Asymptotical Mechanics of Thin-Walled Structures

Andrianov, Igor V.; Awrejcewicz, Jan; Manevich, L. I.

doi:10.1007/978-3-540-45246-1

Cited by 72 publications

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“…Shortened polynomial dispersion relations, governing long-wave low-frequency behaviour, e.g. see Kaplunov et al (1998) (1975) and Andrianov et al (2013), valid only over non-overlapping vicinities of zero and the lowest thickness resonance frequencies.…”

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confidence: 99%

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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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confidence: 99%

“…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-…”

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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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“…By means of asymptotic approaches ( [7], [8], [9]) complex eigenvalue problems of the stiffened shells theory can be transformed into problems which have simple analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Low-Frequency Vibrations of Thin Cylindrical Shell Stiffened by Rings With T-Shaped Cross-Section

Filippov¹

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. Small free low-frequency vibrations of a thin elastic cylindrical shell stiffened by the rings with T-shaped cross-section are analyzed. The narrow rings are considered as circular beams. The wide rings are treated as annular plates stiffened at one edge by a circular beam. In the both cases problem is reduced to solution of the eigenvalue problem for systems of linear differential equations containing a small parameter. By means of various asymptoticapproaches simple approximate formulas for the low frequencies are obtained. These formulas are used for the evaluation of optimal parameters corresponding to the maximal fundamental frequency of the ring-stiffened shell with a given mass.

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“…Using the correspondence principle, we reduce the solution of the governing viscoelastic boundary value problem to the solution of the elastic one. Then, we use the homogenization approach [2,15]. The derivation of the homogenized equations for the periodic composites is based on the investigation of the problem within a single unit cell.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section

2012

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The present paper provides details on the application of asymptotic homogenization techniques to the analysis of viscoelastic composite materials with fibres of diamond-shaped cross-section. The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. Then, we apply the homogenization approach. For solving the cell problem for small volume fractions, the boundary shape perturbation procedure and the composite cylinder assemblage model are used. For a volume fraction equal to 1/2, we use the Dykhne-Keller-Mendelson formula. Matching of limit solutions by two-point Padé approximants gives a formula for the effective properties valid for any volume fraction from the interval [0, 0.5].

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Asymptotical Mechanics of Thin-Walled Structures

Cited by 72 publications

References 0 publications

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

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

Low-Frequency Vibrations of Thin Cylindrical Shell Stiffened by Rings With T-Shaped Cross-Section

Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section

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