By Thor I. Fossen
Parametric Resonance in Dynamical structures discusses the phenomenon of parametric resonance and its incidence in mechanical structures, cars, bikes, airplane and marine craft, alongside micro-electro-mechanical structures. The members offers an advent to the foundation explanations of this phenomenon and its mathematical an identical, the Mathieu-Hill equation. additionally integrated is a dialogue of ways parametric resonance happens on ships and offshore platforms, and its frequency in mechanical and electric platforms. This quantity is perfect for researchers and mechanical engineers operating in program fields equivalent to MEMS, maritime, plane and floor automobile engineering.
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Extra resources for Parametric Resonance in Dynamical Systems
Data show that the shape parameter is approximately the same under both hypothesis, β1 = β0 = β , then the GLRT reads υ0 υˆ 1 + N β ln υ0 υˆ 1 N β ln υˆ1β − υ0β (υ0 υˆ1 )β +N N−1 β ∑ zk > ln γ ⇒ k=0 β β υˆ1 − υ0 β υ0 > ln γ . 35) Therefore the test quantity g(k) is g(k) = υˆ1 (k) υ0 β − 1 − β ln and the threshold where H1 is decided is g(k) > ln γ ≡ γg . 5 0 0 1 2 3 4 5 6 7 g(k) Fig. 6 Test statistics g(k) observed in heavy weather conditions with forced roll. Data from Atlantic passage during a storm.
In head seas, conventional forced roll cannot occur since forces and moments from wave pressure on the hull have no components perpendicular to the ship, but motions in the vertical plane are clearly excited. Heaving and pitching cause periodic variations of the submerged hull geometry. In particular, during a wave passage, the intercepted water-plane area S W changes from the still water case S W0 , causing a variation of the position of the center of buoyancy . This in turn gives rise to a modification of the transverse metacentric height GM and also to a new position of the metacenter M.
Journal of Ship Research, 3(1):36–46 (1959). 33. Shin, Y. , Belenky, V. , Paulling, J. , Weems, K. , Lin, W. : Criteria for parametric roll of large containeships in longitudinal seas. Transactions of SNAME, 112 (2004). 34. Spyrou, K. : Prediction potential of the parametric rolling behaviour of a post-panamax container ship. Ocean Engineering, 35:1235–1244 (2008). 35. : Autoparametric Resonance in Mechanical Systems. Cambridge University Press, United States of America (2000). 36. : An investigation of different methods for the prevention of parametric rolling.
Parametric Resonance in Dynamical Systems by Thor I. Fossen