Vibration analysis for elastic multi‐beam structures by the C0‐continuous time‐stepping finite element method

Abstract

AbstractSome C0‐continuous time‐stepping finite element method is proposed for investigating vibration analysis of elastic multi‐beam structures. In the time direction, the C0‐continuous Galerkin method is used to discretize the generalized displacement field. In the space directions, the longitudinal displacements and rotational angles on beams are discretized using conforming linear elements, while the transverse displacements on beams are discretized by the Hermite elements of third order. The error of the method in the energy norm is proved to be O(h+k3), where h and k denote the mesh sizes of the subdivisions in the space and time directions, respectively. The finite difference analysis in time is developed to discuss the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low‐frequency regime. The method has also been extended to study some nonlinear problems. A number of numerical tests are included to illustrate the computational performance of the method. Copyright © 2008 John Wiley & Sons, Ltd.