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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。
According to the structural characteristics of the variable section beam bridge, a simplified calculation model of the dynamic characteristics of the elastic beam with variable section with arbitrary additional mass is established. Based on the Bernoulli-Euler beam theory, the improved perturbation method (IPM) is improved for the direct mode perturbation method. In the modal subspace of fully elastic support beam, the IPM method transforms the variable coefficient differential equation of a variable cross-section elastic support beam with any additional mass into a linear algebraic system. The IPM method is suitable for solving the vibration equations of simply supported and continuous beams (bridges) with variable cross-sections with arbitrary additional mass. The case study shows that the IPM method has higher computational accuracy and faster convergence speed. According to the modal symmetry of variable section symmetrical beam (bridge), a simple calculation method (SIPM) for the dynamic characteristics of symmetrical beam (bridge) is given. The SIPM method can reduce the unknowns and the unknown coefficients by about 50%. The calculation accuracy is close to that of the IPM method and the calculation efficiency is higher. Finally, the influence of the additional mass and the elastic support on the dynamic characteristics of the three-span continuous beam bridge is studied.