Dynamics of interaction of elastic elements of a vibrating machine with the compressed liquid layer lying between them

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

doi:10.3103/s1052618810040047

Cited by 28 publications

(17 citation statements)

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“…Among the last studies on the dynamics and stability of the pipelines and its elements during the flow inside them of liquid or gas flow should be noted the next studies [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and many others. Among the works of the authors of this article by the investigations of the dynamics and stability of elastic bodies interacting with the gas flow, note the monographs and articles [17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic stability of deformable elements of one class of aeroelastic constructions

Velmisov¹,

Ankilov²,

Semenova³

2016

AIP Conference Proceedings

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At designing of the constructions and the devices interacting with the flow of gas or liquid, it is necessary to solve the problems associated with the investigation of the stability required for their functioning and operational reliability. The definition of stability of an elastic body corresponds to the Lyapunov's concept of stability of dynamical system. A mathematical model of the device relating to the vibration technique, which is intended for intensification of technological processes, for example, the process of mixing, is considered. The action of these devices is based on the oscillations of elastic elements at the flowing around gas or liquid flow. The dynamic stability of the elastic element, located inside of the flow channel with the subsonic flow of gas or liquid (in an ideal model of a compressible environment) is investigated. The model is described by coupled system of partial differential equations for the unknown functionsthe potential of the gas velocity and deformation of the elastic element. On the basis of the construction of functional, the sufficient conditions of the dynamical stability, imposing restrictions on the free-stream velocity of the gas, the flexural stiffness of the elastic element, and other parameters of the mechanical system are obtained. The examples of construction of the stability regions for particular parameters of the mechanical system are presented.

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Section: Introductionmentioning

confidence: 99%

“…If we consider the functional (12), then according to Lemma 1, we can conclude that the functions ( , , ) x x y t , ( , , ) y x y t , ( , ) w x t are stable with respect to perturbations of the initial data. The estimate (40) implies that the solution ( , ) w x t is stable with respect to perturbations of the initial data …”

mentioning

confidence: 96%

Dynamic stability of deformable elements of one class of aeroelastic constructions

Velmisov¹,

Ankilov²,

Semenova³

2016

AIP Conference Proceedings

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“…The present paper studies the case, where the discs are considered to be rigid and the case with one of the discs being elastic. The analogous problem in a two-dimensional setting for two plates of finite sizes is solved in [12]. The investigation of a beam hydroelastic oscillations in a viscous liquid flow with an application to piezoelectric elements, aimed at obtaining energy from the flow, is made in [13].…”

Section: Introductionmentioning

confidence: 99%

Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation

Kondratov

Mogilevich

Popov

et al. 2018

J. Phys.: Conf. Ser.

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Abstract. The forced hydroelastic oscillations of a circular plate resting on elastic foundation are investigated. The oscillations are caused by a stamp vibration under interaction with a plate through a thin layer of viscous incompressible liquid. The axis-symmetric problem for the regime of the steady-state harmonic oscillations is considered. On the basis of hydroelasticity problem solution the laws of plate deflection and pressure in the liquid are found. The functions of the amplitudes deflection distribution and liquid pressure along the plate are constructed. The presented mathematical model provides for investigating viscous liquid layer interaction dynamics with a circular plate resting on an elastic foundation. The above-mentioned model makes it possible to define the plate oscillations resonance frequencies and the corresponding amplitudes of deflection and liquid pressure, as well. Keywords -circular plate; hydroelastic oscillations; vibration stamp; viscous liquid; Winkler foundation IntroductionThe investigations of the plates and supporting elastic foundations interaction are of theoretical, as well as of practical interest. For example, the review [1], devoted to this subject matter, considers the items of elastic foundations development models, as well as various approaches to analytical and numerical investigation of beams and plates with elastic foundations interaction. Reference [2] studies free and forced oscillations of a circular plate, the plate resting on Winkler foundation. The investigation is carried out in axis-symmetric setting for the cases of a simply supported edge and a clamped one. Reference [3] studies stability and oscillations of circular polar orthotropic plates of variable thickness resting on Winkler foundation. The cases of the simply supported and clamped edge of the plates are considered. Reference [4] deals with investigation of oscillations of a thin circular plate with elastic fixation along the contour, the plate resting on Winkler elastic foundation. Reference [5] studies free oscillations of thin circular plate on Winkler foundation. The axis-symmetric problem under the condition of foundation rigidity change in radial direction is investigated in the above-mentioned reference. References [6,7] consider oscillations and stability of multi-layered circular plates on elastic foundation under the impact of local and distributed loadings of various nature. The Winkler and Pasternak models are used for foundation reactions modelling. On the other hand, the investigations of hydroelastic interaction of circular plates with an ideal liquid are of

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“…The present paper studies the case when the discs are considered being solid, as well as the case with one of the discs being elastic. The analogous problem in a flat setting for the two vibrating plates of finite sizes is studied in reference [12]. Reference [13] investigates hydroelastic oscillation of the beam in a viscous liquid flow for the case of piezo-electric elements with the aim of obtaining energy from the flow.…”

Section: Introductionmentioning

confidence: 99%

Hydroelastic oscillation of a plate resting on Pasternak foundation

Kondratov¹,

Mogilevich²,

Popov³

et al. 2017

Vib. proced.

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Abstract. The bending oscillations of the plate, resting in Pasternak foundation and interacting with a vibrating stamp through a thin layer of viscous incompressible liquid, are investigated. On the basis of hydroelasticity problem solution, the laws of the plate deflections and pressure in the liquid are found. The functions of the deflections amplitude distribution and liquid pressure along the channel are constructed. The obtained results allow to define oscillations resonance frequencies and to study viscous liquid interaction with elastic plates, resting on Pasternak foundation.

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Dynamics of interaction of elastic elements of a vibrating machine with the compressed liquid layer lying between them

Cited by 28 publications

References 0 publications

Dynamic stability of deformable elements of one class of aeroelastic constructions

Dynamic stability of deformable elements of one class of aeroelastic constructions

Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation

Hydroelastic oscillation of a plate resting on Pasternak foundation

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