Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T07:48:58.766Z Has data issue: false hasContentIssue false
  • English
  • Français

The Use of Normal Modes in Problems of Forced Vibration and Impact

Published online by Cambridge University Press:  28 July 2016

R. P. N. Jones
R. P. N. Jones*
Affiliation:
University of Sheffield
Get access Rights & Permissions [Opens in a new window]

Summary

A simple exposition, using d'Alembert's principle and methods of virtual work, is given of the properties and applications of the normal modes of vibration of a linear elastic system. The use of the normal modes in problems of free and forced vibration and dynamic loading is discussed with the aid of simple examples, and it is shown that by these methods dynamical problems for any linear system may be solved without the use of the fundamental equations of motion, provided the natural frequencies and modes of the system are known. In most problems the solutions converge rapidly, so that only the first few modes of vibration need be considered, and in these cases the solution may be modified to give further improvement in convergence. Unsatisfactory convergence may be obtained, however, in problems where there is an exciting force of very high frequency, or an impact of short duration. An approximate allowance may be made for damping, provided this is small.

Type
Research Article
Information
The Aeronautical Journal , Volume 61 , Issue 560 , August 1957 , pp. 552 - 559
Copyright
Copyright © Royal Aeronautical Society 1957

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

1.Rayleigh, Lord (1894). The Theory of Sound. Second Edition, Macmillan, 1894.Google Scholar
2.Timoshenko, S. and Young, D. H. (1948). Advanced Dynamics. McGraw-Hill, 1948.Google Scholar
3.Thomson, W. T. (1948). Mechanical Vibrations. Prentice- Hall, 1948.Google Scholar
4.Biezeno, C. B. and Grammel, R. (1955). Engineering Dynamics, Vol. I, Blackie, 1955.Google Scholar
5.Jones, R. P. N. (1956). The Orthogonal Property—a Proof by Virtual Work. Journal of Applied Mechanics. Vol. 23, p. 318, 1956.Google Scholar
6.Bishop, R. E. D. (1954). On the Graphical Solution of Transient Vibration Problems. Proceedings of the Institution of Mechanical Engineers, Vol. 168, p. 299, 1954.Google Scholar
7.Williams, D. and Jones, R. P. N. (1948). Dynamic Loads in Aeroplanes under Given Impulsive Loads. R. & M. 2221, 1948.Google Scholar
8.Williams, D. (1949). Displacements of a Linear Elastic System under a Given Transient Load. The Aeronautical Quarterly, Vol. I, p. 123, 1949.CrossRefGoogle Scholar
9.Bishop, R. E. D. (1953). The Phase-Plane Construction in Problems of Elastic Impact. The Engineer, Vol. 196, p. 168, 1953.Google Scholar
10.Jones, R. P. N. (1954). The Wave Method for Solving Flexural Vibration Problems. Journal of Applied Mechanics, Vol. 21, p. 75, 1954.Google Scholar