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Keywords = natural vibrations of thin plates in fluid

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30 pages, 9216 KB  
Article
Stochastic Vibrations of a System of Plates Immersed in Fluid Using a Coupled Boundary Element, Finite Element, and Finite Difference Methods Approach
by Michał Guminiak, Marcin Kamiński, Agnieszka Lenartowicz and Maciej Przychodzki
Materials 2023, 16(9), 3583; https://doi.org/10.3390/ma16093583 - 7 May 2023
Cited by 2 | Viewed by 1922
Abstract
The main objective of this work is to investigate the natural vibrations of a system of two thin (Kirchhoff–Love) plates surrounded by liquid in terms of the coupled Stochastic Boundary Element Method (SBEM), Stochastic Finite Element Method (SFEM), and Stochastic Finite Difference Method [...] Read more.
The main objective of this work is to investigate the natural vibrations of a system of two thin (Kirchhoff–Love) plates surrounded by liquid in terms of the coupled Stochastic Boundary Element Method (SBEM), Stochastic Finite Element Method (SFEM), and Stochastic Finite Difference Method (SFDM) implemented using three different probabilistic approaches. The BEM, FEM, and FDM were used equally to describe plate deformation, and the BEM was applied to describe the dynamic interaction of water on a plate surface. The plate’s inertial forces were expressed using a diagonal or consistent mass matrix. The inertial forces of water were described using the mass matrix, which was fully populated and derived using the theory of double-layer potential. The main aspect of this work is the simultaneous application of the BEM, FEM, and FDM to describe and model the problem of natural vibrations in a coupled problem in solid–liquid mechanics. The second very important novelty of this work is the application of the Bhattacharyya relative entropy apparatus to test the safety of such a system in terms of potential resonance. The presented concept is part of a solution to engineering problems in the field of structure and fluid dynamics and can also be successfully applied to the analysis of the dynamics of the control surfaces of ships or aircraft. Full article
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25 pages, 1078 KB  
Article
Analytical Solution of Sloshing in a Cylindrical Tank with an Elastic Cover
by Mohammad Yaghoub Abdollahzadeh Jamalabadi
Mathematics 2019, 7(11), 1070; https://doi.org/10.3390/math7111070 - 7 Nov 2019
Cited by 13 | Viewed by 4039
Abstract
Coupled fluid-structure is significant in many aspects of engineering applications such as aerospace fuel tanks, the seismic safety of storage tanks and tuned liquid dampers. Numerical investigation of the effects of thin plate cover over a cylindrical rigid fuel tank filled by an [...] Read more.
Coupled fluid-structure is significant in many aspects of engineering applications such as aerospace fuel tanks, the seismic safety of storage tanks and tuned liquid dampers. Numerical investigation of the effects of thin plate cover over a cylindrical rigid fuel tank filled by an inviscid, irrotational, and incompressible fluid is investigated. Governing equations of fluid motion coupled by plate vibration are solved analytically. A parameter study on the natural frequency of coupled fluid-structure interaction is performed. The results show the non-dimensional natural frequency of coupled fluid-structure is a function of mass ratio, plate elasticity number and aspect ratio. This function is derived numerically for high aspect ratios which in companion with a semi-analytical could be used in the engineering design of liquid tanks with a cover plate. Full article
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