On application of the Floquet theory for radially periodic membranes and plates. (3rd February 2018)

• Record Type: Journal Article
• Authors: Hvatov, Alexander; Sorokin, Sergey
• Is Part Of: Journal of sound and vibration. Volume 414(2018)
• Page Start: 15
• Page End: 30
• Publication Date: 2018-02-03
• Subjects: Periodic structures -- Wave propagation -- Floquet theory -- Eigenfrequency spectra -- Polar coordinates; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2017.11.003
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: The paper is concerned with the vibro-isolation effects in radially periodic membranes and plates. Alternative formulations of the canonical Floquet theory for analysis of wave propagation in these elastic structures are compared with each other. An extension of this theory beyond the applicability limits of the well-known theory of Bragg fiber is proposed. The similarities and differences in performance of infinite and finite structures periodic in Cartesian and polar coordinates are highlighted and explained. Highlights: Alternative formulations of algebraic equations for propagation parameters for radially periodic structures. Exact differential equations of Floquet theory in polar coordinates for a periodic membrane. Distribution of eigenfrequencies of radially periodic finite membranes in view of location of stop-bands.