Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

Éshmatov, B. Kh.

doi:10.1007/s11071-006-9163-4

Cited by 10 publications

(3 citation statements)

References 22 publications

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“…Khudayarov and Bandurin [4] studied the effects of the viscoelastic parameters on the nonlinear vibrations of cylindrical panels in a gas flow and showed that the viscoelastic properties have significant effect on the vibrations of the cylindrical panel. Based on the Kirchhoff-Love hypothesis, Eshmatov et al [5][6][7][8][9] investigated the linear and nonlinear vibration and dynamic stability of a viscoelastic cylinder. They considered the effect of viscoelastic properties, concentrated masses, rotary inertia, and shear deformation on the dynamic stability of a cylindrical panel.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration analysis of fractional viscoelastic cylindrical shells

2020

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Nonlinear vibrations of viscoelastic thin cylindrical shells are studied in this paper. The viscoelastic properties are modeled using the Kelvin-Voigt fractional-order constitutive relationship. Based on the nonlinear Love thin shell theory, the structural dynamics of the cylindrical shell is modeled by using the Newton's second law, and the Galerkin method is used to discretize the nonlinear partial differential equations into the set of nonlinear ordinary differential equations. The method of multiple scales is used to solve the nonlinear ordinary differential equations, and the amplitude-frequency and phase-frequency equations are extracted. The obtained results are verified with available investigations, and the effects of fractional parameters, excitation, and nonlinearity on the amplitude-frequency and phase-frequency responses of the viscoelastic cylindrical shells are outlined.

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Section: Introductionmentioning

confidence: 99%

Nonlinear vibration analysis of fractional viscoelastic cylindrical shells

2020

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“…The nonlinear governing equation were solved by using the Runge-Kutta method. The vibration problem of a viscoelastic cylindrical shell in a geometrically nonlinear formulation was studied using the refined Timoshenko theory by Eshmatov [5]. He solved the equations by the Bubnov-Galerkin procedure combined with a numerical method based on the quadrature formulas.…”

Section: Introductionmentioning

confidence: 99%

An analytical procedure for dynamic response determination of a viscoelastic beam with moderately large deflection using first-order shear deformation theory

Malek-Hosseini

Eipakchi

2016

Mechanics of Advanced Materials and Structures

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In this paper, the dynamic response of a viscoelastic beam with moderately large deflection and subjected to transverse and axial loads is studied using the first order shear deformation theory.The von-Karman strain displacement relations and the Hooke's law are used for formulation. The solution of the equations which are a system of nonlinear partial differential equations are obtained analytically using the perturbation technique in conjunction with the eigenfunction expansion method. The results are compared with the finite elements method. Also a sensitivity analysis is performed and the effects of geometrical and material properties are investigated on the response.

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“…In a series of papers [11,12,13,14,15,16] the vibrations and dynamic stability of viscoelastic cylindrical shells and cylindrical panels, with and without concentrated masses, using the Kirchhoff-Love hypothesis and Timoshenko theories and taking into account shear deformation and rotary inertia were considered.…”

Section: Introductionmentioning

confidence: 99%

Geometry Effects on the Nonlinear Oscillations of Viscoelastic Cylindrical Shells

Prado¹,

Amabili²,

Gonçalves³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In this work the influence of geometry, load and material properties on the nonlinear vibrations of a simply supported viscoelastic circular cylindrical shell subjected to lateral harmonic load is studied. Donnell's non-linear shallow shell theory is used to model the shell, assumed to be made of a Kelvin-Voigt material type, and a modal solution with six degrees of freedom is used to describe the lateral displacements. The Galerkin method is applied to derive a set of coupled non-linear ordinary differential equations of motion.Obtained results show that the viscoelastic dissipation parameter has significant influence on the instability loads and resonance curves.

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Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

Cited by 10 publications

References 22 publications

Nonlinear vibration analysis of fractional viscoelastic cylindrical shells

Nonlinear vibration analysis of fractional viscoelastic cylindrical shells

An analytical procedure for dynamic response determination of a viscoelastic beam with moderately large deflection using first-order shear deformation theory

Geometry Effects on the Nonlinear Oscillations of Viscoelastic Cylindrical Shells

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