HIGH-FREQUENCY VIBRATIONS IN A STIFF PROBLEM

The stiff problem here considered models the vibrations of a body cons isting of two materials, one of them very stiff with respect to the ot her. We study the asymptotic behavior of the eigenvalues and eigenfunc tions of the corresponding spectral problem, when the stiffness consta nt of only one of the materials tends to 0. We show that the associate d operator has a discrete spectrum ''converging'', in a certain sense, towards a continuous spectrum in [0, infinity) corresponding to an op erator. We also provide information on the structure of the eigenfunct ions associated with the high frequencies.