Application of Volterra Series Analysis for Parametric Rolling in Irregular Seas

Moideen, Hisham; Somayajula, Abhilash; Falzarano, Jeffrey

doi:10.5957/josr.58.2.130047

Cited by 11 publications

(4 citation statements)

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“…Parametric resonance in floating bodies has become an increasingly important area of study due to its relevance in offshore engineering [1][2][3][4][5][6][7], wave energy conversion [8][9][10][11][12][13][14], and naval architecture [15][16][17][18][19][20][21]. Understanding the dynamics of floating structures and the interaction with waves is crucial for the development of efficient and reliable marine systems.…”

Section: Introductionmentioning

confidence: 99%

A Computationally Efficient Analytical Modelling Approach for Parametric Oscillations in Floating Bodies

Fujiyama,

Lelkes,

Kalmár-Nagy

et al. 2024

Preprint

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Parametric resonance in floating bodies presents a complex nonlinear dynamic problem with significant implications for offshore engineering, wave energy systems, and naval architecture. Addressing the computational challenges inherent in modelling such phenomena, this paper introduces an innovative analytical model that incorporates position dependence into the hydrodynamic coefficients for the wave excitation force, enabling conventional analytic hydrodynamic models to be augmented and recast into a form akin to the Mathieu equation. Originally conceived for analysing heave-to-heave Mathieu instability in floating bodies, this research extends the model's applicability to the investigation of heave-to-pitch Mathieu instability, thereby broadening its utility in understanding the nonlinear dynamics of marine structures. The effectiveness of the model in capturing parametric resonance is substantiated through a comparison with the results from a high-fidelity, computationally expensive, nonlinear Froude-Krylov force model. The proposed model boasts a speed advantage of over 1000 times compared to the nonlinear Froude-Krylov force model, while also offering the considerable benefit of facilitating analytical investigation methods. The capacity of the model to generalize appears promising, as the extension to a 2 Degrees of Freedom system demonstrates favourable outcomes.

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Section: Introductionmentioning

confidence: 99%

A Computationally Efficient Analytical Modelling Approach for Parametric Oscillations in Floating Bodies

Fujiyama,

Lelkes,

Kalmár-Nagy

et al. 2024

Preprint

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“…The focus is on a single-degree-offreedom (SDOF) system with nonlinear damping force proportional to even or/and odd orders of velocity. Such systems have been widely used for analysis of rolling ship subjected to beam waves, [21][22][23][24] and they are adopted to investigate potential benefits in vibration control [25][26][27] and energy harvesting, [28][29][30] where iterative algorithm is essentially required in a numerical method. As shall be shown in this paper, the present temporal finite element method (TFEM) stemming from EHP formalism adopts non-iterative algorithm and this method with small size of time step is equivalent to the Runge-Kutta-Fehlberg (RKF45) method with default error criteria.…”

Section: Introductionmentioning

confidence: 99%

Extended framework of Hamilton’s principle for single-degree-of-freedom nonlinear damping systems

Kim

2020

Journal of Low Frequency Noise, Vibration and Active Control

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The paper explores application of the variational formalism called extended framework of Hamilton’s principle to nonlinear damping systems. Single-degree-of-freedom systems with dominant source of nonlinearity from polynomial powers of the velocity are initially considered. Appropriate variational formulation is provided, and then the corresponding weak form is discretized to produce a novel computational method. The resulting low-order temporal finite element method utilizes non-iterative algorithm, and some examples are provided to verify its performance. The present temporal finite element method using small time step is equivalent to the adaptive Runge–Kutta–Fehlberg method with default error tolerances in MATLAB, and additional simulation shows its good convergence characteristics.

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“…Kim and Kim [18] suggested the use of impulse response functions and a Rakine panel method to estimate the hydrodynamic coefficients to perform the simulation of parametric roll. Moideen et al [26] developed a Volterra series model to capture the GM variation through a first-and second-order transfer functions (e.g., Hua et al [15]) and used it to simulate parametric roll in irregular head seas. Somayajula and Falzarano [38] extended this work by adding a cubic softening stiffness to the model and studied the ergodicity of the resulting roll motion.…”

Section: Introductionmentioning

confidence: 99%

Large-amplitude time-domain simulation tool for marine and offshore motion prediction

Somayajula

Falzarano

2015

Mar Syst Ocean Technol

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Although linear ship motions theory is sufficiently accurate in predicting the motions of a ship/offshore platform in irregular seas, it cannot capture many of the nonlinear dynamic phenomena (e.g., parametric resonance) which might be very important in the design phase. In order to accurately simulate the motions of a structure, one has to resort to 6 degrees of freedom coupled nonlinear time-domain simulations. This paper presents the theoretical development of such a tool (called SIMDYN) which solves the nonlinear equations of motion while considering the large-amplitude rotations of the body. It also accounts for the nonlinearity of Froude-Krylov and hydrostatic forces. The validity of the developed tool is verified by comparing the predicted motions against the linear theory for small amplitude motions. The paper also shows an example of parametric roll simulation of a container ship to demonstrate the ability of the tool to capture nonlinear phenomena accurately. This tool is then applied to perform 30 3-h coupled simulations of a container ship in head seas, and the resultant time series from each simulation are analyzed to study the ergodicity of parametric roll in irregular longitudinal seas.

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Application of Volterra Series Analysis for Parametric Rolling in Irregular Seas

Cited by 11 publications

References 0 publications

A Computationally Efficient Analytical Modelling Approach for Parametric Oscillations in Floating Bodies

A Computationally Efficient Analytical Modelling Approach for Parametric Oscillations in Floating Bodies

Extended framework of Hamilton’s principle for single-degree-of-freedom nonlinear damping systems

Large-amplitude time-domain simulation tool for marine and offshore motion prediction

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