Vibration and buckling of a rectangular plate with an internal support

The vibration and buckling of a rectangular plate with a centrally located, rigid, internal line support is solved. Dual series equations which result from the mixed boundary conditions along the line of internal support are derived. The singular part of the solution is isolated and treated analytically, and the problem is reduced to determining the eigenvalues of a homogeneous integral equation. Rapid convergence to the correct eigenvalue is demonstrated. Numerical results are provided for the fundamental frequency and critical buckling load of a square plate with an internal support.