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为具有非对称开口截面的薄壁曲梁的非线性自由振动分析构建了一个有限元公式,由虚功原理推导出动能和势能,并考虑了弯曲-扭转耦合、扭曲和剪心位置等影响。有限元分析中,2结点薄壁曲线构件的形状函数采用三次多项式计算。每个结点具有7个自由度,其中包括扭曲自由度。采用直接迭代法计算非线性特征值。将计算结果与直线梁的计算结果相对比。同时归纳了具有多种半径和对角的曲梁的非线性自由振动分析结果。
A finite element formula is established for the nonlinear free vibration analysis of thin-walled curved beams with asymmetric open cross section. The kinetic energy and potential energy are deduced from the principle of virtual work, and the influences of bending-torsional coupling, torsion and shear center position are considered. In finite element analysis, the shape function of 2-node thin-walled curve component is calculated by cubic polynomial. Each node has seven degrees of freedom, including twist degrees of freedom. The direct iterative method is used to calculate nonlinear eigenvalues. The calculation results are compared with the linear beam calculation results. At the same time, the results of nonlinear free vibration analysis of curved beams with various radii and diagonals are summarized.