带任意附加质量的变截面弹性支承梁动力特性的解析解

ANALYTIC SOLUTION OF DYNAMIC CHARACTERISTICS OF NON-UNIFORM ELASTICALLY SUPPORTED BEAM WITH ARBITRARY ADDED MASSES

根据变截面梁桥的结构特点,建立了带任意附加质量的变截面弹性支承梁(桥)动力特性的简化计算模型。基于Bernoulli-Euler梁理论,对直接模态摄动法进行改进得到改进摄动方法(IPM)。在完全弹性支承梁的模态子空间内,IPM法将带任意附加质量的变截面弹性支承梁的变系数微分方程转化为线性代数方程组。IPM法适用于求解带任意附加质量的变截面弹性支承简支和连续梁(桥)的振动方程。算例分析表明:IPM法具有较高的计算精度和较快的收敛速度。根据变截面对称梁(桥)的振型对称性给出了对称梁(桥)动力特性的简便计算方法(SIPM)。SIPM法可以减少未知系数和未知数约50%,计算精度与IPM法接近,计算效率更高。最后,研究了附加质量和弹性支承对三跨变截面连续梁桥动力特性的影响规律。

A practical model for calculating the dynamic characteristics of non-uniform elastically supported beam（bridge） with arbitrary added masses is given according to the structure characteristics of non-uniform beam bridges. The improved perturbation method（IPM） is obtained by modifying the mode perturbation method based on Bernoulli-Euler beam theory. In the modal subspace of the beam, the variable coefficient differential vibration equation of the beam with arbitrary added masses is converted to nonlinear algebraic equations. IPM is suitable for solving the vibration equation of a simply supported and continuous non-uniform beam（bridge）. The examples that are analyzed, demonstrate the high precision and fast convergence speed of the IPM. A timesaving method（SIPM） for the dynamic characteristics of a symmetrical beam（bridge） based on the symmetry of mode shape is developed. SIPM has about half the number of coefficients and unknowns as does IPM. SIPM has higher computational efficiency and the accuracy of SIPM is very close to IPM. Eventually, the effects of elastic supports and added masses on dynamic characteristics of a three-span non-uniform beam bridge are reported.