In this paper the authors consider the response of rectangular plates to transient forces. It is shown that for an impulse applied to a cantilever plate, there is reasonable agreement between theoretical and experimental curves for the resulting transient vibration, when the response in a small number of modes is considered and approximate expressions are used for the natural frequencies and nodal patterns of these modes.
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References
1.
WarburtonG. B.1954Proc. Instn mech. Engrs, Lond., vol. 168, p. 371, ‘The Vibration of Rectangular Plates’.
2.
EringenA. C.1953J. appl. Mech., Trans. Amer. Soc. mech. Engrs, vol. 75, p. 461, ‘Transverse Impact on Beams and Plates’.
3.
YoungD.1950J. appl. Mech., Trans. Amer. Soc. mech. Engrs, vol. 72, p. 448, ‘Vibration of Rectangular Plates by the Ritz Method’.
4.
TimoshenkoS.YoungD. H.1955‘Vibration Problems in Engineering’, third edition, p. 442 (Van Nostrand, Macmillan, New York, London).
5.
BartonM. V.1951J. appl. Mech., Trans. Amer. Soc. mech. Engrs, vol. 73, p. 129, ‘Vibration of Rectangular and Skew Cantilever Plates’.
6.
HallA. H.PinkneyH. F. L.TullochH. A.1953 National Aeronautical Establishment, Canada, Report No. 21, ‘On the Analytical Determination of the Normal Modes and Frequencies of Swept Cantilever Vibrations’.
7.
RayleighLord1894‘The Theory of Sound’, second edition, vol. 1, Art. 101 (Macmillan, London). Reprinted in 1945 (Dover, New York).
8.
ZenerC.FeshbachH.1939J. appl. Mech., Trans. Amer. Soc. mech. Engrs, vol. 61, p. A67, ‘A Method of Calculating Energy Losses during Impact’.
9.
LeeE. H.1940J. appl. Mech., Trans. Amer. Soc. mech. Engrs, vol. 62, p. A129, ‘Impact of a Mass Striking a Beam’.
10.
Hoppmann-IiW. H.1948J. appl. Mech., Trans. Amer. Soc. mech. Engrs, vol. 70, p. 125, ‘Impact of a Mass on a Damped Elastically Supported Beam’.
11.
TimoshenkoS.GoodierJ. N.1951‘Theory of Elasticity’, second edition, p. 384 (McGraw-Hill Book Co., New York and London).
12.
JonesR. P. N.1954J. appl. Mech., Trans. Amer. Soc. mech. Engrs, vol. 76, p. 75, ‘The Wave Method for Solving Flexural Vibration Problems’.
13.
FranklandJ. M.1948Proc. Soc. exp. Stress Anal., vol 6, No. 2, p. 7, ‘Effects of Impact on Simple Elastic Structures’.
14.
GreensponJ. E.1955 David W. Taylor Model Basin Report No. 774, ‘Stresses and Deflections in Flat Rectangular Plates under Dynamic Lateral Loads based on Linear Theory’.
15.
BishopR. E. D.JohnsonD.C.1956‘Vibration Analysis Tables’ (Cambridge University Press).
