Stability Analysis Of The Non-Linear Mathieu Equation
β Scribed by M. Mond; G. Cederbaum; P.B. Khan; Y. Zarmi
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 348 KB
- Volume
- 167
- Category
- Article
- ISSN
- 0022-460X
No coin nor oath required. For personal study only.
β¦ Synopsis
The non-linear Mathieu equation is analyzed within the framework of the method of normal forms. Analytical conditions for explosive instability are obtained, and expressions for the period as well as the amplitude of the stable response are derived.
π SIMILAR VOLUMES
## Abstract The estimation of the parameters (βfictitious densitiesβ) which control the convergence and numerical stability of a nonβlinear Dynamic Relaxation solution is described. The optimal values of these parameters vary during the iterative solution and they are predicted from the GerschgΓΆrin
We consider a non-linear plate equation of Bernoulli-Euler type with a locally distributed damping term. Our main result asserts that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially. The method we use is a combination of multiplier techniques and o
A linear stability theory for non-linear periodic solutions is presented in which higher order phase-integral asymptotic approximations are used. The stability matrix is derived in an exact formalism which combines Floquet and phase-integral theory. The periodic responses are assumed given in analyt
XMMARY