On the three-dimensional vibrations of elastic prisms with skew cross-section

Zhou, Ding; McGee, O. G.

doi:10.1007/s11012-012-9648-9

Cited by 4 publications

(1 citation statement)

References 65 publications

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“…As is pointed by Zhou and McGee [27], the structures with complex cross-sections are mathematically difficult. So far, available literatures on guided waves in bars with complex cross-sections all resorted to various numerical methods, such as Finite Element method, Semi-analytical Finite Element method and Boundary Element method.…”

Section: Introductionmentioning

confidence: 98%

Dispersion curves of 2D rods with complex cross-sections: double orthogonal polynomial approach

Lefebvre

Zhang

et al. 2014

Meccanica

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Orthogonal polynomial series approach has been used to analyze the guided wave propagation in structures for about 20 years. These structures have always one infinite dimension in the waveguiding direction and, sometimes a regular finite crosssection (axially infinite solid or hollow cylinder for instance) and mostly often an infinite cross-section (infinite flat plate or half-space for instance). This paper presents a double orthogonal polynomial approach to investigate guided wave propagation in structures with only one infinite dimension in the waveguiding direction and a finite but complicated cross-sectional geometries as, rectangular type, L-type, 工-type and 回-type cross-sections. Through a numerical comparison with results available in literature, the validity of the extended polynomial approach is illustrated for a specific geometry. The dispersion properties of guided waves in rods with complex cross-sections as mentioned above are discussed.

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Section: Introductionmentioning

confidence: 98%

Dispersion curves of 2D rods with complex cross-sections: double orthogonal polynomial approach

Lefebvre

Zhang

et al. 2014

Meccanica

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Free vibration of an isotropic elastic skewed parallelepiped – A closed form study

Hanukah

Givli

2015

European Journal of Mechanics - A/Solids

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Free Vibration Analysis of Rotating Mindlin Plates with Variable Thickness

Fang

Zhou

2017

Int. J. Str. Stab. Dyn.

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The modal analysis of rotating cantilevered rectangular Mindlin plates with variable thickness is studied. The Ritz method is used to derive the governing eigenfrequency equation by minimizing the energy functional of the plate. The admissible functions are taken as a product of the Chebyshev polynomials multiplied by the boundary functions, which enable the displacements and rotational angles to satisfy the geometric boundary conditions of the plate. The Chebyshev polynomials guarantee the numerical robustness, while the Ritz approach provides the upper bound of the exact frequencies. The effectiveness of the present method is confirmed through the convergence and comparison studies. The effects of the dimensionless rotational speed, taper ratio, aspect ratio and thickness ratio on modal characteristics are investigated in detail. The frequency loci veering phenomenon along with the corresponding mode shape switching is exhibited and discussed.

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On the three-dimensional vibrations of elastic prisms with skew cross-section

Cited by 4 publications

References 65 publications

Dispersion curves of 2D rods with complex cross-sections: double orthogonal polynomial approach

Dispersion curves of 2D rods with complex cross-sections: double orthogonal polynomial approach

Free vibration of an isotropic elastic skewed parallelepiped – A closed form study

Free Vibration Analysis of Rotating Mindlin Plates with Variable Thickness

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