We investigate the dynamics of a circular membrane with an eccentric circular areal constraint under arbitrary initial conditions. The membrane is assumed to be fixed at its outer boundary and the constraint is assumed to impose zero displacement over a circular area of the membrane. The symmetric and antisymmetric modes of vibration of the membrane are derived and their orthogonality properties are established. Using the orthogonality conditions established in this paper, the complete solution to the constrained vibratory motion of the membrane is determined for arbitrary initial conditions. Two sets of numerical simulation results are presented.

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