- Email: [email protected]
Comment on “Fundamental frequency of vibration of stepped thickness plates”
Journal
of Sound and Vibration (1977) 53(3), 458
COMMENT
ON “FUNDAMENTAL FREQUENCY OF VIBRATION THICKNESS PLATES”
OF STEPPED
In a recent note Laura and Filipich [I] obtained the fundamental frequency in flexure for rectangular plates with various boundary conditions, when the plate consisted of two sections having different thicknesses h, and hz. They used the Rayleigh-Ritz method and compared their results with those obtained previously by Chopra [2], who obtained a solution from the plate equation for simply supported boundary conditions. Unfortunately, as pointed out previously by the writer [3], the numerical results of Chopra, which are quoted in Table 1 of reference [l], are in error (except for the special case when h, = h, and the step is absent), as Chopra applied incorrect continuity conditions at the step. The numerical effect of this error on natural frequencies is not known to the writer, but it is expected that the errors in Chopra’s values will increase as the thickness ratio h,/h, moves away from unity. It is noted that there is a tendency for the frequencies obtained by Laura and Filipich and those quoted from Chopra to differ by increasing amounts as this thickness ratio decreases from unity. Department of Mechanical Engineering, University of Nottingham, Nottingham NG7 2RD, England
G. B. WARBURTON
(Received 26 March 1977) REFERENCES 1. P. A. A. LAURA and C. FILIPICH 1977 Journal of Soundand
Vibration 50, 157-158. Fundamental frequency of vibration of stepped thickness plates. 2. I. CHOPRA 1974 International Journal qf Mechanical Sciences 16, 337-344. Vibration of stepped thickness plates. 3. G. B. WARBURTON1975 International Journal of Mechanical Sciences 17, 239. Comment on “Vibration of stepped thickness plates”. AUTHORS’ REPLY
We are grateful to Professor Warburton for his constructive criticism. We agree wholeheartedly with his comments and we apologize sincerely for not being aware of his previous discussion of the subject matter. On the other hand, our results are approximate but correct. A thorough investigation on the subject matter is underway and a complete paper will follow up shortly. P.A.A.
Institute of Applied Mechanics, Naval Base of Puerto Belgrano, Argentina
LAURA C. FILIPICH
(Received 13 April 1977)
458
of Sound and Vibration (1977) 53(3), 458
COMMENT
ON “FUNDAMENTAL FREQUENCY OF VIBRATION THICKNESS PLATES”
OF STEPPED
In a recent note Laura and Filipich [I] obtained the fundamental frequency in flexure for rectangular plates with various boundary conditions, when the plate consisted of two sections having different thicknesses h, and hz. They used the Rayleigh-Ritz method and compared their results with those obtained previously by Chopra [2], who obtained a solution from the plate equation for simply supported boundary conditions. Unfortunately, as pointed out previously by the writer [3], the numerical results of Chopra, which are quoted in Table 1 of reference [l], are in error (except for the special case when h, = h, and the step is absent), as Chopra applied incorrect continuity conditions at the step. The numerical effect of this error on natural frequencies is not known to the writer, but it is expected that the errors in Chopra’s values will increase as the thickness ratio h,/h, moves away from unity. It is noted that there is a tendency for the frequencies obtained by Laura and Filipich and those quoted from Chopra to differ by increasing amounts as this thickness ratio decreases from unity. Department of Mechanical Engineering, University of Nottingham, Nottingham NG7 2RD, England
G. B. WARBURTON
(Received 26 March 1977) REFERENCES 1. P. A. A. LAURA and C. FILIPICH 1977 Journal of Soundand
Vibration 50, 157-158. Fundamental frequency of vibration of stepped thickness plates. 2. I. CHOPRA 1974 International Journal qf Mechanical Sciences 16, 337-344. Vibration of stepped thickness plates. 3. G. B. WARBURTON1975 International Journal of Mechanical Sciences 17, 239. Comment on “Vibration of stepped thickness plates”. AUTHORS’ REPLY
We are grateful to Professor Warburton for his constructive criticism. We agree wholeheartedly with his comments and we apologize sincerely for not being aware of his previous discussion of the subject matter. On the other hand, our results are approximate but correct. A thorough investigation on the subject matter is underway and a complete paper will follow up shortly. P.A.A.
Institute of Applied Mechanics, Naval Base of Puerto Belgrano, Argentina
LAURA C. FILIPICH
(Received 13 April 1977)
458