行波激励下单层单跨结构地震响应解析解

Analytical Solutions for Earthquake Responses of Single-span,One-story Structure to Wave Passage Excitation

目的研究地震波中频率成分对小跨度结构响应行波效应的影响,以探究小跨度结构地震行波效应的产生机理。方法给出地震行波激励下单层单跨结构的动力平衡方程,使用相对运动法对方程进行求解;推导地震行波激励下屋面绝对位移和柱剪力的解析解,分别研究低频成分丰富和低频成分不丰富地震波激励下的峰值柱剪力。结果地震行波激励下柱剪力解析解不仅与时间延迟有关,还与结构基频和激励频率比值的平方有关;对于低频成分丰富的地震波,行波激励下峰值柱剪力大于一致激励下峰值柱剪力;相反,对于低频成分不丰富的地震波,行波激励下峰值柱剪力要小于一致激励下峰值柱剪力。结论结构响应地震行波效应除取决于时间延迟外,还取决于地震波中的低频成分;在低频成分丰富的地震波激励下,小跨度结构会产生行波效应,且低频成分越丰富的地震波,行波效应越显著;在低频成分不丰富的地震波激励下,不会产生行波效应。

In order to explore the mechanism of earthquake wave passage effect for small-span structure,the influence of frequency content in earthquake wave on wave passage effect is studied in this paper.The analytical solutions of structural responses to earthquake wave passage excitation for a single-span,one-story structure are given in this paper.The dynamic equilibrium equation for the structure subjected to earthquake wave passage excitation is given,and the relative motion method is adopted to solve the equation.The analytical solutions in series form of absolute displacement of the roof and column shear forces are derived respectively.The peak column shear forces for earthquake waves with sufficient and insufficient frequency contents are studied respectively.It is found that the analytical solutions of column shear forces to wave passage excitation are not only related to the time delay,but also related to the square of the ratio of structural fundamental frequency to excitation frequency.For the earthquake waves with sufficient low-frequency content,the peak column shear forces under wave passage excitation are larger than those under uniform excitation.On the contrary,the peak column shear forces under wave passage excitation are smaller than those under uniform excitation for the earthquake waves with insufficient low-frequency content.The results show that the earthquake wave passage effect for small-span structure depends not only on the time delay,but also on the low-frequency content.There are wave passage effects for small-span structures subjected to the earthquake waves with sufficient low-frequency content,and the more sufficient low-frequency content in earthquake wave,the more obvious wave passage effect.The wave passage effects will not occur for those earthquake waves in which the low-frequency contents are not sufficient.