Affiliation:
1. College of Mechanical and Electrical Engineering, Hohai University, Changzhou, China
Abstract
The following paper presents a Hermite element method based on one-dimensional higher-order beam theory, to analyze the vibrations of thin-walled beams under various loading and boundary conditions. To derive cross-sectional shape functions for the higher-order deformation modes, a set of mutually orthogonal basis functions is utilized to linearly superpose the displacement field. The initial governing differential equations of the thin-walled beam are constructed by using C2 continuous Hermite polynomials as shape functions. Subsequently, the singular value decomposition (SVD) is employed to process the generalized characteristic matrix of the thin-walled beam to obtain physically meaningful characteristic deformations of the cross-section. Moreover, an improved one-dimensional higher-order beam model can be obtained by updating the initial governing equations with a set of predetermined cross-sectional deformation modes. Here, to illustrate the application and capabilities of the Hermite element method, numerical examples are given and demonstrate that the proposed Hermite element achieves superior computational accuracy with much fewer elements.