【作者】 鲍文博； 常明飞； 孙晓燕； 遇瑞；

【Author】 BAO Wen-bo, CHANG Ming-fei, SUN Xiao-yan, YU Rui (School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110023, China)

【机构】 沈阳工业大学建筑工程学院；

【摘要】 承受循环荷载作用的动力基础,由于土-结构的相互作用,其反力-位移关系呈现2个显著特点,即非线性和滞回性。采用定参集总参数体系,以三次幂多项式模型反映动力地基的非线性特性,将非线性幂函数作为循环荷载作用下系统位移-力关系的主干骨线:在此基础上,按照Masing二倍法则,将骨线拓展为位移-力的滞回曲线,以此反映系统的滞回特性,从而建立了三次幂非线性粘性阻尼双曲线滞回动力基础系统的动力学模型。由于本构函数的复杂性,直接利用一般解法比较困难。采用Fourier级数展开法得到了系统的解析解,给出了动力基础的时间历程响应曲线和幅频特性曲线,并与基础模型的实验数据进行了比较。分析结果表明,利用Fourier级数展开法求解滞回动力学非线性模型,精度高、收敛快,且与实验结果吻合较好。更多还原

【Abstract】 The resistance-displacement relationship of dynamic foundation systems subjected to cyclic loading exhibits two significant characteristics-nonlinearity and hysteresis, due to soil-structure interaction effects. In this study, foundation-basement is abstracted as fixed parameter lumped parameter system for simplicity. A nonlinear dynamic model possessing viscous damping is set up with the third power polynomial function, which is used to represent the nonlinear behavior of force-displacement interacting between soil and foundation. And a new hyperbolic hysteresis loop model of dynamic foundations is presented exteriorly adopting Masing rules extend the exponential backbone curve into the loop which simulates nonlinear and hysteresis characteristics of the system. The nonlinear mathematical model developed includes the parameters such as soil stiffness, nonlinearity of passive earth pressure, displacement scale and velocity direction. It’s difficult to solve the constitutive function intactly by using general analytical method for its complexity, so the paper makes use of Fourier progression approach in study. The paper investigates periodic solution of the dynamic system with the hyperbolic hysteresis loop model and obtains the time-history and frequency response characteristics of the foundations under harmonic excitation. The studies show that the Fourier method, which is used to analyze the systems of dynamic foundations with the hyperbolic hysteresis model, is precise and convergent, and the results of emulation agree with the specific experimental data.更多还原