A study of the eigenvalue sensitivity by homotopy and perturbation methods

G. Sliva (1) , Anthony Brézillon (1) , Jean-Marc Cadou (1) , Laëtitia Duigou (1)

1 LIMATB - Laboratoire d'Ingénierie des Matériaux de Bretagne

In this work, the sensitivity to material characteristics of eigenvalues is studied. From an initial structure, some defects of material or/and geometry are introduced. A method is proposed to solve the new eigenvalue problem from the initial one without using classical techniques. This method is based on the association of a homotopy transformation and the perturbation method.

Mots clés: Sensitivity of eigenvalue; Homotopy technique; Perturbation method; Vibration of plates

Domaines: Mécanique des structures [physics.class-ph]

G. Sliva, Anthony Brézillon, Jean-Marc Cadou, Laëtitia Duigou. A study of the eigenvalue sensitivity by homotopy and perturbation methods. Journal of Computational and Applied Mathematics, 2010, 234 (7), pp.2297-2302. ⟨10.1016/j.cam.2009.08.086⟩. ⟨hal-01859500⟩