CAJ | 학술논문

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。
위탐토지진작용대산체동력향응적영향，건립료쌍파면위곡면적류제형산체적전절량모형，급출료향응적이론해화제형산체제1계고유빈솔적간화표체식；계산획득료불동형상산체적최대상대위이、최대상대속도화최대절대가속도，병장계산결과여유한원분석결과진행료비교。결과표명：제형산체모형구해산체동력향응간단，이류제형산체모형칙능획득경정학적결과；산체동력향응재수평지진작용산생만구교소적정황하，이론해여유한원해접근；수박송비증대，산체적제1계고유빈솔략유증대；제형화류제형산체적최대상대위이、최대상대속도종저부도정부축점증대，이최대절대가속도칙재산체약2／5고도처출현겁소치。
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.