Limitation on the Method of Strained Coordinates for Vibrations with Weak Grazing Unilateral Contact

Stéphane Junca (1, 2) , Ly Tong (3)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 COFFEE - COmplex Flows For Energy and Environment
3 RUPP - Royal University of Phnom Penh

The NNM (Nonlinear normal modes) have recently been investigated with the method of strained coordinates for spring mass models with some springs with piecewise linear stiffness. The N d.o.f. case and the mathematical validity of the method for large time were rigorously proved. The time validity is related to the nature of contact. For grazing contact, this method and also the multiscale expansion lose nonlinear features. For a small piecewise linear stiffness, we show that this method is less precise for a weak unilateral grazing contact. Thus, the validity of the asymptotic expansion for large time can not be improved and the method has to be modified.

Mots clés: Lindstedt-Poincaré method; perturbation; asymptotic analysis; grazing con-tact; piecewise-linear; vibration

Domaines: Systèmes dynamiques [math.DS]; Sciences de l'ingénieur [physics]; Vibrations [physics.class-ph]

Stéphane Junca, Ly Tong. Limitation on the Method of Strained Coordinates for Vibrations with Weak Grazing Unilateral Contact. Nonlinear Dynamics, 2015, 80, pp.197-207. ⟨10.1007/s11071-014-1860-9⟩. ⟨hal-01143612⟩