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In the paper the exact solution of a boundary value problem for a rectangle clamped at one end is constructed. The solution is given in the form of explicit expansions in Papkovich–Fadle eigenfunctions. The coefficients of the expansions are clearly determined by means of functions biorthogonal to Papkovich–Fadle eigenfunctions.

Plate; clamp; Papkovich–Fadle eigenfunctions; exact solution