Longitudinal and Transverse Oscillations of an Elastically Fixed Wall of a Wedge-Shaped Channel Installed on a Vibrating Foundation

Mogilevich, L. I.; Popov, V. S.; Popova, A. A.

doi:10.3103/s1052618818030093

Cited by 17 publications

(5 citation statements)

References 8 publications

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“…However, in recent years, most of the works have been devoted to the study of the stability of pipeline systems and cylindrical shells interacting with a liquid or gas flow. Among the latter, we note the works [Abdelbaki et al, 2019;Blinkov et al, 2018;Butt et al, 2021;Chehreghani et al, 2021;Kheiri and Paidoussis, 2015;Kontzialis et al, 2017;Moditis et al, 2016;Mogilevich et al, 2017;Mogilevich et al, 2018;Mogilevich and Ivanov, 2020;Moshkelgosha et al, 2017] and many others. Among the works of the authors of this article on the study of the dynamics, stability and controllability of pipeline systems, we note the works [Gladun and Velmisov and Ankilov, 2016;Velmisov and Ankilov, 2017;Velmisov and Ankilov, 2018;Velmisov and Ankilov, 2019;Velmisov and Ankilov, 2021].…”

Section: Introductionmentioning

confidence: 80%

Mathematical modeling in problems about dynamics and stability of elastic elements of wing profiles

Velmisov

Ankilov

2021

CAP

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The mathematical models describing the dynamics of elastic elements of wing structures and representing the initial-boundary value problems for systems of partial differential equations are proposed. The dynamics and stability of elastic elements of wings, flown around by a gas or liquid stream in a model of an incompressible medium, are investigated. To study the dynamics of elastic elements and a gas-liquid medium, both linear and nonlinear models of the mechanics of a solid deformable body and linear models of the mechanics of liquid and gas are used. On the basis of the constructed functionals for partial differential equations, the sufficient stability conditions are obtained in analytical form. The conditions impose restrictions on the parameters of mechanical systems. The obtained stability conditions are necessary for solving the problems of controlling the parameters of the aeroelastic system. On the basis of the Galerkin method, a numerical study of the dynamics of elastic elements was carried out, the reliability of which is confirmed by the obtained analytical results.

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Section: Introductionmentioning

confidence: 80%

Mathematical modeling in problems about dynamics and stability of elastic elements of wing profiles

Velmisov

Ankilov

2021

CAP

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“…Many experimental and theoretical studies have been devoted to stability analysis of elastic bodies interacting with gas and liquid. Among them we should note [Abdelbaki et al, 2019;Blinkov et al, 2018;Kheiri and Paidoussis, 2015;Kontzialis et al, 2017;Moditis et al, 2016;Mogilevich et al, 2017;Mogilevich et al, 2018;Moshkelgosha et al, 2017;Zvyagin and Gur'ev, 2017] and many others. Among the works of the authors of this article about fluid-structure interaction, note the monograph and articles [Ankilov and Velmisov, 2013;Ankilov and Velmisov, 2016;Velmisov and Ankilov, 2017;.…”

Section: Introductionmentioning

confidence: 94%

About dynamic stability of deformable elements of vibration systems

Velmisov

Ankilov

2019

CAP

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The dynamics and stability of the elastic elements of vibration devices, modeled by a channel containing elastic elements, are investigated. Inside the channel flows a stream of stirred liquid. The model of the device with two elastic elements is considered. The solution of the aerohydrodynamic part of the problem, based on the methods of the theory of functions of a complex variable, is given. The solution of the original problem is reduced to the study of a coupled system of partial differential equations for the deformations of elements, which makes it possible to study their dynamics. On the basis of the constructed functional for this system, the sufficient conditions of stability are obtained. The conditions impose restrictions on the parameters of the mechanical system. Based on the Galerkin method, the numerical experiments for specific examples of mechanical systems were carried out, confirming the reliability of the investigations. A special case of the model of device with one elastic element is considered. Based on this case, a comparison with the model of the vibration device considered earlier is made.

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“…Traditionally, when calculating the vibrations of the mechanical systems elements, they are limited to the linear theory for elastic elements [1,2]. For example, in this approach, the hydroelastic vibrations of plates and beams interacting with a liquid [3][4][5][6][7][8][9][10][11], as well as elastically fixed channel walls [12][13][14][15], are studied. In particular, in paper [3], a model was developed for studying the natural vibrations of a clamped circular plate, on one side of which there is an unlimited volume of an ideal liquid.…”

Section: Introductionmentioning

confidence: 99%

“…The forced vibrations simulation for the end seal flexibly restrained at the edge of a narrow channel filled with a viscous liquid was performed in [13,14]. Longitudinal and transverse vibrations of a wall suspended on linear springs, as applied to a wedge-shaped channel filled with a viscous liquid, were studied in [15]. On the other hand, at present, elastic elements with significantly nonlinear characteristics are increasingly being used, which requires consideration of nonlinear oscillations [16].…”

Section: Introductionmentioning

confidence: 99%

Non-Linear Oscillations of the Channel Wall Filled with a Viscous Liquid Induced by the Vibrating Foundation

Popov

Popova

Christoforova

2022

J. Phys.: Conf. Ser.

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The paper considers the issues of mathematical modelling nonlinear vibrations for the wall of a narrow parallel walled channel filled with a viscous incompressible liquid. The upper channel wall is a rigid rectangular plate supported by nonlinear spring with a cubic restoring force, while the bottom one is a fixed rigid rectangular plate. The case of nonlinear oscillations of the upper channel wall due to channel’s foundation vibration has been investigated in the frame of hydroelasticity problem. The main attention is paid to the consideration of steady-state nonlinear oscillations for the upper channel wall and the creeping motion of the liquid in the channel. The liquid layer reaction acting on the upper channel wall is found and the channel’s wall nonlinear oscillation equation is obtained taking into account the energy dissipation due to the liquid viscosity. It was shown that this equation coincided with the Duffing one. The solution of the nonlinear oscillation equation was carried out by the harmonic balance method. Based on the found solution, the hydroelastic response of the channel wall on a nonlinear elastic suspension to the channel foundation vibration was determined.

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Longitudinal and Transverse Oscillations of an Elastically Fixed Wall of a Wedge-Shaped Channel Installed on a Vibrating Foundation

Cited by 17 publications

References 8 publications

Mathematical modeling in problems about dynamics and stability of elastic elements of wing profiles

Mathematical modeling in problems about dynamics and stability of elastic elements of wing profiles

About dynamic stability of deformable elements of vibration systems

Non-Linear Oscillations of the Channel Wall Filled with a Viscous Liquid Induced by the Vibrating Foundation

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