Dynamic analysis of concrete arch dams by ideal-coupled modal approach

A new modal technique is proposed for dynamic analysis of concrete arch dam–reservoir systems in frequency domain. The approach relies on the new mode shapes that are entitled “ideal-coupled modes”. These modes are employed in somehow similar to decoupled modes of the dam–reservoir system. However, they are actually coupled modes of ideal systems which correspond to fictitious systems. These are calculated by assuming incompressible fluid to obtain the first set and massless solid idealization to compute the second set. These two ideal systems are replacing the actual system temporarily just to obtain the mode shapes. It should be realized that although, these ideal mode shapes are not the true coupled modes of the original system, they are utilized to solve the true coupled problem. It is also worthwhile to emphasize that the employed mode shapes can be envisaged as some kind of Ritz vectors for the original system. The accuracy of the proposed technique is examined thoroughly and it is concluded that ideal-coupled procedure is very accurate under all practical conditions. It is also shown that the decoupled modal approach proposed in a previous study can be considered as a special case of the present more general procedure.