Dynamic Analysis of Suction Stabilized Floating Platforms

Subramanian, Susheelkumar C.; Dye, Michaela; Redkar, Sangram

doi:10.3390/jmse8080587

Cited by 11 publications

(2 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, a brief outline of the Floquet theory and Normal Forms theory is provided along with a proposed approach. A detailed explanation of these theories and the proposed approach are provided in the prior work [20].…”

Section: Mathematical Background and Methodologymentioning

confidence: 99%

Comparison of Poincaré Normal Forms and Floquet Theory for Analysis of Linear Time Periodic Systems

Subramanian

Redkar

2020

Journal of Computational and Nonlinear Dynamics

Self Cite

View full text Add to dashboard Cite

In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique and apply them towards the investigation of stability bounds for linear time periodic systems. Though the Normal Forms technique has been predominantly used for the analysis of nonlinear equations, in this work the authors utilize it to transform a linear time periodic system to a time-invariant system, similar to the Lyapunov Floquet (L-F) transformation. The authors employ an intuitive state augmentation technique, modal transformation and near identity transformations to facilitate the application of time independent Normal Forms. This method provides a closed form analytical expression for the state transition matrix. Additionally, stability analysis is performed on the transformed system and the comparative results of dynamical characteristics and temporal variations of a simple linear Mathieu equation are also presented in this work.

show abstract

Section: Mathematical Background and Methodologymentioning

confidence: 99%

Comparison of Poincaré Normal Forms and Floquet Theory for Analysis of Linear Time Periodic Systems

Subramanian

Redkar

2020

Journal of Computational and Nonlinear Dynamics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, the authors have demonstrated the computation of the closed-form expression for the Lyapunov–Floquet (L-F) transformation matrix and stability analysis for a time periodic system, using the normal form and state augmentation techniques in Subramanian and Redkar (2020), Subramanian et al (2020). They have also applied similar approach toward the analysis and control of attitude motion of spacecrafts and reduction of nonlinear systems using the center manifold technique in Waswa and Redkar (2020a), Waswa et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Computation of Lyapunov–Perron transformation for linear quasi-periodic systems

Subramanian

Waswa

Redkar

2021

Journal of Vibration and Control

Self Cite

View full text Add to dashboard Cite

The transformation of a linear time periodic system to a time-invariant system is achieved using the Floquet theory. In this work, the authors attempt to extend the same toward the quasi-periodic systems, using a Lyapunov–Perron transformation. Though a technique to obtain the closed-form expression for the Lyapunov–Perron transformation matrix is missing in the literature, the application of unification of multiple theories would aid in identifying such a transformation. In this work, the authors demonstrate a methodology to obtain the closed-form expression for the Lyapunov–Perron transformation analytically for the case of a commutative quasi-periodic system. In addition, for the case of a noncommutative quasi-periodic system, an intuitive state augmentation and normal form techniques are used to reduce the system to a time-invariant form and obtain Lyapunov–Perron transformation. The results are compared with the numerical techniques for validation.

show abstract

Coexisting attractors in floating body dynamics undergoing parametric resonance

2022

View full text Add to dashboard Cite

This study pertains to analysing the dynamical behaviour of a floating body undergoing parametric resonances. A simple vertical cylinder, representing a classical spar-buoy, is considered, limiting its motion to heave and pitch degrees of freedom. Its geometry and mass distribution are chosen such that a 2:1 ratio of heave to pitch/roll natural frequency makes the spar-buoy prone to parametric resonance. The system is then studied by the shooting method, combined with a pseudo-arclength continuation, and the harmonic balance procedure. Results show that an extensive bistable region exists, where stable parametric resonance coexists with a regular resonance response. The analysis also unveiled the existence of stable quasiperiodic motions existing in correspondence of both pitch and heave resonance. Results are qualitatively validated using a model based on the explicit nonlinear Froude–Krylov force calculation.

show abstract

Dynamic Analysis of Suction Stabilized Floating Platforms

Cited by 11 publications

References 54 publications

Comparison of Poincaré Normal Forms and Floquet Theory for Analysis of Linear Time Periodic Systems

Comparison of Poincaré Normal Forms and Floquet Theory for Analysis of Linear Time Periodic Systems

Computation of Lyapunov–Perron transformation for linear quasi-periodic systems

Coexisting attractors in floating body dynamics undergoing parametric resonance

Contact Info

Product

Resources

About