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Comments on “Influence of unsymmetric boundary conditions on vibrations of tapered plates”
Journal of Sound and Vibration (1986) 108(1), 165
LETTERS T O T H E E D I T O R COMMENTS ON "INFLUENCE OF UNSYMMETRIC BOUNDARY CONDITIONS ON VIBRATIONS OF TAPERED PLATES" The writer wishes to congratulate the authors for their useful study [1]. They show in a very eloquent manner that unsymmetric (or mixed) boundary conditions greatly influence the natural frequencies of tapered rectangular plates. It is interesting to point out that in the case of (a) tapered circular plates elastically restrained against rotation along the boundary and (b) tapered simply supported and clamped plates of regular polygonal shape the fundamental natural frequencies can be calculated by using the average thickness ho and the corresponding frequency coefficients for plates of uniform thickness [2] or in other words: the fundamental frequencies of the aforementioned structural elements are practically independent of the taper ratio provided the average thickness of the plate is kept constant. Admittedly the numerical experiments described in reference [2] deal with plates where the taper parameter is rather small. Institute of Applied Mechanics, 8111 Puerto Belgrano Naval Base, Argentina
P. A. A. LAURA
(Received 2 July 1985)
REFERENCES 1. S. NAGARAJARAO and N. GANESAN1984 Journal of Sound and Vibration 97, 526-530. Influence of unsymmetric boundary conditions on vibrations of tapered plates. 2. P. A. A. LAURA,R. H. GUTIERREZand G. SANCHEZSARMIENTO 1981 Journal of Sound and Vibration 77, 291-294. Vibration of plates of variable thickness.
165
0022-460X/86/130165+01 $03.00/0
O 1986AcademicPress Inc. (London) Limited
LETTERS T O T H E E D I T O R COMMENTS ON "INFLUENCE OF UNSYMMETRIC BOUNDARY CONDITIONS ON VIBRATIONS OF TAPERED PLATES" The writer wishes to congratulate the authors for their useful study [1]. They show in a very eloquent manner that unsymmetric (or mixed) boundary conditions greatly influence the natural frequencies of tapered rectangular plates. It is interesting to point out that in the case of (a) tapered circular plates elastically restrained against rotation along the boundary and (b) tapered simply supported and clamped plates of regular polygonal shape the fundamental natural frequencies can be calculated by using the average thickness ho and the corresponding frequency coefficients for plates of uniform thickness [2] or in other words: the fundamental frequencies of the aforementioned structural elements are practically independent of the taper ratio provided the average thickness of the plate is kept constant. Admittedly the numerical experiments described in reference [2] deal with plates where the taper parameter is rather small. Institute of Applied Mechanics, 8111 Puerto Belgrano Naval Base, Argentina
P. A. A. LAURA
(Received 2 July 1985)
REFERENCES 1. S. NAGARAJARAO and N. GANESAN1984 Journal of Sound and Vibration 97, 526-530. Influence of unsymmetric boundary conditions on vibrations of tapered plates. 2. P. A. A. LAURA,R. H. GUTIERREZand G. SANCHEZSARMIENTO 1981 Journal of Sound and Vibration 77, 291-294. Vibration of plates of variable thickness.
165
0022-460X/86/130165+01 $03.00/0
O 1986AcademicPress Inc. (London) Limited