FUNDAMENTAL FREQUENCY OF A WAVY NON-HOMOGENEOUS CIRCULAR MEMBRANE

✍ Scribed by C.Y. WANG

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 72 KB
• Volume: 227
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2373

✦ Synopsis

The study of the vibration of membranes is important in the design of drums, speakers and receivers. The vibration of homogeneous membranes have been discussed by Rayleigh [1] and Kuttler and Sigillito [2]. Composite membranes composed of joining many strips of di!erent homogeneous pieces were studied by Vodicka [3], Kato [4], Bhadra [5], Kalotas and Lee [6]. In these cases, the governing equation was solved for each piece, then matched at the interfaces. The continuously non-homogeneous rectangular membrane has been considered by Masad [7], Laura et al. [8] and Wang [9]. The last source also reported an exact solution of a continuously non-homogeneous annular membrane.

The present note studies the fundamental frequencies of a continuously non-homogeneous circular membrane. The density (or thickness) is assumed to be a sinusoidal function of radius. This class includes important wavy, ribbed membranes and also convex or concave lens-like membranes.

The equation of motion for a non-homogeneous membrane is