Author(s)

S.M. Hashemi

Abstract

The use of trigonometric interpolation functions for vibration analysis of beam structures - bridging gap between FEM and exact formulations S.M. Hashemi Department of Mechanical, Aerospace & Industrial Engineering, Ryerson University, Canada Abstract The small linear harmonic oscillations of linearly elastic coupled beam structures are addressed. The Finite Element Method (FEM), conventional Hermite beam formulation, and the resulting element matrices are then briefly discussed. The so-called exact Dynamic Stiffness Matrix (DSM) formulation for the longitudinal vibration of axially loaded beams is presented. Finally, the Dynamic Finite Element (DFE) approach is introduced and its application to the axial vibration of beams is displayed. The comparison is made between the standard static and (frequency dependent) Dynamic beam shape functions. The DFE formulation, combines the generality of the FEM and the high precision provided by DSM methods. The weighting functions and shape functions are

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