Time-domain spectral finite element based on third-order theory for efficient modelling of guided wave propagation in beams and panels

We develop a computationally efficient time-domain spectral finite element (SFE) based on Levinson–Bickford–Reddy’s third-order theory to accurately predict guided wave propagation in beam- and panel-type structures. The deflection is interpolated using the C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {C}^1$$\end{document}-continuous Lobatto spectral interpolation function recently developed by the authors, while the axial displacement and shear rotation are interpolated using the C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {C}^0$$\end{document}-continuous Lobatto basis functions. A comprehensive numerical study assesses the accuracy and efficiency of the developed element for free vibration and wave propagation response of beams and infinite strips under narrowband tone burst and broadband impact excitations. In terms of accuracy, convergence, and computational effort, we show that the new spectral element performs far better than its conventional counterpart and other available one-dimensional spectral elements with a similar number of degrees of freedom. Although SFEs in the literature often use under-integration for mass matrices to make them diagonal or near-diagonal to gain efficiency, we evaluate the relative performance of full integration and under-integration of mass matrices in terms of convergence rate and computational efficiency. The element will be of immense use for model-based structural health monitoring applications requiring fast and accurate analysis.