Stability Research on Configuration Transformation of the Complex-Surface Cutting Metamorphic Mechanism

Hu, Sheng Hai; Liu, Xiu Lian; Wang, Hong Guang; Zhang, Xiao Dong

doi:10.4028/www.scientific.net/amr.655-657.421

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Draught (Mm) 8121

Time-domain Formulation1

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2021

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“…31.64 I (kg • m 2 ) 4.45 The jth component of the radiation force evaluated by convolution is given in Equation (29). In addition, the jth component of the radiation force evaluated with the state-space model is given in Equation (24).…”

Section: Draught (Mm) 812mentioning

confidence: 99%

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Kernel Function Definition Completion for Time–Domain State–Space Representations of Radiation Forces: Application to the Hankel Singular Value Decomposition

Bris

Boulluec

Charpentier

et al. 2021

JMSE

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This paper focuses on the formulation of state–space representations of radiation forces for marine structures using Hankel Singular Value Decomposition (HSVD), a method used to obtain a state–space realization from a Hankel matrix, with the classical definition of the kernel function and its new definition given in this paper. The first part shows the influence of a term commonly neglected and the resulting improvement by taking this term into account. The second part will focus on the feedthrough matrix to understand why some models have none and why some others, such as HSVD, have one. An exact definition of the kernel function will be given underlying its discontinuity and its causality. This study also shows the interest of extrapolating hydrodynamic coefficients before approaching radiation forces by a state–space model.

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Section: Draught (Mm) 812mentioning

confidence: 99%

“…As in [29], the function K (defined in Equation ( 8)) can be approached by Equation (38) using Prony's series. Thus, it is also possible for K b :…”

Section: Time-domain Formulationmentioning

confidence: 99%