不同移动载荷速度下简支桥梁的变形及振动响应研究

利用奇异函数,基于梁挠曲线近似微分方程及横向强迫振动的微分方程,分别利用积分法及分离变量法推导出移动载荷作用下简支桥梁的弯曲变形方程及振动响应方程。应用Mathcad软件,研究不同移动载荷速度对简支梁静、动态变形的影响规律。结果表明:随移动载荷速度的增加,在相同时间内,简支梁的最大挠度和最大振动位移先增大后减小,呈近似抛物线规律分布;对于简支梁的给定截面,其最大静挠度不随载荷移动速度的改变而变化,但达到最大挠度所需的时间随着载荷移动速度的增大而减少;移动载荷速度一定时,简支梁不同截面最大挠度值随载荷的移动方向呈先增大后减小的趋势。

Deformation and Vibration Response Study on Simply Supported Bridge under Different Moving Load Speed

Bending deformation equation and vibration response equation of simply supported bridge under moving load is derived respectively with integral and variables separation methods and by use of singular function which is based on beam deflection line approximate differential equation and lateral forced vibra-tion differential equation.The affecting rule of different moving load speed versus simply supported beam still and dynamic deformation is studied with Mathcad software,and the result shows that:in same time, with moving load speed increasing,maximum deflection and maximum vibration displacement of simply supported beam first increase and then decrease,presenting similar to parabola rule distribution;for given section of simply supported beam,its maximum static deflection doesn't change with load moving speed changing,but the time needed to get to maximum deflection decreases with load moving speed increasing;under certain moving load speed,maximum deflection of different section of simply supported beam first increases and then decreases towards load moving direction.