UPPER AND LOWER BOUNDS FOR FREQUENCIES OF ELASTIC ARCS

Upper and lower bounds of the first four natural frequencies of elastic clamped arcs, which vibrate in a plane perpendicular to that of the initial curvature of the arcs, are obtained by applying to curved beams a method, based on differential operator theory, originally proposed by Lehmann and Maehly. The principal advantage of the method is that it provides, at the same time, the set of upper and lower bounds of natural frequencies of vibrating systems. The center lines of the arcs are in the forms of circles, cycloids, catenaries, and parabolas. Numerical results are presented in tabular form. The upper bound frequencies so obtained are compared with those obtained by the application of the Rayleigh Ritz method. © 1969, Acoustical Society of America. All rights reserved.