Standing waves in rotationally periodic structures

✍ Scribed by D.L. Thomas

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 119 KB
• Volume: 37
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(74)80337-8

✦ Synopsis

STANDING WAVES IN ROTATIONALLY PERIODIC STRUCTURES

A rotationally periodic structure consists of a finite number of identical sub-structures forming a closed ring. By considering normal modes of vibration as standing waves, for which there are only certain allowed values of the propagation constant, all the modes can be found from matrix analyses of a single sub-structure. A simple example is given.

In a recent paper [1] Orris and Petyt discussed wave propagation in periodic structures. The structures considered were infinitely long "chains" of identical substructures. Free wave propagation was discussed, and described in terms of the complex propagation constant,/~, with the ratio of the amplitudes of motion at corresponding points on adjacent substructures being e u. For a purely imaginary p, the corresponding vibration frequencies were found by imposing constraints on the finite element equations of motion of a single substructure. The constraints are of the form