用Lagrange乘子法研究连续梁的自由振动

Study on free vibration of continuous beam with lagrange multiplier method

在Rayleigh法的基础上,利用Lagrange乘子法构造了连续梁自由振动的能量函数,把能量函数对有关参数求导,得到了使能量函数有驻值的条件方程,再令条件方程的系数矩阵行列式等于零,即可方便求得连续梁自由振动的基频。

Based on Rayleigh method, the energy function of continuous beam＇s free vibration was proposed with Lagrange multiplier method, and its derivatives of the parameters concerned were gained, then the conditional expression was got where energy function has station, thus fundamental vibration frequency of continuous beam could be educed when the determint of coefficient matrix equaled zero.