, integrated and then added algebraically. Considering that systems are non-conservative, the quasi-variational principle and the generalized quasi-variational principle of non-conservative analytical mechanics are established. Finally, based on quasi-Hamiltonian principle, an example on non-conservative systems of the two degree of freedom with damping is studied.