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Floating Wave Energy Converter
Published in Srinivasan Chandrasekaran, Faisal Khan, Rouzbeh Abbassi, Wave Energy Devices, 2022
Srinivasan Chandrasekaran, Faisal Khan, Rouzbeh Abbassi
Response amplitude operator (RAO) is the transfer function, which is a system property. It represents the motion characteristics of the device and is useful in estimating the dominant frequency band within which the device shall absorb the maximum power. RAO is expressed as a ratio of the response amplitude to the wave amplitude. It is quite easy to infer that the peak RAO amplitude is seen at the resonance band. However, in a multi-body FWEC, the peaks can occur at various frequencies, activating the device to absorb energy over a wider range of frequencies. The phase term of the complex RAO gives the phase difference between the motion of the device and the incident waves. To optimize an FWEC, it is necessary to optimize the response amplitude while keeping the device’s velocity in phase with that of the incident waves; it is done by passive controlling. However, the external actuating system needs to actuating a zero-phase difference, termed active controlling. Usually, this is modeled and assessed in the time domain due to the virtue of nonlinearities present in the scheme.
Introduction
Published in Srinivasan Chandrasekaran, Offshore Semi-Submersible Platform Engineering, 2020
The most straightforward wave theory is Airy’s linear wave theory, or small-amplitude wave theory. According to this theory, the waveform has a sinusoidal profile. This theory also provides the kinematic and dynamic amplitudes as a linear function of wave amplitude or wave height. Thus, the normalized amplitude value is unique and invariant to the wave amplitude. It helps to represent the response of the offshore structures as a normalized value. The normalized responses, as a function of wave height, are called the transfer function or the Response Amplitude Operator (RAO). This method is simple and predicts the extreme response of the structures.
Ship hull structural scantling optimization
Published in C. Guedes Soares, Y. Garbatov, Progress in the Analysis and Design of Marine Structures, 2017
MAESTRO-Wave is an integrated component of the software suite MAESTRO (2016). MAESTRO-Wave first computes the response of ship motions, hull girder loads, and panel pressures for an incident wave of unit amplitude, with frequency ω and direction φ. The response amplitude per unit wave amplitude is often referred to as the Response Amplitude Operator (RAO). RAOs are effectively transfer functions which give the proportion of wave amplitude “transferred” by the ship system into ship response. Fig. 8 shows a RAO envelope of longitudinal bending moment.
A framework for quantifying fatigue deterioration of ship structures under changing climate conditions
Published in Ships and Offshore Structures, 2022
Mohammad F. Tamimi, Omid Khandel, Mohamed Soliman
The response amplitude operator (RAO) is a transfer function that establishes a relationship between the spectral density functions of sea waves and the ship response. This relationship is expressed as (Drummen et al. 2009) where is the output spectral density function representing the response of interest is the input spectral density function of sea waves, is the transfer function, and ω is the frequency (rad/s). The RAO is a function of the ship geometry and operational conditions. Several variables such as the sea state, ship speed, and heading angle are involved in defining the operational conditions. To properly account for these parameters, it is essential to evaluate the encountered wave frequency defined as (ABS 2017) in which is the encountered wave frequency (rad/s), is the ship speed (m/s), is the gravitational acceleration (m/s2), and is the heading angle. In this paper, the computer program SPECTRA (Michaelson 2000) is employed to generate the RAOs of the VBM. This program is capable of generating RAOs considering wave-induced (low-frequency) and slam-induced (high-frequency) bending moments associated with vertical, lateral, and torsional conditions (Sikora 1998).
Effect of keel plate on the performance of FPSO suitable for arctic ice environment
Published in Ships and Offshore Structures, 2020
The motion responses in surge (X), heave (Z) and pitch (θ) modes were measured using accelerometers. The responses are expressed in terms of Response Amplitude Operator (RAOs) by normalising with respect to incident wave amplitude. The surge, heave and pitch RAOs for the non-ship-hull-shaped FPSO with different mooring configurations are shown in Figures 12(a–c), respectively. From Figure 12(a), it is observed that the surge response increases with the increase in wave period and there is no significant difference in surge response for different mooring configurations. This suggests that the stiffness offered by the different mooring configurations does not change significantly in the surge direction. Also the scope of the mooring line of the three configurations does not significantly differ. The rate of increase is found to be high up to the wave period of nearly 2.9 s and after which, the maximum thrust on the vessel occurs. For wave period less than 1.2 s, the wave length is less than the characteristic vessel dimension and the surge is insignificant. For the ranges of wave period tested the max surge RAO is found to be 0.92 m/m and occurred at a max wave period of 6 s. This translates to about 27 m surge for a typical extreme wave height of 30 m and 30 s periods and is about 25% of the vessel characteristic prototype diameter. For the normal sea state the values of surge RAO gives acceptable ranges of surge motion for operating conditions. The behaviour of surge RAO for this non-ship-shaped FPSO vessel is similar to that of ship-shaped FPSO with a turret mooring located near the bow and heave RAO and pitch RAO increase with an increase in wave period (Guedes et al. 2005).