An exact solution for the free vibration problem of non-linear cubic spring mass system with Coulomb damping is obtained during each half cycle, in terms of elliptic functions. An expression for the half cycle duration as a function of the mean amplitude during the half cycle is derived in terms of
Step function response of non-linear spring mass systems in the presence of Coulomb damping
โ Scribed by V.A. Bapat; P. Srinivasan
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 489 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0022-460X
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โฆ Synopsis
The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.
๐ SIMILAR VOLUMES
A new approximate technique developed by Mansour and Hussein [1] has been used to solve a non-linear differential equation model that describes the underdamped and the overdamped motion of systems subjected to step function excitation. The analytical results obtained in this work have been compared
In previous work, the title problem was studied. Unfortunately, a sign reversal in the damping term led to a misinterpretation of the effect of linear damping of the modal system. In the present paper this is corrected and the work previously reported is extended. ## M,[[-to + wi]ai + 2r = Fcq~i(