Analysis of the vibrations of inflatable dams under overflow conditions
A two-dimensional analysis is applied to the vibrations of inflatable dams under overflow conditions. The static analysis yields the equilibrium state for both the free surface profile and the shape of the dam. The dynamic analysis investigates the small vibrations of the inflatable dam about the equilibrium state.
The dam is inextensible, air-inflated, and has two anchored points. The base width, curved perimeter, and internal air pressure are given. The overflow is incompressible, inviscid, and irrotational, and the total head is specified.
In the static analysis, the self-weight of the dam is neglected, and the equations of equilibrium from membrane theory are solved by a multiple shooting method. The boundary element method is used to solve Laplace’s equation defined on the overflow domain. An iterative scheme is adopted to obtain the shape of the dam, as well as the location of the free surface.
From the equilibrium state, the dynamic analysis is established by a finite difference form of the membrane’s equations of motion and the velocity potential problem is formulated by the boundary element method. After the eigenvalue problem is solved, the eigenvalues and eigenvectors obtained are employed to describe the vibrations of the dam. The effects of the dam‘s density and damping coefficient are illustrated.