Modeling the End Seal Oscillations of the Channel Filled with Pulsating Viscous Fluid

Kondratov, Dmitry; Popov, V. S.; Popova, A. A.

doi:10.1007/978-3-030-54814-8_77

Cited by 1 publication

(2 citation statements)

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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%

“…In paper [12], the vibrations of a die supported by a linear spring and located at the channel bottom, during its interaction with an ideal liquid with a free surface, were studied. 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].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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