According to the Kirchhoff kinetic analogy method, the elastic deformation of a thin elastic rod with mutation of either curvaturetwisting vector or strain vector at section center was analogized as the striking motion. Based on the Cosserat and Kirchhoff thin elastic rod model, respectively, the Lagrange equations of the elastic rod with mutation of curvaturetwisting vector or section center strain vector were derived. It was found that the derived equations have the same forms as the Lagrange equation of striking motion. Finally, the effects of the mutation of curvaturetwisting vector or strain vector at section center on the smoothness of the deflection curve were analyzed. This study provides an analytical mechanics method for the equilibrium analysis of the elastic rod with mutation of curvaturetwisting vector or strain vector at section center.
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薛纭,王鹏.弹性细杆弯扭度有突变时的Lagrange方程[J].动力学与控制学报,2019,17(5):473~477; Xue Yun, Wang Peng. Lagrange equations of thin elastic rod with mutation of curvature-twisting vector[J]. Journal of Dynamics and Control,2019,17(5):473-477.