A mathematical approach to study fluid-coupled vibration of eccentric annular plates. (October 2020)

• Record Type: Journal Article
• Authors: Askari, Ehsan; Jeong, Kyeong-Hoon; Ahn, Kwang-Hyun; Amabili, Marco
• Is Part Of: Journal of fluids and structures. Volume 98(2020)
• Publication Date: 2020-10
• Subjects: Eccentric annular plate -- Rayleigh–Ritz method -- Fluid–structure interaction -- Hydroelastic vibration; Fluid-structure interaction -- Periodicals; Fluid mechanics -- Periodicals; Structural dynamics -- Periodicals; Structural analysis (Engineering) -- Periodicals; 620.106
• DOI: 10.1016/j.jfluidstructs.2020.103129
• Languages: English
• ISSNs: 0889-9746

Abstract

Abstract: A mathematical method is proposed to study fluid-coupled vibration of axisymmetric plate structures with asymmetries due to either imperfection or practical reasons, e.g. the weight reduction of structure, natural frequency shifting, and accessibility. The suggested approach makes use of the separation of variables to determine general solutions of the partial differential equation of the plate transverse displacement, whilst defining multiple polar coordinate systems, each of which offers its own formulation of the plate deformation with respect to its coordinate system. Moreover, closed-form geometric equations and the chain rule for determining derivatives are implemented to move from one coordinate system to the other in order to satisfy boundary conditions. The mode shapes of the vibrating plate in the dry condition are determined and in turn used in the Rayleigh–Ritz method to characterize vibrational properties of the fluid-coupled plate structure. While implementing such an energy method, the fluid motion is formulated employing the velocity potential and solved using the separation of variables. Fluid–structure interaction is also taken into account satisfying the compatibility condition on the fluid–plate​ interface. The developed methodology to predict natural frequencies has been validated by comparison with results obtained by a commercial finite element program. It is also found that the eccentricity tends to reduce natural frequencies of the fluid-coupled system for the lower serial mode, but increases them for the higher serial modes regardless of the presence of liquid. Highlights: A mathematical method was proposed to study fluid-coupled vibration of eccentric annular plates. Closed-form relations were derived to transform solutions from a polar coordinate system to another. The proposed methodology was validated against finite element outcomes. The approach included fluid–structure interaction and fulfilled the fluid volume conservation law. Eccentricity size reduced system frequencies with lower modes, but increased those of higher modes.