Recurrent integration of beam functions

Abstract

Felgar's recurrence formula for ∝ θφ dξ was corrected by the author recently. While the new formulae are correct, the table quoted from Gartner and Olgac [J. Sound Vibr. 34, 481–489 (1982)] for the integration constants is found to be incorrect. Because of the importance of the correctness of the admissible comparison functions in a Rayleigh-Ritz analysis, the formulae are rederived with detailed immediate steps, so that a cautious user may check for any possible errors, including printing errors, before implementation. Methods to generate the coefficients of the formulae are discussed and a computer program for the integration by parts many times is given.