On effect of initial imperfections on parametric vibrations of cylindrical shells with geometrical non-linearity

Kochurov, Roman; Аврамов, К. В.

doi:10.1016/j.ijsolstr.2011.10.023

Cited by 15 publications

(3 citation statements)

References 25 publications

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“…The effect of initial imperfections on the parametric vibrations of cylindrical shells is analyzed in [19]. The shell has moderate amplitudes of vibrations; therefore, geometrically nonlinear theory is used.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

et al. 2019

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The problem of parametric oscillations of an isotropic viscoelastic shallow shell of variable thickness under periodic load is considered. It is believed that under the influence of specified load, the shallow shell allows displacements (in particular, deflections), commensurate with its thickness. In a geometrically nonlinear statement, taking into account the viscoelastic properties of material, a mathematical model of the problem has been developed using the classical Kirchhoff-Love hypothesis. Using the Bubnov-Galerkin method based on the polynomial approximation of the deflections, the problem is reduced to the study of the system of integro-differential equations, where time is the independent variable. The solution of the system of integrodifferential equations is determined by the proposed numerical method. Based on this method, a numerical solution algorithm is described. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. At the same time, the effect of geometric nonlinearity, viscoelastic properties of material, as well as other physicomechanical and geometric parameters and factors (rheological parameters, thickness, initial shape imperfections, aspect ratios, boundary conditions, excitation coefficient) on the area of dynamic instability is taken into account. The results obtained in this study are in good agreement with the results and data obtained by other authors.

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Section: Introductionmentioning

confidence: 99%

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

et al. 2019

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“…and periodic loads since dynamic instabilities interact with the static potential well. The effect of initial geometric imperfections on the parametric vibrations of circular cylindrical shells was also investigated by Kochurov and Avramov [101]. In their analysis, Donnell's non linear shallow shell theory was used and an expansion of transverse displacement with eight degrees of freedom including six asymmetric modes (driven and companion modes), one axisymmetric mode and a constant term was utilized to obtain the equations of motion via the Galerkin approach.…”

Section: Dynamics and Stability Of Shells Subjected To Axial Loadsmentioning

confidence: 99%

Non-linear vibrations of shells: A literature review from 2003 to 2013

Alijani

Amabili

2014

International Journal of Non-Linear Mechanics

211

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International audienceThe present literature review focuses on geometrically non linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non linear vibrations of shells subjected to normal and in plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non linear vibrations of shells and panels, including (i) fluid structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non linear normal modes and meshless methods are reviewed in depth

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“…In [5], based on Donnell's theory, the results of studying the influence of initial irregularities on parametric vibrations of geometrically nonlinear cylindrical shells are presented.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of an orthotropic viscoelastic cylindrical panel of variable thickness

et al. 2021

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The intensive development of the modern industry is associated with the emergence of a variety of new composite materials. Plates, panels, and shells of variable thickness made of such materials are widely used in engineering and machine building. Modern technology for the manufacture of thin-walled structures of any configuration makes it possible to obtain structures with a given thickness variation law. Such thin-walled structures are subjected to various loads, including periodic ones. Nonlinear parametric vibrations of an orthotropic viscoelastic cylindrical panel of variable thickness are investigated without considering the elastic wave propagation. To derive a mathematical model of the problem, the Kirchhoff-Love theory is used in a geometrically nonlinear setting. The viscoelastic properties of a cylindrical panel are described by the hereditary Boltzmann-Volterra theory with a three-parameter Koltunov-Rzhanitsyn relaxation kernel. The problem is solved by the Bubnov-Galerkin method in combination with the numerical method. For the numerical implementation of the problem, an algorithm and a computer program were developed in the Delphi algorithmic language. Nonlinear parametric vibrations of orthotropic viscoelastic cylindrical panels under external periodic load were investigated. The influence of various physical, mechanical, and geometric parameters on the panel behavior, such as the thickness, viscoelastic and inhomogeneous properties of the material, external periodic load, were studied.

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On effect of initial imperfections on parametric vibrations of cylindrical shells with geometrical non-linearity

Cited by 15 publications

References 25 publications

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

Non-linear vibrations of shells: A literature review from 2003 to 2013

Dynamic analysis of an orthotropic viscoelastic cylindrical panel of variable thickness

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