Propagation of elastic surface waves along a cylindrical cavity of arbitrary cross section
نویسندگان
چکیده
— The propagation of elastic surface waves, guided by the free surface of an infinitely long cylinder, of arbitrary cross section, is formulated as on eigenvalue problem, for an unbounded self adjoint operator. We prove the existence of a hierarchy of guided modes. Two of them propagate for any value of the wave number, whereas all of the others only exist beyond a cut-off wave number. For any fixed value of the wave number, only a finite number of modes propagate. Resumé. — Nous formulons la propagation des ondes élastiques, guidées par la surface libre d'une cavité cylindrique de section arbitraire, sous la forme d'un problème de valeurs propres pour un opérateur auto-adjoint, non-borné. Nous prouvons l'existence d'une famille dènombrable de modes guidés. Les deux premiers se propagent pour toute valeur du nombre d'onde, alors que les suivants n'existent qu'au-delà d'un nombre d'onde de coupure. Pour chaque valeur fixée du nombre d'onde, seul un nombre fini de modes se propagent.
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