竖向地震作用下考虑剪切变形和转动惯量对桥梁的弯曲振动

The Bending Vibration of Bridge Under Action of Vertical force when Shear Strain and Moment of Inertia are Considered

本文对高跨比较大的梁式桥,在竖向地震作用下考虑剪切变形和转动惯量影响,来研究桥梁的振动解。对于桥梁为简支时,假设挠度函数为三角函数,把方程简化为常微分方程,从而得到精确解答。对于支座为固定时,假设挠度函数,并应用伽辽金法得到问题的近似解。然而,两种情况的解答中,时间项都为Duhamel积分形式。

In case the height span ratio is comparatively big, the shear strain and the moment of inertia of a beam bridge must be taken into consideration under vertical seismic force. In this study,we give the vibrational solution for such a bridge. For a simply supported bridge, we obtain the exact solution by assuming the deflection to be functions of Fourier series and then derive the governing equation to be an ordinary differential equation. In case the bridge is of fixed supports, we obtain its asymptotic solution by assuming the deflection in known spatial form and then solved by the Garliken method. For both cases, the solution is in form of the well known Duhamel integral.