Natural oscillations of the liquid in the tank which has one of the walls in the form of flexible beam

Authors: Sharaborova E.S.
Published in issue: #7(24)/2018
DOI: 10.18698/2541-8009-2018-7-348
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
Keywords: small oscillations, ideal incompressible fluid, flexible beam, symmetrical bending, fluid elasticity, Hooke’s law, Fourier method, Laplace equation, oscillation frequency
Published: 30.07.2018

The paper investigates small oscillations of the ideal incompressible fluid in the rigid rectangular tank of the length l, where one of the walls under x = l is viewed as the flexible beam, which executes bending oscillations together with the liquid filling the tank. The material of the beam follows Hooke’s law. The article considers the case of symmetrical bending. The solution of this problem refers to quite complicated boundary-value problems of fluid elasticity. We suggest an unconventional method of the approximate solution. The results of the investigation can be applied while analyzing the dynamics of the hydraulic facilities and designing the multi-ton vessels (oil-tankers, gas tankers) in the field of shipbuilding.

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