Wave characterization of cylindrical and curved panels using a finite element method

Abstract

This paper describes a wave finite element method for the numerical prediction of wave characteristics of cylindrical and curved panels. The method combines conventional finite elements and the theory of wave propagation in periodic structures. The mass and stiffness matrices of a small segment of the structure, which is typically modeled using either a single shell element or, especially for laminated structures, a stack of solid elements meshed through the cross-section, are postprocessed using periodicity conditions. The matrices are typically found using a commercial FE package. The solutions of the resulting eigenproblem provide the frequency evolution of the wavenumber and the wave modes. For cylindrical geometries, the circumferential order of the wave can be specified in order to define the phase change that a wave experiences as it propagates across the element in the circumferential direction. The method is described and illustrated by application to cylinders and curved panels of different constructions. These include isotropic, orthotropic, and laminated sandwich constructions. The application of the method is seen to be straightforward even in the complicated case of laminated sandwich panels. Accurate predictions of the dispersion curves are found at negligible computational cost.

Wave Propagation in Pipes With Helical Patterns

“…The WFE formulation for axisymmetric structures [10,11] can be applied to predict the wave characteristic of structures with helical geometry. As an example a helically reinforced pipe is considered as in Figure 2(a), but the approach presented here can be equally applied to any other curved panels with helical orthotropy.…”

“…Wave characteristics are obtained by means of an analytical method and a Wave Finite Element (WFE) method. The latter is an extension of the WFE approach for 2D waveguides [9,10] to structures showing a helical pattern. In the first part of the paper the approaches are illustrated.…”

Using Periodicity to Mitigate Ground Vibration

“…Simple problems can be analysed analytically by means of Floquet analysis, and combining this approach with, for example, the finite-element method, periodic two and three-dimensional structures of complex geometries can be studied regarding their wave propagation properties. Such models have been used, for example, by Manconi and Mace [4] to study curved panels, and by Domadiya et al [5] to study wave propagation in beams with periodically placed masses or changes to the cross section. The combination of Floquet theory and finite-elements has also be used for analysis of railways [6], mainly to allow studying long structures with low computational cost.…”

Vibration Attenuation in Pipes: Design and Experimental Validation of a Resonant Metamaterial Solution

“…shown in [15]. Therefore, next to studies on the stopband behavior in flat metamaterial plates, it is worth to investigate the effect of curvature on the behavior of locally resonant metamaterials.…”