Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T06:23:05.744Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on One-Term Approximate Solutions for Non-Linear Vibration Problems

Published online by Cambridge University Press:  04 July 2016

S. Mahalingam
S. Mahalingam*
Affiliation:
Department of Mechanical Engineering, University of Ceylon
Get access Rights & Permissions [Opens in a new window]

Extract

Several methods are available for the solution of problems of forced vibration of systems with nonlinear elastic characteristics. Of these, the Martienssen, Den Hartog and Rauscher methods may be applied even if the restoring force characteristic is only known graphically, while the Duffing and Perturbation methods are only applicable when the restoring force characteristic is expressed in a convenient mathematical form. Successive approximations are used in the Duffing, Perturbation and Rauscher methods and therefore any desired degree of accuracy can be obtained. The Den Hartog and Martienssen methods give a two-term and one-term solution respectively.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 62 , Issue 570 , June 1958 , pp. 450 - 451
Copyright
Copyright © Royal Aeronautical Society 1958

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.Ludeke, C. A. (1946). An Experimental Investigation of Forced Vibrations in a Mechanical System Having a Non-linear Restoring Force. Journal of Applied Physics, Vol. 17, p. 603, July 1946.CrossRefGoogle Scholar
Ludeke, C. A. (1949). Method of Equivalent Linearization of Non-linear Oscillatory Systems with Large Non-linearity. Journal of Applied Physics, Vol. 20, p. 694, July 1949.Google Scholar
2.Mahalingam, S. (1957). Forced Vibration of Systems with Non-linear, Nonsymmetrical Characteristics. Journal of Applied Mechanics, Vol. 24, p. 435, September 1957.Google Scholar
3.Roberson, R. E. (1952). On the Relationship Between the Martienssen and Duffing Methods for Non-linear Vibrations. Quarterly of Applied Mathematics, Vol. 20, p. 270, 1952.Google Scholar
4.Brock, J. E. (1951). Iterative Numerical Method for Non-linear Vibrations. Journal of Applied Mechanics, Vol. 18, p. 1, January 1951.Google Scholar