高墩梁桥的水平向主导振型理论分析

A theoretical study on the horizontal dominant vibration mode of a girder bridge with tall piers

单自由度模型被广泛应用于规则中、低墩梁桥的抗震分析和设计,而高墩梁桥由于墩身高阶振型的影响,有必要发展多自由度甚至分布参数体系的简化分析模型和方法。基于分布参数欧拉梁理论对单墩-质点体系进行解析推导,分析了体系动力特性和振型质量分布的控制因素和规律,从纯解析角度更为严格的证明梁-墩质量比是决定体系水平向振型质量参与系数的主要因素。解释了已有数值分析结果给出的统计规律,纯解析给出比已有数值拟合公式精度更高、适用范围更广的分析公式,探讨了高阶振型的影响,最后给出手算评估等效单自由度模型有效性的建议公式。

The single degree of freedom model was widely applied in anti-seismic analysis and was designed for regular girder bridges with medium-length or short-length piers.For girder bridges with tall piers,due to the obvious influence of higher-order modes,a simplified model and a method with multiple degrees of freedom or even with distributed parameters still need to be developed.In this paper,based on the theory of the Euler beam with distributed parameters,analytical derivation is presented for the single column and the mass system.The dynamical characteristics and modal mass distributions,as well as their control factors and properties,are studied.It is proved analytically and more clearly that the girder-pier mass ratio plays a dominant role in determining horizontal modal mass participation. Thus,interpretation of the previous conclusion based on statistical and numerical analysis is presented.Purely analytical formulas,which show higher accuracy and better applicability than the previous numerical fitting formulas,are also given. The influence of a higher-order vibration mode is analyzed and discussed.Finally,the manual calculation formula,for efficiency assessment of the single degree of freedom model,is also proposed.