Abstract

<p>The Dynamic Finite Element (DFE) theory is employed to calculate the natural frequencies and mode shapes of three-layered sandwich beams. Three formulations are developed and tested using a number of different numerical cases. The first two theories pertain to the analysis of straight beams while the third one is developed for the analysis of curved beams. The results from all three derivations agree well with published data that uses Classical Finite Element (FEM) theory and the Dynamic Stiffness Method (DSM) in the analysis of the free vibration behaviour of sandwich beams. For all test cases, the DFE results agree well with the published results as well as the FEM developed as an additional benchmark for the DFE. The results of the research are very encouraging and demonstrate that DFE is a valuable structural analysis tool that can be used in conjunction with FEM and DSM. </p>

Highlights

  • Introduction to Sandwich ConstructionApplications of sandwich construction and composites continue to expand

  • The first four coupled natural frequencies of the beam were calculated using the developed Dynamic Finite Element (DFE) and finite element method (FEM) theory and compared to those published by Banerjee [8] obtained using the Stodola method, Dynamic Stiffness Method (DSM) and other FEM models, which are shown in the last column of Table 2-1

  • A dynamic finite element formulation has been developed for a symmetrical three-layered sandwich beam based on the Galerkin-type weak integral form of the differential equations of motion

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Summary

Introduction

Introduction to Sandwich ConstructionApplications of sandwich construction and composites continue to expand. The dynamic finite element formulation developed in the previous chapter is only applicable to the free vibration analysis of symmetric three-layered straight sandwich beams in which the top and bottom (face) layers have common cross-sections and material properties. This is rarely the case in many real applications of and the need for a more general formulation is required which allows for variations in the cross-sections and material properties of the layers. Core layer 2, governed by Timoshenko beam theory, possesses a linearly varying axial displacement; the cross-section of the core does not rotate in order to be normal to the common flexure, but shears as necessary. The middle layer has consequential shear as its imposed motion is determined by the continuity of the two face layers and the assumed variation across its thickness (the core mid-layer axial displacement u2 is no longer used)

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