Conditions for periodic vibrations in a symmetric \(n\)-string. (English) Zbl 1146.35057
Summary: A symmetric \(N\)-string is a network of \(N \geq 2\) sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form \(N\) angles of \(2 \pi /N\) at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the \(N\)-string at rest, we obtain conditions under which the solution will be periodic with an integral period.
MSC:
| 35L55 | Higher-order hyperbolic systems |
| 35L05 | Wave equation |
| 35B10 | Periodic solutions to PDEs |
| 74K05 | Strings |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
Keywords:
networks of strings; star graphs; initial boundary value problem; small-amplitude oscillationsReferences:
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