【摘要】 结合虚拟激励法与Galerkin法,研究弹性圆拱在水平随机地震作用下随机响应的半解析解.在建立圆拱平面内动力平衡微分方程的基础上,通过选取适当的试函数,应用Galerkin法将动力平衡微分方程转化为线性常微分方程组.通过设定虚拟荷载,采用确定性方法求解响应量的功率谱密度函数的近似解,得到圆拱随机振动问题的闭合解.该方法无须计算拱的振型,对非正交阻尼同样适用.通过算例分析和与有限元计算结果的比较,验证了该方法的计算精度.当采用的试函数与圆拱振型接近时,采用较少的试函数就能获得较高的精度,该方法是一种简便、高效的方法.更多还原

【Abstract】 Combining pseudo-excitation method and Galerkin method,the semi-analytical solution of elastic circular arch’s random responses under horizontal random seismic excitation was studied.The dynamical equilibrium differential equations of circular arch were established and then transformed into a system of linear ordinary differential equations by choosing appropriate trial functions and using Galerkin method.The closed-form solution of random vibration and the approximate solution of power spectrum density of response were solved by assuming pseudo-excitation load and using the deterministic method.The method is also applicable to the non-orthogonal damping due to unnecessarily calculating the mode shape of arch.A numerical example was given to demonstrate the accuracy of the proposed method by comparing the results with those of finite element method.The method is highly efficient and convenient by using a few trial functions when the trial functions are very close to the mode shape of the circular arch.更多还原