Dynamic Analysis of Flexible Large Displacement Beam System with Second-Order Effect

Dynamic equations of flexible large displacement beam elements with considering second-order effect are derived by accurate finite element method of beam element under the condition of small deformation and concomitant coordinate method of large displacement. Starting with small deformation structure, mechanical model of flexible compression bending beam is built. Accurate finite element equations of planar beam are deduced and accurate stiff matrices of beam elements are obtained with considering second-order effect. Concomitant coordinate method of large displacement is adopted to build geometric nonlinear balanced equations of elastic beam elements. Dynamic equations of large displacement beam elements are derived in local coordinate system by relative description method of flexible multi body dynamics. According to geometrical relations of nodal displacements in concomitant and global coordinate system, dynamic equations of elements can be transformed to global coordinate system in order to achieve building of global dynamic equations with considering second-order effect. Taking amplitude condition of flexible arm support for a port crane as an example, elastic dynamic analysis is performed with considering second-order effect. The results show second-order effect should be considered in kinetic-elastic analysis for heavy load machinery with big flexibility.