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Nonlinear vibrations of rotating system near resonance

Starosta R., Sypniewska-Kamińska G.

Vibrations in Physical Systems

2014

Vol. 26

265--272

The paper concerns analysis of nonlinear vibration of the rotating system consisted of two disks and shaft. The analytical multiple time scale method is applied to the analysis dynamics of the system near main resonance. The transition phenomenon depending on the value of the nonlinearity parameter is discussed. All the analytical results have been confirmed numerically.

Asymptotics of solution for singularly perturbed nonlinear discrete periodic optimal control problems

Kurina G., Nekrasova N.

Systems Science

2008

Vol. 34, no 1

23-37

The asymptotic expansion of the solution of a singularly perturbed nonlinear discrete time periodic optimal control problem is constructed as series with respect to non-negative integer powers of a small parameter. The terms of asymptotic expansion are the solutions of optimal control problems which are essentially simpler than the original perturbed problem. The solvability of the perturbed problem is established in the neighborhood of a solution of the simpler non-perturbed problem of the lower dimension. The estimates are obtained for the proximity of the approximate solutions to the exact one. The nice property is proved, namely, the values of the minimized functional do not increase when higher-order approximations to the optimal control are used. Numerical examples are given in order to illustrate the method proposed.

Asymptotic Analysis of Anisotropic Nonlinear Elastic PlatesSławian

Sławianowska A., Telega J.J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

1999

Vol. 47, nr 2

115-126

The aim of this contribution is to derive the membrane model of geometrically non-linear elastic plates from the three-dimensional theory of a thin anisotropic body.