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- Title
On Multiparameter Spectral Theory of 3-Parameter Aeroelastic Flutter Problems.
- Authors
Bora, Niranjan; Chutia, Bikash; Bhattacharyya, Surashmi
- Abstract
In this paper, we consider the aeroelastic flutter problem (AEFP) in terms of matrix equations. We provide a general framework on the spectral theory of three parameter AEFP in tensor product space under the auspices of the techniques of multiparameter eigenvalue problems (MEP) in matrix form. It is to noted that, the AEFP of an undamped system can be converted to a linear singular two parameter eigenvalue problem (2PEP) in double dimension and by quasilinearization technique it can be converted to a linear three parameter eigenvalue problem (3PEP) of the same dimension. The de-facto way to find the numeric of MEP is by solving associated joint generalised eigenvalue problem (GEP) using conventional numerical method, provided the problem being nonsingular. Since the transformed version of AEFP in matrix form is singular, so the usual solution techniques for MEP can not be applied to address AEFP and it necessitates to adopt alternate numerical techniques for the same. In the current paper, it is intended to address singular AEFP under certain assumptions. The paper also serves as a report on the Kronecker product method, so called Delta method developed by Atkinson for finding finite eigenvalues of singular three parameter AEFP.
- Subjects
KRONECKER products; TENSOR products; SPECTRAL theory; QUASILINEARIZATION; EIGENVALUES
- Publication
IAENG International Journal of Applied Mathematics, 2023, Vol 53, Issue 4, p1341
- ISSN
1992-9978
- Publication type
Article