Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-29T03:58:30.821Z Has data issue: false hasContentIssue false
  • English
  • Français

Damped vibration of a string

Published online by Cambridge University Press:  29 March 2006

S. P. Lin
S. P. Lin
Affiliation:
Clarkson College of Technology, Potsdam, New York 13676
Get access Rights & Permissions [Opens in a new window]

Abstract

The bounded solution of the unsteady Stokes equations is obtained for the flow of a viscous incompressible fluid about a circular cylinder which undergoes a linear translation starting from rest. A drag formula which consists of the known added-mass term and an additional term arising from the presence of viscosity is obtained. The drag obtained is applied locally in a study of damped vibration of a string. It is shown that the usual theory based on the quasi-steady drag formula overestimates considerably the period and the decay rate of damped vibration of a string in a viscous fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 4 , 23 December 1975 , pp. 787 - 797
Copyright
© 1975 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. 1968 Handbook of Mathematical Functions. Washington: Nat. Bur. Stand.
Basset, A. B. 1888 Phil. Trans. 179, 43.
Batchelor, G. K. 1954 Quart. J. Mech. Appl. Math. 7, 179.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids. Oxford University Press.
Hasimoto, H. 1956 Proc. 9th Int. Congr. Appl. Mech., Brussels, vol. 3, p. 135.
Holtsmark, J., Johnsen, I., Sikkeland, T. & Skavlem, S. 1954 J. Acoust. Soc. Am. 26, 26.
Hussey, R. G. & Vujacic, P. 1967 Phys. Fluids, 10, 96.
Kaplun, S. 1957 J. Math. Mech. 6, 595.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, p. 91. Pergamon.
Lin, S. P. 1976 Quart. J. Mech. Appl. Math. (to appear).
Lin, S. P. & Gautesen, A. K. 1972 J. Fluid Mech. 56, 61.
Meyer, O. E. 1871 J. Math. 73, 31.
Milne-Thomson, L. M. 1960 Theoretical Hydrodynamics. Macmillan.
Ockendon, J. R. 1968 J. Fluid Mech. 34, 229.
Phillips, G. M. 1970 Computer J. 13, 297.
Proudman, I. & Pearson, J. R. A. 1957 J. Fluid Mech. 2, 237.
Rayleigh, Lord 1945 The Theory of Sound. Dover.
Stokes, G. G. 1851 Trans. Camb. Phil. Soc. 9, 8.
Stuart, J. T. 1963 In Laminar Boundary Layers (ed. L. Rosenhead), p. 398. Oxford University Press.