Free Vibration Analysis of Stiffened Lock Gate Coupled with Reservoir Fluid considering Linearised Free Surface Condition

Abstract

The effect of surrounding reservoir fluid on the stiffened lock gate structure is investigated using the finite element method. A single stiffener is used to stiffen the plate, which is placed edge to edge along the height on the plate's center nodal line. Mindlin’s plate bending and Euler’s beam theories are used to formulate plate and stiffener, respectively. The stiffened lock gate material is assumed to be isotropic, homogeneous, uniformly thick and elastic in nature. The fluid is assumed to be incompressible and inviscid, resulting in an irrotational flow field. The fluid domain's top free surface is assumed to be linear based on Airy’s linear wave theory. The far boundary of the fluid domain is truncated numerically close to the lock gate to control the size of computation without influencing the results, very much. It is truncated by solving the Laplace equation using Fourier half range cosine series expansion in the finite element formulation. Pressure and displacement are considered as nodal variables for the fluid domain and the lock gate, respectively. The interaction between the fluid domain and the lock gate is established by finite element formulation and transformed into a computer code, written in FORTRAN. The natural frequencies of clamped and simply supported stiffened lock gates are evaluated by the varying extent of the fluid. Both stiffened and unstiffened gates are compared. The results are beneficial to the engineers/designers when the gate structure is subjected to cataclysmic events.