考虑剪力滞效应的曲线箱梁自振特性研究

Vibration properties research on curved box girder considering shear lag effects

通过假设曲线箱梁翼板纵向位移函数,分别建立了曲线箱梁形变势能和振动动能表达式。综合运用能量变分法和哈密顿原理推导出了曲线箱梁受弯、扭、剪力滞耦合作用的自由振动微分方程,由位移场函数对简支曲线箱梁一阶竖向弯曲频率进行了近似求解,获得了自振频率显示解。然后将理论计算值与ANSYS有限元数值解相比较,误差仅为0.37%,二者吻合良好,证明了理论公式推导的正确性。在此基础上重点研究了剪力滞效应对曲线箱梁自振频率的影响,分析结果表明:剪力滞效应削弱了弯梁的刚度,降低了结构的自振频率,剪力滞效应对弯梁刚度的削弱程度主要取决于宽跨比,当宽跨比由0.15增大到0.4的过程中,曲线箱梁刚度的削弱程度由2.05%增大到12.8%。实际工程中,对于多室箱梁和扁平箱梁,应充分考虑剪力滞效应对自振频率的不利影响。

Strain potential energy and vibration energy expression of curved box-girder are respectively established by assuming longitudinal displacement function of flange, according to the energy variation method and Hamilton principle, differential equations of free vibration of curved box girder considering bending, torsion and shear lag effect are deduced, an approximate solution to the first set bending frequency of simply supported curved box girder is carried out based on the displacement field function, and the explicit solution to vibration frequency is obtained. then compared the theoretical calculating value with numerical solution of ANSYS, the error between them is only 0.37%, the result that they agree well demonstrates the correctness of proposed formula, based on it, the influence of shear lag effects on vibration frequency of curved box girder is mainly research, the results indicate that shear lag effects impair the stiffness of bending beam, leading to the decreasing of vibration frequency of the structure, the impair extent of shear lag effect to bending beam stiffness mainly depends on the width-span ratio, when the width- span ratio increases from 0.15 to 0.4, the impair extent of stiffness of curved box girder also increases from 2.05% to 12.8%. In practical engineering, for mutil cell box girder and flat box girder, full attention should be paid to the unfavorable influence of shear lag effect on vibration frequency.