Free Vibration Analysis of Lock Gate Structure

Abstract

The effect of fluid on the natural frequencies of a vertical rectangular lock gate is investigated. The fluid is assumed to be inviscid and incompressible having an irrotational flow field. The far boundary of fluid domain is truncated near the lock gate structure by solving the Laplace equation using Fourier half range cosine series expansion. The formulation of lock gate structure is governed using Mindlin’s plate theory. The coupled interaction between the fluid domain and the lock gate structure is established using finite element method (FEM) and a computer code is written using FORTRAN. Convergence study and validation of the formulation are carried out to minimise the computational error. The natural frequencies of lock gate coupled with and without fluid are determined for undisturbed and linearised free surface conditions. By varying extent of fluid domain, the effect on the natural frequencies of lock gate is evaluated. The results of natural frequencies obtained may be useful to the designer when the reservoir lock gate structure is exposed to the natural disasters.

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

“…The coupling between the two is established utilising the finite element formulation and finally converted into a FORTRAN computer program to determine the natural frequencies of the gate structure. The detailed formulation is found elsewhere [11,12].…”

“…A liquid-filled container is investigated to extract the free vibration frequencies using a meshless local Petrov-Galerkin (MLPG) approach [8][9]. Unstiffened and stiffened lock gates are investigated to determine the free vibration frequencies [10][11][12].…”

Dynamic pressure on lock gate structure coupled with fluid

“…The weighted average integral of Eq. (1) using Galerkin's weighted residual method may be written in concise form to represent the fluid domain as [8]:…”

“…refers to the total boundary surface of the fluid domain and = , , , … , . The boundary term { } may split into several components considering the boundary conditions mentioned earlier and are available in literature [8]:…”

“…where, is formed due to the dynamic pressure of fluid at the interface. After further simplification, the above equation may be represented as [8]:…”