Computer modeling of tasks in dynamics of viscoelastic thin-walled elements in structures of variable thickness

Abdikarimov, Rustamkhan; Khodzhaev, Dadakhan

doi:10.5862/mce.49.9

Cited by 19 publications

(7 citation statements)

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“…Full and initial deflections, as well as the displacement of the shell are approximated in the form The integration of system (3) is performed using the numerical method proposed in [21]. The weakly singular Koltunov-Rzhanitsyn kernel of the form [27] is used as a relaxation kernel.…”

Section: Methodsmentioning

confidence: 99%

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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: Methodsmentioning

confidence: 99%

“…A vector-matrix method for solving nondecaying systems of nonlinear integrodifferential equations with variable coefficients and with weakly singular kernels of the hereditary theory of viscoelasticity based on the use of quadrature formulas is proposed in [21].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

et al. 2019

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“…Integrating the system of resolving equations of an orthotropic viscoelastic cylindrical panel of variable thickness twice in t, it can be written in integral form. Then, according to the numerical method proposed in [21], assuming that t=t i , t i =it, i=1,2,… (t is the integration step) and replacing the integrals with quadrature trapezoidal formulas for calculating unknowns w inm =w inm (t i ),  inm = inm (t i ), we obtain a recurrent formula.…”

Section: Methodsmentioning

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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“…Along with this, a number of publications were devoted to the study of the dynamics of various inhomogeneous systems, taking into account their features and operating conditions, in which the behavior of various structures under dynamic loading was evaluated [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Damping of high-rise structure vibrations with viscoelastic dynamic dampers

et al. 2020

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The paper is devoted to the study of dissipative properties of inhomogeneous viscoelastic systems of structures with dynamic vibration dampers. A detailed analysis of well-known studies concerning this problem is given. A mathematical model, technique and algorithm for studying the dissipative properties of inhomogeneous viscoelastic systems of high-rise buildings with dynamic vibration dampers are developed in the paper, taking into account the real geometry of structures. The hereditary BoltzmannVolterra theory was used to describe the viscoelastic properties of the damper and springs material. To solve the problem, the finite element method and the Muller method were used. The natural vibration modes of the Novo-Angren TPP smokestack with dynamic vibration dampers were investigated for various damper parameters. The imaginary part of complex eigenfrequency of the system was used as a dissipative index. A number of new mechanical effects were identified. The developed technique can be used to optimize the parameters of a viscoelastic damper for a structure.

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Computer modeling of tasks in dynamics of viscoelastic thin-walled elements in structures of variable thickness

Cited by 19 publications

References 0 publications

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

Dynamic analysis of an orthotropic viscoelastic cylindrical panel of variable thickness

Damping of high-rise structure vibrations with viscoelastic dynamic dampers

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