幂函数模量成层土上剪切梁式结构的随机地震反应

Random earthquake response of shearing beam structure on the stratified foundations with power function modulus

按照剪切梁理论,给出了幂函数剪切模量成层土上剪切梁式结构的自振频率方程及任意阶振型函数的解析表达式.在此基础上,用振型叠加原理计算了该梁式结构的地震反应,然后利用随机振动理论,并基于基岩输入地震加速度的功率谱密度函数:白噪声谱和过滤白噪声谱,研究了该梁式结构对地震的随机动力响应问题.计算表明:1)在基岩输入地震加速度的功率谱为白噪声谱的情况下,土层和梁式结构的最大期望反应,均有别于过滤白噪声谱时的相应值;2)平稳输入与输出过高地估计了土层和梁式结构的随机响应.

In this paper, formulas for computing natural frequencies and modes of shearing beam structure on the stratified foundations with power function shear modulus are derived according to shear beam theory. Furthermore, the seismic response of this kind of beam structure is calculated by using the mode-superposition scheme. Dynamic responses of the beam structure and the soil layer to earthquake are studied under the theory of random vibration. Two cases of power spectral intensity function for the earthquake acceleration input at the base rock are considered： the white noise spectrum and filter white noise spectrum. The numerical calculation results show that： （1）Under the case that the power spectral density of the earthquake acceleration input at the base rock is the white noise spectrum, the maximum expected responses of the soil layer and the beam structure are different from that for the case of the filter white noise spectrum. （2） Both the earthquake acceleration putin the base rock and the response are stationary random process, which over-estimates the random responses of the soil layer and the beam structure.