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Resonance phenomena in infinite strings with periodic ends
Author(s) -
Werner P.
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670170205
Subject(s) - mathematics , resonance (particle physics) , homogeneous , string (physics) , mathematical analysis , periodic function , harmonic , distribution (mathematics) , pure mathematics , physics , mathematical physics , combinatorics , quantum mechanics
We study the propagation of linear waves, generated by a compactly supported time‐harmonic force distribution, in an infinite string under the assumption that the material properties are p 1 ‐periodic for x > a and p 2 ‐periodic for x < − a . As has been pointed out in two preceding papers devoted to related configurations ([4], [5]), the combination of a time‐periodic force and a periodic spatial structure may lead to resonance phenomena. We show that the present configuration also permits resonances of orders t and t 1/2 for a discrete set of frequencies. The occurrence of resonances is closely related to the presence of non‐trivial solutions of the corresponding time‐independent homogeneous problem which satisfy certain asymptotic properties (‘standing waves’).