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通过假设薄壁曲梁翼缘应力的横向分布函数,得到结构的变形势能。结构的自由振动能量,则用惯性力势能表示。根据能量泛函变分原理,推导了均质薄壁曲梁考虑剪力滞影响的自由振动微分方程,并采用分离变量法求解,计算了简支薄壁曲梁考虑剪力滞影响的基本自振频率,分析了剪力滞效应、曲梁圆心角、曲率半径和跨度对自振频率的影响。
The deformation potential energy of the structure is obtained by assuming the horizontal distribution function of the stress of the flange of the thin-walled curved beam. The free vibration energy of the structure is expressed by the potential energy of inertial force. According to the principle of energy functional variational principle, the free vibration differential equation of homogeneous thin-walled curved beam considering shear lag effect is deduced and solved by the method of separating variables. The basic self-damping of thin-walled curved beam considering shear strength is calculated The influence of shear lag effect, the central angle of curved beam, the radius of curvature and the span on the natural frequency were analyzed.