A semi-analytical vibration analysis of partially wet square cantilever plate with numerical and experimental verification: partially wet modeshapes

[+] Author and Article Information
Yogesh Verma

IIT Kharagpur West Bengal Kharagpur, West Bengal 721302 India yogesh.nitkl@gmail.com

Nabanita Datta

IIT Kharagpur West Bengal Kharagpur, West Bengal 721302 India ndatta@naval.iitkgp.ernet.in

Rajendra Praharaj

IIT Kharagpur Kharagpur, 721302 India rajendra.praharaj@gmail.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received April 25, 2018; final manuscript received March 22, 2019; published online xx xx, xxxx. Assoc. Editor: Mahmoud Hussein.

ASME doi:10.1115/1.4043351 History: Received April 25, 2018; Accepted March 26, 2019


A semi-analytical study of a uniform homogenous partially submerged square cantilever plate vibration is presented. The structure is assumed to be a Kirchhoff's plate, clamped on one edge and free on the other three edges. The length wise section of the plate is a cantilever clamped-free (CF) beam, while the width-wise section is a free-free (FF) beam. The plate modeshape is a weighted superposition of the product of the beam modeshapes, with unknown weights. The CF beam has only flexural modes. The FF beam has two rigid-body modes, i.e. translational and rotational modes. Rayleigh-Ritz method of energy-minimization is used to set up the free vibration Eigen value problem. The Eigenvector give the unknown weights. The modeshapes generated are further used in the Boundary Element Method (BEM) to calculate the fluid inertia, which participates in the vibration and leads to a consistent drop in frequencies. The dependence of this reduction on the submergence level is studied for the first six frequencies of the plate. The frequencies are also experimentally generated by the impact hammer test, both in the dry state, and under three distinct levels of submergence: 25%, 50%, and 75% from the free edge opposite to the clamped edge. The frequencies and modeshapes are also verified through numerical analysis using the commercial code ANSYS 16.0. Conclusions are drawn regarding the influence of fluid inertia distribution on the final plate modeshape, leading to insights into sound structural designs.

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