【摘要】 为探讨地震作用对山体动力响应的影响,建立了双坡面为曲面的类梯形山体的剪切梁模型,给出了响应的理论解和梯形山体第1阶固有频率的简化表达式;计算获得了不同形状山体的最大相对位移、最大相对速度和最大绝对加速度,并将计算结果与有限元分析结果进行了比较.结果表明:梯形山体模型求解山体动力响应简单,而类梯形山体模型则能获得更精确的结果;山体动力响应在水平地震作用产生弯矩较小的情况下,理论解与有限元解接近;随泊松比增大,山体的第1阶固有频率略有增大;梯形和类梯形山体的最大相对位移、最大相对速度从底部到顶部逐渐增大,而最大绝对加速度则在山体约2/5高度处出现极小值.更多还原

【Abstract】 In order to investigate the effect of earthquake loading on the dynamic responses of a mountain,a shear-beam model,an analytical method,for trapezoid-like mountains with two curved slopes was set up. The analytical solutions of the dynamic responses were obtained. A simplified empirical expression of the first order natural frequency of a trapezoid mountain was given. The maximum relative displacements,maximum relative velocities and maximum absolute accelerations of trapezoid and trapezoid-like mountains were calculated and compared with those obtained by FEM(finite element method). The research results show that the trapezoid model is easy to obtain the responses,but the trapezoid-like model is more accuracy. The analytical solutions are close to those obtained by FEM under the condition of a small moment. The first order natural frequency of a mountain increases slightly with the growth of Poisson’s ratio. The maximum relative displacements and maximum relative velocities of a mountain become larger from its bottom to its top,while its maximum absolute accelerations reach the minimum at the height of its approximately 2 /5 height.更多还原