Hermite element for vibration analysis of thin-walled beams with higher-order beam theory

This paper presents a Hermite element method based on one-dimensional higher-order beam theory to analyse 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 utilised 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 is employed to process the generalised 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 it is demonstrated that the proposed Hermite element achieves superior computational accuracy with much fewer elements.