Solomon C. Yim

Chaotic roll motion and capsize of ships under periodic excitation with random noise

Abstract A stochastic analysis procedure is developed to examine the properties of chaotic roll motion and the capsize of ships subjected to periodic excitation with a random noise disturbance. To take into account the presence of randomness in the excitation and the response, a generalized Melnikov method is developed to provide an upper bound on the domain of the potential chaotic roll motion. The associated Fokker—Planck equation governing the evolution of the probability density function (PDF) of the roll motion is derived and numerically solved by the path integral solution procedure to obtain joint probability density functions (JPDFs) in state space. A chaotic response can be found in two regions (near the homoclinic and heteroclinic orbits). The global behavior of the roll motion can be depicted by the JPDF. It is found that the presence of noise enlarges the boundary of the chaotic domains and bridges coexisting attracting basins in the local regimes. The attracting domain of capsize is of the greatest strength. The probability of capsize is considered in this paper as an extreme excursion problem with the time-averaged PDF as an invariant measure. With this measure, the heteroclinic region is identified as an ‘unsafe’ regime. Numerical results indicate that, under the presence of noise, all roll motion trajectories of a ship that visit the regime near the heteroclinic orbit will eventually lead to capsize.

Analysis of a Nonlinear System Exhibiting Chaotic, Noisy Chaotic, and Random Behaviors

This study presents a stochastic approach for the analysis of nonchaotic, chaotic, random and nonchaotic, random and chaotic, and random dynamics of a nonlinear system. The analysis utilizes a Markov process approximation, direct numerical simulations, and a generalized stochastic Melnikov process. The Fokker-Planck equation along with a path integral solution procedure are developed and implemented to illustrate the evolution of probability density functions. Numerical integration is employed to simulate the noise effects on nonlinear responses. In regard to the presence of additive ideal white noise, the generalized stochastic Melnikov process is developed to identify the boundary for noisy chaos. A mathematical representation encompassing all possible dynamical responses is provided. Numerical results indicate that noisy chaos is a possible intermediate state between deterministic and random dynamics. A global picture of the system behavior is demonstrated via the transition of probability density function over its entire evolution. It is observed that the presence of external noise has significant effects over the transition between different response states and between co-existing attractors.

NONLINEAR OSCILLATIONS, BIFURCATIONS AND CHAOS IN A MULTI-POINT MOORING SYSTEM WITH A GEOMETRIC NONLINEARITY

A taut multi-point mooring system with a large geometric nonlinearity under wave and current excitation is examined in this paper. The system is found to exhibit local instability and global bifurcations leading to complex nonlinear and chaotic responses. A semi-analytic method based on stability analyses of approximate solutions to the exact nonlinear system is shown to be an efficient predictor of bifurcations and chaos. Thus the method may supplant or significantly reduce the effort of a numerical parametric analysis for the strongly nonlinear ocean system.

Numerical Modeling and Ocean Testing of a Direct-Drive Wave Energy Device Utilizing a Permanent Magnet Linear Generator for Power Take-Off

For the past several years an inter-disciplinary research group at Oregon State University (OSU), working in conjunction with Columbia Power Technologies (CPT) has been researching innovative direct-drive wave energy systems. These systems simplify the conversion of wave energy into electricity by eliminating intermediate energy conversion processes. In support of this research OSU and CPT have developed a hybrid numerical/physical modeling approach utilizing a large scale linear test bed (LTB), and a commercial coupled analysis tool. This paper will present an overview of this modeling approach and its application to the design of a 10kW prototype wave energy conversion system that was tested in the open ocean in the fall of 2008. The data gathered during ocean testing was used to calibrate the numerical model of the device and predict the energy capture potential of the system.Copyright

Damage Assessment of the 2010 Chile Earthquake and Tsunami Using Terrestrial Laser Scanning

In the wake of the 2010 Chile earthquake and tsunami, a reconnaissance survey recorded earthquake and tsunami damage using terrestrial laser scanning (TLS), which is capable of detecting details that most traditional reconnaissance methods cannot. TLS enables precise measurements of structural deformations and damage (including shear cracking of concrete walls, concrete spalling, and damage of rebars), as well as soil deformations and damage (including erosion, scour, liquefaction, lateral spread, slope failure, and ground displacement). Advanced measurements such as minute structural rotations, spatial distribution of cracks, volumetric and positional change calculations can also be obtained. Herein, we present various types of detailed measurements and analyses using TLS data obtained at several sites that were damaged by the earthquake and/or tsunami in Concepción, Constitución, Dichato, and Talcahuano. Moreover, this high-resolution data has enabled a unique avenue for virtual, post-visit analysis, providing additional insights that were not readily observable during the field visit.

Experimental and numerical investigations of tethered spar and sphere buoys in irregular waves

A series of large-scale experiments were conducted to examine the motions of buoys in a variety of wave climates. In conjunction with these experiments, numerical simulations of selected tests were conducted to test the present ability of a particular computer program to model buoy responses. This paper considers individual wave tests for two of the buoy models used in the experiments, a spar buoy and a sphere buoy. The wave field is generated using a JONSWAP spectrum. A description of the experiments shows that each buoy is subject to significant resonant responses, in heave for the spar and surge for the sphere, even though wave forcing is not present at or immediately adjacent to the resonant frequencies. The numerical simulations show generally good comparisons with the experimental data.

Recent tsunami highlights need for awareness of tsunami duration

On Wednesday, 15 November 2006, Crescent City Harbor, in Del Norte County, Calif., was hit by surges resulting from the tsunami generated by the Mw= 8.3 Kuril Islands earthquake. The strong currents caused an estimated US

Chaotic rocking behavior of freestanding objects with sliding motion

700,000 to

DRAG-INDUCED INSTABILITIES AND CHAOS IN MOORING SYSTEMS

1 million in losses to the small boat basin at Citizens Dock, destroying or damaging three floating docks and causing minor damage to several boats (Figure l).The event highlighted a persistent problem for tsunami hazard mitigation: Most people are still unaware that the first tsunami waves rarely are the largest and that the potential for damaging waves may last for many hours.

Tsunami Modeling, Fluid Load Simulation, and Validation Using Geospatial Field Data

This paper examines the influence of effects of sliding on the non-linear rocking response behavior of freestanding rigid objects (blocks) subjected to harmonic horizontal and vertical excitations. It is well known that the rocking responses depend strongly on the impact effect between object and the base, which takes place with abrupt reduction in kinetic energy. In this study, it is shown that the rocking behavior is significantly affected by the presence of the sliding motion. A parametric response analysis is carried out over a range of excitation amplitudes and frequencies. Chaotic responses are observed over a wide response region, particularly for the case of large vertical amplitude excitation with significant sliding motions. The chaotic characteristics are demonstrated using time histories, Poincare sections, power spectral density and Lyapunov exponents of the rocking responses. The complex chaotic response behavior is illustrated by Poincare section in the phase space. The distribution of various types of rocking responses and the effects of sliding motion are examined via bifurcation diagrams and examples of typical rocking responses.