AXISYMMETRIC VIBRATIONS OF SOLID CIRCULAR AND ANNULAR MEMBRANES WITH CONTINUOUSLY VARYING DENSITY

✍ Scribed by R.H. Gutierrez; P.A.A. Laura; D.V. Bambill; V.A. Jederlinic; D.H. Hodges

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 173 KB
• Volume: 212
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.1418

✦ Synopsis

The present paper reports the results from a series of numerical experiments dealing with the determination of the lower natural frequencies for the transverse vibration of annular membranes (including the special case of a solid circular membrane) when the mass per unit area varies linearly, quadratically, and cubically with the radial co-ordinate. The frequency coefficients have been determined using: (1) the differential quadrature method;

(2) the finite element technique; (3) an optimized and/or improved Rayleigh quotient method; and (4) a lower bound based on the Stodola-Vianello method. Excellent agreement is achieved among the different methodologies.