Asymptotic numerical method and Padé approximants for eigenvalue. Application in linear vibration of plates and shells. (June 2020)

• Record Type: Journal Article
• Authors: Cadou, J.M.; Ounis, H.; Boutyour, E.H.; Potier-Ferry, M.
• Is Part Of: Mechanics research communications. Volume 106(2020)
• Publication Date: 2020-06
• Subjects: Eigenvalue problem -- Perturbation method -- Padé approximants -- Vibration; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2020.103538
• Languages: English
• ISSNs: 0093-6413

Abstract

Highlights: Numerical method for eigenvalue problem. Perturbation method and Padé approximants. Multiple eigenvalues. Less sensitive to ill-conditioned matrices. Abstract: In this work, perturbation method and Padé approximants are used to compute the eigenvalues of linear problems. This algorithm is based on the introduction of perturbation loads in the eigenvalue problem. This modified problem is solved by using the perturbation method and the Padé approximants. The computation of the eigenvalues consists then on finding the roots of the numerator of a rational fraction. To demonstrate the efficiency of the proposed method, examples of linear vibrations of plates and shells are considered. The obtained results showed that the proposed method can deal with problems with close or multiple eigenvalues. Furthermore, the results also showed that the proposed algorithm is less sensitive to the ill-conditioning of the matrices.