Waveguide finite elements for curved structures

Finnveden, Svante; Fraggstedt, Martin

doi:10.1016/j.jsv.2007.11.020

Cited by 68 publications

(37 citation statements)

References 15 publications

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“…For circular cylinders and car tires one way to achieve this within the framework of the finite element method is to use the waveguide FEM. For a formulation of the method for curved structures, including linear viscoelasticity, see [35]. The waveguide finite elements have been successfully applied, for example, to study the sound radiation of a rolling tire [36], an acoustical problem closely related to the mechanical one of this study from the wave dispersion perspective.…”

Section: Physical Interpretation and Critical Speedmentioning

confidence: 99%

A numerical study of traveling waves in a viscoelastic cylinder cover under rolling contact

Karttunen

Hertzen

2013

International Journal of Mechanical Sciences

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Polymer-covered cylinders are widely used in high-speed industrial rolling contact machines. In this paper, traveling waves which appear at high speeds in the viscoelastic polymer cover of a cylinder due to rolling contact are studied using a 2D finite element (FE) model for a two-cylinder system. Through eigenmode analysis of the polymer cover, it is found that an infinite number of natural mode families exist for the cylinder cover due to its finite thickness. A critical speed below which the traveling waves do not appear can be calculated on the basis of a resonance condition using the modal information. In dynamic analyses, traveling waves in the cover are identified as modified quasi-elastic Rayleigh waves composed of the eigenmodes of the polymer cover. The symbiosis of the eigenmode and wave propagation aspects allows the formation of a coherent overall picture of the traveling wave phenomenon. The critical speed according to the resonance condition is also the minimum phase velocity of the waves propagating in the cover. At the critical speed and above, there is a spectrum of resonant speeds due to wave dispersion. It is found that the traveling wave phenomenon is best described as a Rayleigh wave resonance in which contact-induced modified quasi-elastic Rayleigh waves arising at critical and supercritical speeds superpose to form a strong traveling shock wave.

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Section: Physical Interpretation and Critical Speedmentioning

confidence: 99%

A numerical study of traveling waves in a viscoelastic cylinder cover under rolling contact

Karttunen

Hertzen

2013

International Journal of Mechanical Sciences

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“…For this purpose, special shell finite elements based on the waveguide finite element method would be suitable. Such finite element analyses have so far been used to tackle stationary shell structures [43,44]. Alternatively, the homogeneity of the cylinder around the circumference and along the axis has been exploited to post-process the FE model of a small rectangular segment of the cylinder using periodic structure theory to obtain the wave characteristics of a cylinder [45].…”

Section: Introductionmentioning

confidence: 99%

“…Although the semi-analytical waveguide approaches of [43][44][45] may be very convenient and useful for a variety of problems, none of the semi-analytical finite element formulations developed so far a) allow for considering the typical effects of rotation (rotating modes and frequency veering) or b) can take into account the effects of pre-stress due to possible pressurisation and/or centrifugal forces. Therefore, the state-of-the-art in the considered field motivates further developments of finite elements especially tailored to model rotating and pre-stressed cylindrical shells.…”

Section: Introductionmentioning

confidence: 99%

A finite strip for the vibration analysis of rotating cylindrical shells

Senjanović

Ćatipović

Alujević

et al. 2018

Thin-Walled Structures

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In this article, a two-node finite strip with eight degrees of freedom for the free vibration analysis of pre-stressed rotating cylindrical shells is formulated. The circumferential mode shape profiles are described exactly using trigonometric functions. The axial mode shape profiles are approximated by bar and beam shape functions for membrane and bending displacements, respectively. In this way, a semi-analytical formulation is facilitated so that discretisation is required only in the axial direction. The accuracy and convergence of the developed finite strip are confirmed by comparisons with the analytical results. Excellent agreement is observed both for stationary and rotating shells.

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“…Damljanovic and Weaver [2] developed the linear triangular elements for SAFE method using Lagrange's equations to investigate the elastic waves in waveguides of arbitrary cross-section. Gavric [3] calculated the dispersion relationship in a free rail by using triangular and quadrilateral elements, with those elements obtained from Hamilton's principle. The SAFE method has also be adopted to investigate the wave propagation characteristics for thin-walled structures in [4], where the polynomial interpolation is used in the propagation axis thus leads to the polynomial eigenvalue problems.…”

Section: Introductionmentioning

confidence: 99%