A one-dimensional higher-order dynamic modeling method for thin-walled beams with circular cross-sections

Abstract

This paper addresses the construction of a dynamical model for a thin-walled beam with circular cross-section in the framework of one-dimensional higher-order beam theory. And a method for pattern recognition of circular thin-walled structures is proposed based on principal component analysis. Initially, a set of equal length linear segments are defined to discretize the mid-line of a circular section. Preliminary deformation modes of thin-walled structures, defined over the cross-section through kinematic concept, are parametrically derived through changing the discretization degree of the section. Next, the generalized eigenvectors are derived from the governing equations, and the characteristic deformation modes of circular sections with different discretization degrees are solved based on principal component analysis. In addition, a reduced higher-order model can be obtained by updating the initial governing equations with a selective set of cross-section deformation modes. The features include further reducing the number of degree of freedoms (DOFs) and significantly improving computational efficiency while ensuring accuracy. For illustrative purposes, the versatility of the procedure is validated through both numerical examples and comparisons with other theories.