Vibrations of Shells and Rods

Le, Khanh Chau

doi:10.1007/978-3-642-59911-8

Cited by 80 publications

(110 citation statements)

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“…see [4,5] for greater detail. The lowest of them is associated with bending of the mid-surface strongly effected by shell curvature, see also [6].…”

Section: Dispersion Relationmentioning

confidence: 99%

“…These are based on appropriate physical assumptions or originate from asymptotic expansions, e.g. see [1][2][3][4][5] and references therein. Each of the approaches has its own advantages.…”

Section: Introductionmentioning

confidence: 99%

“…see [4,5,[15][16][17]. The developed long wave approximations have been applied to trapped mode analysis [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

2016

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A new asymptotic approximation of the dynamic equations in the 2D classical theory of thin elastic shells is established for a circular cylindrical shell. It governs long wave vibrations in the vicinity of the lowest cut-off frequency. At a fixed circumferential wave number the latter corresponds to the eigen frequency of in-plane vibrations of a thin almost inextensible ring. It is stressed that the well-known semi-membrane theory of cylindrical shells is not suitable for tackling a near-cut-off behaviour. The dispersion relation within the framework of the developed formulation coincides with the asymptotic expansion of the dispersion relation originating from full 2D shell equations. Asymptotic analysis also enables refining the geometric hypotheses underlying various adhoc setups, including the assumption on vanishing of shear and circumferential midsurface deformations used in the semi-membrane theory. The obtained results may be of interest for dynamic modelling of elongated cylindrical thin walled structures, such as carbon nanotubes.

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“…see [4,5] for greater detail. The lowest of them is associated with bending of the mid-surface strongly effected by shell curvature, see also [6].…”

Section: Dispersion Relationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

2016

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“…Van Dyke (1975) and Andrianov et al (2013), asymptotically justified only at the local highfrequency and low-frequency long-wave limits, but not over the whole frequency range. For example, composite structural models, see Berdichevsky (2009) and Le (1999), may bring a sort of mathematical validation for ad hoc Timoshenko-…”

mentioning

confidence: 99%

Dispersion of elastic waves in a strongly inhomogeneous three-layered plate

Kaplunov

Приказчиков

Prikazchikova

2017

International Journal of Solids and Structures

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Elastic wave propagation in a three-layered plate with high-contrast mechanical and geometric properties of the layers is analysed. Four specific types of contrast arising in engineering practice, including the design of stiff and lightweight structures, laminated glass, photovoltaic panels, and electrostatic precipitators in gas filters, are considered. For all of them the cut-off frequency of the first harmonic is close to zero. Two-mode asymptotic polynomial expansions of the Rayleigh-Lamb dispersion relation approximating both the fundamental bending wave and the first harmonic, are derived. It is established that these can be either uniform or composite ones, valid only over non-overlapping vicinities of zero and the lowest cut-off frequencies. The partial differential equations of motion associated with two-mode shortened dispersion relations are also presented.

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“…The problem of reduction of a three-dimensional dynamic problem of elasticity theory to a two-dimensional problem of shell theory is described in particular in the works of Aynola and Nigul (1965) and Grigolyuk and Selezov (1973), Achenbach (1969), Berdichevskii and Khan'Chau (1980), Goldenveizer et al (1993). Here, we also note the monographs by Kilchevsky's (1963), Berdichevskii (1983), Kaplunov et al (1998), Le (2012), Aghalovyan (2015) where these issues are rather thoroughly discussed and where a bibliography on the discussed topics can also be found. As it is hardly possible to find a detailed literature survey on the topics mentioned above, it is both practically impossible and there is no need to give an overview of the results on shell theory carried out at different times by means of different methods.…”

Section: Prefacementioning

confidence: 89%

Vibrations of Hollow Elastic Bodies

Mekhtiev¹

2018

Advanced Structured Materials

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Vibrations of Shells and Rods

Cited by 80 publications

References 0 publications

Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

Dispersion of elastic waves in a strongly inhomogeneous three-layered plate

Vibrations of Hollow Elastic Bodies

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