4apg . . m-1 (-1)-1 A + -s in u>t y - = co s \my +

in which mi is the minimum value of m such that Am > C. If mi = 1 which is an indication of Ai > c or u < ui, then the term involving sinut vanishes and the solution of the wave equation is same as Westergaard's solution. Here, again it can be noticed that the Westergaard's solution is valid if the frequency of the excitation is less than the fundamental frequency of the reservoir system. For u > ui the term involving sin ut does not vanish and represent existence of pressure at infinite distance up the reservoir. The pressure response has two terms one is in phase with ground motion and the other is in opposite phase of ground motion. Therefore, the hydrodynamic pressure cannot be represented by added mass approach.

For mi > 1 we have pressure at infinite distance. This means that for the case of um < u < um+ithe pressure would be zero at x = to for um+iand higher modes. While for um and lower modes we expect to have pressure at very far-end of the reservoir.

The solution of wave equation subjected to the vertical ground motion for a rigid dam with rectangular reservoir is investigated. The reservoir have the following boundary conditions:

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