Almost periodic motion of a string vibrating against a straight fixed obstacle

Alain Haraux (1) , Henri Cabannes (2)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 LMT - Laboratoire de Mécanique Théorique

In a plane with normalized coordinate system $Oxu$, we consider the small oscillations of a vibrating string with fixed ends $(\pm 1/2,0)$. The free oscillations of this string are perturbed by the presence of a fixed obstacle $\{u = -h\}$, against which it rebounds following a law which insures conservation of the energy $(0 \leq h \le 1)$.

Domaines: Acoustique [physics.class-ph]; Mécanique [physics.med-ph]

Alain Haraux, Henri Cabannes. Almost periodic motion of a string vibrating against a straight fixed obstacle. Nonlinear Analysis: Theory, Methods and Applications, 1983, 7, pp.129-141. ⟨10.1016/0362-546X(83)90076-7⟩. ⟨hal-01527087⟩