An experimental study is described which shows the elementary ‘peak-amplitude’ technique of resonance testing to great disadvantage. On the basis of that method the experimentally determined ‘modal shapes’ are completely misleading. While the Kennedy and Pancu method would produce acceptable modes it would demand a much greater effort. An alternative technique is described which gives excellent results at the cost of much less labour. While the new method appears to have an added advantage over the Kennedy and Pancu method when there is strong coupling between the modes, it may well prove to be less accurate when there are close natural frequencies.
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References
1.
PenderedJ. W.BishopR. E. D.‘A critical introduction to some industrial resonance testing techniques’, J. mech. Engng Sci.19635 (no. 4), 345.
2.
KennedyC. C.PancuC. D. P.‘Use of vectors in vibration measurement and analysis’, J. aero. Sci.194714, 603.
3.
MolyneuxW. G.BroadbentE. G.‘Ground resonance testing of aircraft’, Rep. Memor. aero. Res. Comm., Lond. no. 2155, July 1946.
4.
BishopR. E. D.JohnsonD. C.The mechanics of vibration1960 (Cambridge University Press).
5.
BishopR. E. D.GladwellG. M. L.‘An investigation into the theory of resonance testing’, Phil. Trans. A, 1963255, 241.
6.
RosenbergR. M.Communication, J. mech. Engng Sci. 19624 (no. 2), 190.
7.
HenryR. F.TobiasS. A.Authors' Reply to Communication, J. mech. Engng Sci., 191.
8.
RosenbergR. M.AtkinsonC. P.‘Natural modes and their stability in nonlinear two-degree-of-freedom systems’, J. appl. Mech., Trans. Amer. Soc. mech. Engrs81 (Series E), 377.
9.
RosenbergR. M.‘On normal vibrations of a general class of nonlinear dual-mode systems’, J. appl. Mech., Trans. Amer. Soc. mech. Engrs28 (Series E), 275.
10.
TobiasS. A.‘Free undamped non-linear vibrations of imperfect circular discs’, Proc. Instn mech. Engrs, Lond. 1957171, 691.
11.
HenryR. F.TobiasS. A.‘Modes at rest and their stability in coupled non-linear systems’, J. mech. Engng Sci. 19613 (no. 2), 163.
12.
BradistolovG.‘über periodische und asymptotische Lösungen beim n-fachen Pendel in der Ebene’, Math. Ann.1936116, 181.
13.
BradistolovG.‘über periodische Bewegungen des n-fachen Pendels in der Ebene’, Math. Ann., 602.
14.
PorterJ.AtkinsonC. P.‘A note on a new stability method for the linear modes of nonlinear two-degree-of-freedom systems’, J. appl. Mech., Trans. Amer. Soc. mech. Engrs29 (Series E), 258 (submitted 11th April 1961, based on report dated January 1961).
15.
AtkinsonC. P.‘On the stability of the linearly related modes of certain nonlinear two-degree-of-freedom systems’, J. appl. Mech., Trans. Amer. Soc. mech. Engrs28 (Series E), 71.
16.
HsuC. S.‘On a restricted class of coupled Hill's equations and some applications’, J. appl. Mech., Trans. Amer. Soc. mech. Engrs28 (Series E), 551 (submitted 16th November 1960).
17.
RosenbergR. M.HsuC. S.‘On the geometrization of normal vibrations of nonlinear systems having many degrees of freedom’, Proc. Int. Symp. Nonlinear Vibrations, Kiev, 1961.
18.
EvidonJ. S. Rocketdyne Report Ddr 713-7023, 5th June 1957.
19.
BraggS. L.‘Variation of the discharge coefficient of orifices in incompressible flow’, Rolls-Royce Rocket Department Report 76, 1959.
20.
BraggS. L.CrosbyJ. K.Communcation, Proc. Instn mech. Engrs, Lond. 1959173, 666.
21.
SmithR. E.MatzR. J.‘Verification of a theoretical method of determining discharge coefficients for venturis operating at critical flow conditions’, Arnold Engng Development Center Aedc-Tr-61-8, September 1961.
22.
SpikesR. H.PenningtonG. A.‘Discharge coefficient of small submerged orifices’, Proc. Instn mech. Engrs, Lond. 1959173, 661.
23.
BuntE. A.KirkM. F.‘Correlation of various types of axisymmetric overflows of small vorticity’, J. mech. Engng Sci. 19613 (no. 4), 348.
24.
BergwerkW.‘Flow pattern in diesel nozzle spray holes’, Proc. Instn mech. Engrs, Lond. 1959173, 655.
25.
GraceH. P.LappleC. E.‘Discharge coefficients of small-diameter orifices and flow nozzles’, Trans. Amer. Soc. mech. Engrs195173, 639.
26.
HargroveL. E.ThurstonG. B.‘Optical method for analysis of fluid motion’, J. acoust. Soc. Amer. 195729, 966.
27.
SimmonsF. A.‘Analytic determination of the discharge coefficients of flow nozzles’, Tech. Note nat. adv. Comm. Aero., Wash. 3447, April 1955.
ShapiroA. H.SmithR. D.‘Friction coefficients in the inlet length of smooth round tubes’, Tech. Note nat. adv. Comm. Aero., Wash. 1785, 1948.
30.
BallJ. W.‘Flow characteristics in a pipeline downstream from a square-cornered entrance’, U.S. Bureau of Reclam. Lab. Report no. Hyd-422, 1957.
31.
EngelF. V. A.‘How to improve flow measurement accuracy of orifices, nozzles and venturimeters’, paper C.4 Symp. Flow Measurement in closed conduits (N.E.L.) 1960 (H.M. Stationery Office, 1962).
32.
DallH. E.‘The effect of roughness of the orifice plate on the discharge coefficient’, Instrum. Engr19582 (5), 91.
33.
JohansenF. C.‘Flow through pipe orifices at low Reynolds numbers’, Rep. Memor. aero. Res. Comm., Lond.1252, 1929.
34.
EngelF. V. A.‘New interpretations of the discharge characteristics of measuring orifices—an approach to improved accuracy’, Amer. Soc. mech. Engrs paper 62-Wa-237, 1962.
35.
B.S. 1042:1943‘Code for flow measurement’ (British Standards Institution).
36.
ArnbergB. T.‘Review of critical flowmeters for gas flow measurements’, Trans. Amer. Soc. mech. Engrs, J. Basic Engng1962 (December), 448.
37.
HallG. W.‘Application of boundary layer theory to explain some nozzle and venturi flow peculiarities’, Proc. Instn mech. Engrs, Lond. 1959173, 837.
