Estimation of fundamental frequency of doubly-connected membranes

✍ Scribed by F.E. Eastep

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 481 KB
• Volume: 37
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(74)80255-5

✦ Synopsis

A method for obtaining approximate fundamental frequencies of non-circular, doublyconnected membranes is developed. An approximate expression for the radius of each bounding curve is written as a truncated Fourier series. The deflection, which is written as a perturbation series of the modes of a circular annulus, is forced to vanish on the approximate boundaries. The approximate characteristic equation (either first-order or second-order approximations) is obtained from the vanishing displacement requirement and the fundamental frequency determined as the first root to this equation.

Approximate frequencies of the fundamental mode of ring membranes in shape of an elliptical ring, a circular-eccentric ring, and a square ring are determined to demonstrate the second-order approximation. The use of the method with Neumann-type boundary conditions is indicated in the investigation of a circular-eccentric ring membrane. The approximate fundamental frequencies of art elliptical ring membrane were found to be in error by less than 5 ~o for eccentricities of the inner ellipse of 0.9 or less.