## The Coupled Damreservoir Problem

As it was discussed in previous Chapter, The dam-reservoir interaction is a classic coupled problem which contains two differential equations of the second order. The equations of the dam structure and the reservoir can be written in the following form:

[M]{U}+[C]{U}+[K]{U} = {h}-[M]{U9}+[Q]{p} = {Fi}+[Q]{p} (4.1) [G]{P} + [C]{p} + [K'}{p} = {F} - p[Q]T({U} + {Ug}) = {F2} - p[Q]T{U}

where[M], [C] and [K] are mass, damping and stiffness matrices of the structure and [G], [C'] and [K0]are matrices representing mass, damping and stiffness of the reservoir, respectively. Detailed definitions of the[G],[C0] and [K0] matrices and vector {F}, are presented in the following sections. [Q] is the coupling matrix; {f1} is the vector of body force and hydrostatic force; and {p} and {U} are the vectors of hydrodynamic pressures and displacements. {U9} is the ground acceleration and p is the density of the fluid. The dot represents the time derivative.

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