Computable upper and lower bounds on eigenfrequencies

Li Wang (1) , Ludovic Chamoin (2, 3) , Pierre Ladevèze (2) , Hongzhi Zhong (1)

1 THU - Tsinghua University [Beijing]
2 LMT - Laboratoire de Mécanique et Technologie
3 MATHERIALS - MATHematics for MatERIALS

This paper is a revisit of the work [Ladevèze and Pelle, Int. J. Numer. Methods Engrg. 28 (1989)] where the goal here is to acquire guaranteed, accurate and computable bounds of eigenfrequencies through post-processing of conventional finite element results. To this end, a new theoretical quotient is introduced and thereafter, a practical way to deal with the new quotient is developed where the constitutive relation error estimation featured with guaranteed bounding property acts as a key role. Academic numerical examples are performed to check the accuracy of the bounds.

Mots clés: Model verification; Guaranteed bounds; Eigenfrequency; Constitutive relation error (CRE); Finite element method

Domaines: Sciences de l'ingénieur [physics]

Li Wang, Ludovic Chamoin, Pierre Ladevèze, Hongzhi Zhong. Computable upper and lower bounds on eigenfrequencies. Computer Methods in Applied Mechanics and Engineering, 2016, 302, pp.27-43. ⟨10.1016/j.cma.2016.01.002⟩. ⟨hal-01241742⟩