A COMMENT ON "A NOTE ON VIBRATING TAPERED BEAMS">

✍ Scribed by N.M. Auciello

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 195 KB
• Volume: 187
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1995.0557

✦ Synopsis

Quite recently, Grossi and Bhat published an excellent paper [1], in which they obtained approximate values of the free vibration frequencies of tapered beams, by using the Rayleigh-Schmidt and Rayleigh-Ritz approaches. The fundamental frequency is compared, for a=b=1•5, with the exact value given by Goel in terms of Bessel functions [2]. The above-mentioned authors remarked that the non-dimensional approximate coefficients l 1 are not always upper bounds to the true values, contrary to the well-known properties of the Rayleigh methods. The aim of the present letter is to show that this discrepancy is due to a trivial error of the interesting Goel theory.

In fact, the terms of the second and third equations of formula ( 9) in the Goel paper should read as follows: