Non-linear behavior and chaotic motions of an SDOF system with piecewise- non-linear stiffness
The authors consider a simplified model of an offshore articulated loading platform (articulated buoyant tower, mooring hawser and moored vessel). With some drastic approximations, this leads to the equation \(I\ddot \nu+C \dot \nu+\tilde g(\nu)=M_ 0 \cos \omega t\) with \(\tilde g(\nu)=\begin{cases} k_ 1(\nu-\nu^ 3/6),\;& \nu \geq 0; \\ k_ 2 \nu+k_ 3 \nu^ 3, & \nu<0, \end{cases}\) Here \(\nu\) is the angular displacement, \(I\) the virtual moment of inertia of the towers, \(C\) the linearized damping coefficient, \(M_ 0\) and \(\omega\) are the amplitude and frequency of the wave excitation, respectively; \(\tilde g (\nu)\) is the piecewise nonlinear restoring force. This problem is investigated by a combination of numerical simulation (harmonic balance method and fast Fourier transformation) with the use of classical stability theory. Via a time series analysis of the numerically computed solution it is established that a Lyapunov exponent is positive: an accepted test for chaotic regime. More generally, the authors' results indicate that chaotic motions will be observed under the action of large excitation amplitudes; the onset being very sensitive to any changes in the parameters of the model.
scientific article; zbMATH DE number 91101