On application of the Floquet theory for radially periodic membranes and plates

被引：10
作者：
Hvatov, Alexander [1 ]
Sorokin, Sergey [2 ]
机构：
[1] State Marine Tech Univ St Petersburg, Dept Phys, Lotsmanskaya 3, St Petersburg 190008, Russia
[2] Aalborg Univ, Dept Mat & Prod, Fibigerstr 16, DK-9220 Aalborg, Denmark
来源：
JOURNAL OF SOUND AND VIBRATION | 2018年 / 414卷
关键词：
Periodic structures; Wave propagation; Floquet theory; Eigenfrequency spectra; Polar coordinates; WAVES; PROPAGATION;
D O I：
10.1016/j.jsv.2017.11.003
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
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. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：15 / 30
页数：16
相关论文
共 22 条
  • [1] [Anonymous], 1961, BESSEL FUNCTIONS ENG
  • [2] Waves in periodic structures with imperfections
    Benaroya, H
    [J]. FINITE ELEMENTS IN ANALYSIS AND DESIGN, 1996, 23 (2-4) : 291 - 302
  • [3] Brillouin L, 1953, Chemische reihe. lehrbucher und monographien aus dem gebiete der exakten wissenschaften, V2
  • [4] The deferred limit method for long waves in a curved waveguide
    Chapman, C. J.
    Sorokin, S. V.
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2017, 473 (2200):
  • [5] Fabro A., P ISMA 2016
  • [6] Free vibrations of finite periodic structures in pass- and stop-bands of the counterpart infinite waveguides
    Hvatov, Alexander
    Sorokin, Sergey
    [J]. JOURNAL OF SOUND AND VIBRATION, 2015, 347 : 200 - 217
  • [7] Bloch theorem in cylindrical coordinates and its application to a Bragg fiber
    Kitagawa, Akira
    Sakai, Jun-ichi
    [J]. PHYSICAL REVIEW A, 2009, 80 (03):
  • [8] Korenev B. G., 2002, Bessel Functions and Their Applications
  • [9] Propagation of Lamb waves in one-dimensional radial phononic crystal plates with periodic corrugations
    Li, Yinggang
    Chen, Tianning
    Wang, Xiaopeng
    Yu, Kunpeng
    Chen, Weihua
    [J]. JOURNAL OF APPLIED PHYSICS, 2014, 115 (05)
  • [10] Band structures of bilayer radial phononic crystal plate with crystal gliding
    Ma, Ting
    Chen, Tianning
    Wang, Xiaopeng
    Li, Yinggang
    Wang, Peng
    [J]. JOURNAL OF APPLIED PHYSICS, 2014, 116 (10)
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