完全弹性支承变截面梁动力特性半解析解

摘要

基于 Bernoulli-Euler 梁理论对直接模态摄动方法进行改进，建立求解完全弹性支承变截面梁振动方程的半解析方法。改进摄动法（IPM）在等效等截面完全弹性支承梁的模态空间内将变截面简支、连续梁的变系数微分方程组转化为非线性代数方程组，获得完全弹性支承变截面梁动力特性的半解析解；推导弹性边界条件下系数Δkki的具体计算公式。算例分析表明，改进摄动法计算精度高、收敛速度快，可有效考虑弹性支承对结构动力特性影响；据振型的对称性给出完全弹性支承变截面对称梁动力特性的简便计算方法（SIPM）；研究支座出现损伤对变截面简支梁桥自振频率影响。%The mode perturbation method was modified and the improved perturbation method (IPM)was used to solve the vibration problem of non-uniform beam with complete elastic supports based on Bernoulli-Euler beam theory.In the modal subspace of an equivalent uniform beam with complete elastic supports,the variable coefficient differential vibration equation of the non-uniform simply supported continuous beam with complete elastic supports was converted to nonlinear algebraic equations.The semi-analytical solution of dynamic characteristics of non-uniform beam with complete elastic supports was obtained and the formula of coefficient Δkki was given.An example analysis indicates that the improved perturbation method not only has high precision and good convergency but also considers the elastic supports effect on dynamic characteristics.A simplified calculating method (SIPM)for symmetrical beam was proposed based on the symmetry of mode shapes.The bearing damage effects on dynamic characteristics of non-uniform simply supported beam bridge were discussed.