Stability analysis and response characteristics of two-degree of freedom nonlinear systems
Understanding the behavior of nonlinear systems is important in laboratory testing. Sine sweep-up and sweep-down tests are routinely done to reveal all of the stable roots in this type of system. There are, however, certain types of softening-hardening restoring force characteristics for which sine sweep testing, whether up or down, will not reveal all of the stable roots. In such cases, it is important that the stable roots be identified so that proper testing procedures are used and the test results are correctly evaluated. The stability of a nonlinear two degree-of-freedom spring-mass system subjected to a sinusoidal exciting force is examined. The solution is perturbed to arrive at a set of coupled variational linear differential equations with periodic coefficients. Floquet theory is used to obtain a characteristic equation. The Routh-Hurwitz stability criterion is adopted to study the stable and unstable regions of the response curves. A computer program is developed to carry out the entire analysis. Extensive information regarding stable zones of the system response is described by means of nondimensional frequency-amplitude diagrams. The results are examined in terms of inferring dynamic response characteristics for sine sweep tests.
- Research Organization:
- Brookhaven National Lab., Upton, NY (USA)
- DOE Contract Number:
- EY-76-C-02-0016
- OSTI ID:
- 5917581
- Report Number(s):
- BNL-NUREG-25846; CONF-7810154-2; TRN: 79-020792
- Resource Relation:
- Conference: 49. shock and vibration symposium, Washington, DC, USA, 17 Oct 1978
- Country of Publication:
- United States
- Language:
- English
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220900* - Nuclear Reactor Technology- Reactor Safety