Implicit Floquet analysis for parametric instabilities in a variable angle tow composite panel. (1st February 2020)

• Record Type: Journal Article
• Authors: Samukham, Surya; Vyasarayani, C.P.; Raju, Gangadharan
• Is Part Of: Composite structures. Volume 233(2020)
• Publication Date: 2020-02-01
• Subjects: Parametric instability -- Variable angle tow composite -- Bolotin's approach -- Floquet theory -- Arnoldi algorithm; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2019.111637
• Languages: English
• ISSNs: 0263-8223

Abstract

Abstract: In the literature dealing with the stability of time-periodic structures, Bolotin's method is widely used for generating the approximate stability charts. Further, increasing the order of approximation in Bolotin's approach requires solving several eigenvalue problems and may not lead to the rapid convergence of stability charts. Floquet theory can be used to calculate accurate stability charts for time-periodic systems. In Floquet theory, a Floquet transition matrix (FTM) is computed, the dominant eigenvalue of the FTM determine the stability of the time-periodic system. For a large degree of freedom systems like finite element models of VAT panels, the calculation of FTM becomes computationally expensive. However, an implicit Floquet analysis can significantly reduce the computational load. In this technique, the dominant eigenvalue of the FTM is computed without calculating the full FTM matrix. In this work, the stability regions obtained from the implicit Floquet analysis are compared with the results from Bolotin's approach and verified using the time response of the panel obtained from numerical integration. Also, unlike Bolotin's method, Floquet analysis provides information about the damping present in different areas of stability charts and the nature of bifurcation through which the stability is lost.