Back to Search
Start Over
INSTABILITY, CHAOS, AND GROWTH AND DECAY OF ENERGY OF TIME-STEPPING SCHEMES FOR NON-LINEAR DYNAMIC EQUATIONS.
- Source :
-
Communications in Numerical Methods in Engineering . May94, Vol. 10 Issue 5, p393-401. 9p. - Publication Year :
- 1994
-
Abstract
- In this paper we present numerical experiments made to investigate the behaviour of the Newmark time- stepping scheme applied to non-linear dynamic systems. Our attention is focused on the instability and chaos in the Newmark scheme when it is applied to the equation ü + P(u) = 0, representing a non-linear elastic spring. Some unusual modes of behaviour, which are of substantial interest, have been observed. In the first case, a stable but chaotic solution is found. In the second case, while a stable solution is obtained with a certain time step, an unstable solution is found by decreasing the time step. In the third case, instability is triggered by neglecting the initial acceleration. A simple modification of the Newmark scheme is proposed which keeps the energy constant for the equation ü + P(u) = 0 and thereby guarantees unconditional stability. Numerical examples in support of such an energy-conserving scheme are presented. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10698299
- Volume :
- 10
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Communications in Numerical Methods in Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 12791032
- Full Text :
- https://doi.org/10.1002/cnm.1640100505