On the modal approach to the stability of certain non-selfadjoint problems in elasto-dynamics

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Abstract
Stability problems involving conservative, selfadjoint mechanical problems can be very conveniently treated using the modal approach. Owing to certain loading conditions, which involve control forces, such mechanical problems may become non-selfadjoint under special conditions. The question then arises whether the modal approach will still be applicable. The paper provides an answer to that question. It is shown that the modal approach remains valid in the so-called regularity domain of the non-selfadjoint operator which governs the problem. The notion of a regularity domain is thoroughly discussed in the paper.

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