Heave Response Control of a Semisubmersible by Passive Dampers

Article information

J. Ocean Eng. Technol. 2025;39(6):559-571

Publication date (electronic) : 2025 December 19

doi : https://doi.org/10.26748/KSOE.2025.046

Ajaya Kumar Das¹, Srinivasan Chandrasekaran²

¹Senior Research Scholar, Department of Ocean Engineering, Indian Institute of Technology, Madras, Tamil Nadu, India

²Professor, Department of Ocean Engineering, Indian Institute of Technology, Madras, Tamil Nadu, India

Corresponding author Srinivasan Chandrasekaran: +91-044-22574821, drsekaran@iitm.ac.in

Received 2025 August 22; Revised 2025 October 23; Accepted 2025 November 17.

Abstract

1. Introduction

Oil and gas production is epicentered at deep waters offshore, where fixed platforms like gravity based structures (GBS) and Jacket structures are unsuitable. Compliant platforms are successfully deployed as alternatives, but with a high capital expenditure (CAPEX). Semisubmersibles are preferred as they can be propelled and deployed like drill ships. High mobility and lower CAPEX are advantages, in addition to several others: a small water plane area, increased stability, and a large deck. However, they face challenges in heave motion (Ma et al., 2018; Chandrasekaran and Uddin, 2020; Zang et al., 2022). Recent studies confirmed the versatility and safety of deploying semi-submersibles in the deep sea through postulated failure analysis (Chandrasekaran et al., 2021; Chandrasekaran and Uddin, 2020). To reduce heave motion, Murray et al. (2007) modified the semisubmersible hull with a trussed heave plate; others suggested the addition of heave plates (Travanca and Hao, 2017). A geometric design of a truss pontoon over the columns helped the resonance response of semisubmersibles (Srinivasan et al., 2006). Lee and Choung (2025) also attempted to improve the design of the parameters of a semisubmersible offshore wind turbine, which results in motion control of the platform. A semisubmersible with buoys along the mooring lines helps reduce the response of the hull, in addition to the reduction in the tension in the mooring lines (Chandrasekaran et al., 2021). Use of passive dampers, such as tuned mass damper (TMD), was successfully deployed in tension leg platform (TLP)s to reduce surge motion (Chandrasekaran et al., 2013; Suja and Chandrasekaran, 2025; Taflanidis et al., 2009). Experimental studies verified the effectiveness of multiple TMDs on the response control for different mass ratios.

An Inerter-based control device, the rotational inerter damper (RID), studied by Ma et al. (2021), Li et al. (2022), and Li et al. (2023) to mitigate the heave motion, was found to be a better option than the addition of heave plates. Heave motion control of SPAR, attempted by Tao and Cal (2004), depends on a few factors, namely the cylinder diameter and the aspect ratio between the deck and cylinder. Liu et al. (2016) proposed a tuned heave plate energy-harvesting (THPEH) system, which also showed an effective control of heave but had a very limited operational frequency band. Chatterjee and Chakraborty (2014) discussed the methodology of response control with a liquid column damper (TLCD) and a tuned liquid column ball damper (TLCBD) of a semisubmersible under various sea states. The latter was found to be more effective in mitigating the heave response. The response control strategies are also extended to an offshore wind turbine supported by a semisubmersible using a semi-active tuned gas damper and were found All to be effective (Nazokkar and Dezvarch, 2022; Liu et al, 2023). Tuned mass dampers (TMDs) and buoyant mass dampers (BMDs) are other alternatives, studied by the researchers to control the undesirable motion of the offshore compliant platforms (Moharrami and Tootkaboni, 2014; Wang et al., 2024; Yang et al., 2019). They used response reduction factors as performance indicators for optimizing the parameters of the passive damper.

Zhang et al (2020) analyzed three semisubmersible floating offshore wind turbines (FOWTs)—V-shaped, Braceless, and OC4-DeepCwind —supporting the National Renewable Energy Laboratory (NREL) 5 MW turbine was conducted, including second-order wave effects. Results show that ignoring drag overestimates platform responses, while second-order wave loads can excite resonant motions, particularly pitch, potentially leading to structural failure. The coupling of a floating body with a submerged auxiliary body offers an effective approach to suppress heave motion by exploiting hydrodynamic interaction effects. The submerged body contributes additional added mass and damping, shifting the system’s natural frequency and reducing motion amplitudes under wave excitation. Shin et al. (2017) demonstrated experimentally that such interaction can significantly decrease the heave response of a floating body by up to 87%—when the stiffness of the connecting member and the area of the submerged body are appropriately tuned. Kim et al. (2019) experimentally demonstrated that expanding the submerged body area and optimizing the stiffness of the connecting spring can substantially suppress the heave response of floating structures. Their findings underscore the significant potential of floating–submerged body interaction systems in enhancing the hydrodynamic performance and stability of floating platforms, breakwaters, and marine energy devices. Shin et al. (2018) numerically demonstrated that coupling a floater with a submerged body can reduce heave motion by up to 80% under optimal conditions of connection stiffness and submerged body area. Their results showed that tuning the natural frequency of the submerged body to be approximately 10% higher than that of the floater achieves the maximum reduction in heave response. The present study investigates the heave motion reduction of the HYSY-981 semisubmersible platform using a novel passive damper that is partially submerged, unlike previous studies where the secondary mass was fully submerged. The vertical stiffeners, in terms of the numbers in parallel and their stiffness, are tuned to the operational frequencies of the chosen semisubmersible. This damper system design and conceptual configuration are patented to the authors (Chandrasekaran and Das, 2024).

2. Numerical Analysis

2.1 Platform Modelling

The present study considers the Hai Yang Shi You (HYSY)-981 semisubmersible platform, developed and operated by the China National Offshore Oil Corporation (CNOOC). The chosen platform is not equipped with the proposed passive damper system, and hence, the novelty lies in examining it in the presence of the passive damper. As seen in Fig. 1, it consists of two large, submerged pontoons, connected by four rectangular columns, and position-restrained using a 12-point spread mooring system, which is further divided into 4 subgroups, each of which has 3 mooring lines having angles of 5 degrees to each other. The mooring arrangement with wave directions is shown in Fig. 2. The details of the semisubmersible platform and its mooring line properties are provided in Tables 1 and 2, respectively. The environmental conditions adopted for the analysis mimic the South China Sea and are summarized in Table 3. In this study, the JONSWAP spectrum is employed to define the sea state, while the API wind spectrum, derived from a 1-hour mean wind speed, is used for wind loading. A depth-dependent nonlinear current profile is also incorporated, extending to 198 m beneath the mean sea level.

Fig. 1

Schematic model of a semisubmersible with a passive damper

Fig. 2

Arrangement of mooring lines

Table 1

Semisubmersible properties

Table 2

Mooring lines properties

Table 3

Sea states (API, 2002)

Semisubmersible is numerically modeled using the hydrodynamic diffraction and response analysis module in ANSYS Workbench 2025 R1. Initially developed in ANSYS Workbench, the model is exported to the hydrodynamic analysis module. The entire structure is modeled as a diffraction convolution element to capture hydrodynamic interactions. A finite element mesh comprising 9432 nodes and 9461 elements is generated, with the maximum element size restricted to 3.25 m to ensure mesh convergence (Fig. 2). Mooring lines are modeled using catenary cable elements, extending from the fairlead points to the fixed anchors located 1500 m below the mean water level (MWL). The hydrodynamic response in the time domain is evaluated for 2000 s under combined wave–wind–current loading, with a constant time step of 0.05 s. External damper consists of mass, stiffeners, and dashpots, whose geometry is also developed in the software. The initial properties of the damper are determined based on a preliminary set of analyses for the chosen load cases. Fig. 3 shows the damper configuration and free-body diagram. Properties are summarized in Table 4. Each mooring line is assigned an axial stiffness of 67.7 kN/m and an equivalent cross-sectional area of 0.014 m². This analysis is conducted for two load scenarios—low and moderate sea states.

Fig. 3

Damper configuration and free-body diagram

Table 4

Damper properties

The secondary mass or damper system is suspended from the deck of the semisubmersible platform using a rod. The assembly comprises a vertical spring, an elastomeric rubber mass, and rigid plates, all enclosed within a thin-sheeted box-like casing. The damper assembly is partially submerged, deriving its reactive force from buoyancy. The system is supported by four bracket connections attached to the platform’s columns. The added mass effect of the damper has already been considered in ANSYS AQWA for both the uncontrolled and controlled cases. However, its influence is relatively small compared to that of a fully submerged heave plate, as the present damper configuration is only partially submerged. Moreover, the primary focus of the current study is on the structural damping behavior of the proposed damper system rather than on the hydrodynamic effects.

The governing equation of motion is expressed as:

(1) [m00md] [x¨x¨d]+[c000] [x˙x˙d]+[k+kd-kd-kdkd] [xxd]=[F(t)0]

Here, m and md denote the masses of the platform and the secondary mass damper, respectively; c represents the damping coefficient of the platform; and k and k_d correspond to the stiffness of the semisubmersible and the damper, respectively. The sum of all the external forces acting on the platform is grouped as F (t) and assumed to act at the mass center of the platform. Fig. 3 shows a free-body diagram of the force balance.

(2) mx¨+cx˙+kx+kd(x-xd)=F(t)

(3) mdx¨d+kd(xd-x)=0

(4) mx¨+cx˙+kx+kdx-kxxd=F(t)

(5) mxx¨d+kdxd-kdx=0

(6) Assuming x=x e-iωt;x˙=iωxe-iωtxd=xde-iωt;x˙d=iωxde-iωt

As the system is tuned, it shall have the same frequency. Then,

(7) x¨=-ω2xe-iωt=-ω2x

(8) x¨d=-ω2xde-iωt=-ω2xd

Substituting Eq. (8) in Eq. (5),

(9) md(-ω2xd)+kdxd-kdx=0xd(kd-mdω2)=kdxxd=kdxkd-mdω2

Substituting Eq. (9) in Eq. (5),

mx¨+cx˙+kx+kxx-kd(kdxkd-mdω2)=F(t)

By dividing both sides of Eq. (10) by the mass m, the equation is simplified as follows:

(11) F(t)=P0e-iωtx¨+cx˙+kx+kdm(x-kdxkd-mdω2)=P0e-iωtm

Simplifying this further, we get:

(12) x¨+cmx˙+kmx+kdm(-mdω2kd-mdω2)x=P0e-iωtmccc=ζc2mωn=ζcm=2ζωnkm=ωn2kdmd=ωd2

After substitution, Eq. (11) can be rewritten as:

(13) -ω2xe-iωt+2ζωniωxe-iωt+ωn2xe-iωt+kdm(-mdω2kd-mdω2)xe-iωt=P0e-iωtm

Simplifying and rearranging Eq. (13) becomes

(14) x=P0m[1ωn2-ω2+kdm(-mdω2kd-mdω2)+2ζωniω]

On dividing ωn2 in both the numerator and denominator of the RHS of Eq. (14)

(15) x=P0k[1ωn2-ω2ωn2+kdk(-mdω2kd-mdω2)+2ζiωωn]

The characteristic parameters in non-dimensional form are given by

μ=mdmf=ωdωnβ*=ωωn

Simplifying, Eq. (15) reduces to the following form:

(16) x=P0k[11-β*2+μf2β*2β*2-f2+2ζiβ*]

To eliminate the imaginary component from the denominator, the term 1-β*2+μf2β*2β*2-f2+2ζiβ* is rationalized by multiplying the expression by its complex conjugate.

(17) x=P0k[1-β*2+μf2β*2β*2-f2+2ζiβ*(1-β*2+μf2β*2β*2-f2)2+4ζ2β*2]

The steady-state response, derived from Eq. (17), is represented on an Argand diagram in the complex plane.

The steady-state displacement response is interpreted using two rotating phasors in the complex plane, as shown in Fig. 4.

Fig. 4

Steady-state response of the damper system

(18) x(t)=ρsin(ω¯t-θ)

(19) ρ=P0k[(1-β*2+μf2β*2β*2-f2)2+4ζ2β*2]-12

(20) θ=tan-1[2ζβ*(1-β*2+μf2β*2β*2-f2)2+4ζ2β*2]

The dynamic magnification factor represents the ratio of the harmonic response amplitude to the static displacement produced by the applied force.

(21) D=ρP0k=[(1-β*2+μf2β*2β*2-f2)2+4ζ2β*2]-12

(22) D=[(β*2-f2)2{(1-β*2)(β*2-f2)+μf2β*2}2+4ζ2β*2(β*2-f2)2]12

The steady-state response amplitude is predominantly influenced by the mass ratio (μ) and the damping ratio (ζ). To identify their optimal values, a dynamic analysis was performed using a force vector generated in the ANSYS AQWA environment. The excitation force was obtained by applying the real JONSWAP wave spectrum. This force vector was then used as input in MATLAB, where the system’s steady-state response was computed based on Eq. (21) for various values of mass ratio (μ).

2.3 Parametric Optimization

The effect of frequency range, mass ratio, and damping ratio on damper performance is investigated. Numerical simulations are carried out using the main vibrational mode parameters of the semisubmersible platform to assess the energy dissipation capacity of the novel damper. Table 5 summarizes the controlled mode characteristics, and the efficiency of the proposed controller is evaluated for 0.5 ≤ f ≤ 1.5.

Table 5

Controlled mode properties of the platform

A sharp resonance peak is observed near β* = 1, corresponding to the system’s natural frequency. At lower damping (smaller μ, the peak amplitude is significantly higher, reaching values above 30, while the response reduces with increasing μ. This demonstrates the strong dependence of vibration amplitude on the mass ratio, where higher μ broadens the response curve and suppresses the resonance magnitude. Additionally, secondary peaks appear at subharmonic frequency ratios (around β* = 0.6 – 0.9), which gradually diminish as μ increases. Beyond the resonance zone, the amplitude response converges to unity, indicating a negligible influence of mass ratio at higher excitation frequencies. These trends confirm that increasing μ improves vibration suppression by reducing the dynamic amplification factor and enhancing overall system stability.

2.4 Influence of mass ratios

The dynamic amplification for various mass ratios is presented in Fig. 5 for a controlled damping ratio of 2.1%. It is observed that higher mass ratios result in lower response amplitudes near resonance. As the wave excitation frequencies remain effective up to 1.5 s, all the peak amplitudes and their corresponding frequency ratios are summarized in Table 6. For mass ratios more than 2%, the response amplitude ratio is too high. Further, a higher mass ratio is not feasible as the platform should remain positively buoyant. Hence, a mass ratio of 2% is an optimized value from the design perspective.

Fig. 5

Dynamic amplification for different mass ratios μ

Table 6

Variations of the amplitude ratio for different mass ratios

Fig. 6 highlights the influence of structural damping for a mass ratio of 2%, chosen as an optimized value. For a damping ratio (ζ) of 1.5%, the peak amplitude of the platform without a damper system rises significantly to 32, which is highly undesirable. With the introduction of the damper system, this amplitude reduces drastically to 10. At an increased damping ratio of 2%, however, the damper system appears to be less effective in the resonance region. For the case of ζ = 2.5%, the undamped platform again exhibits higher amplitudes compared to the previous two cases. Nevertheless, with the inclusion of the damper system, the amplitude is considerably reduced. It is important to note that excessive damping may induce partial structural damage, which is why higher damping ratios are generally avoided. For a higher-damping scenario, the amplitudes unexpectedly increase at higher frequencies due to the greater influence of incident waves. Based on the analysis, 1.5% is identified as the most effective damping ratio, and thus represents the optimal choice for the damper configuration. Hence, from the above analysis, it is concluded that the novel damper system model for this platform has the optimized parameters of (2%) for both mass ratio and damping ratios. The same values are used in the numerical simulation.

Fig. 6

Comparison of the amplitude ratio of the 2% mass ratio for different damping ratios

Fig. 6 highlights the influence of structural damping for a mass ratio of 2%, chosen as an optimized value. For a damping ratio (ζ) of 1.5%, the peak amplitude of the platform without a damper system rises significantly to 32, which is highly undesirable. With the introduction of the damper system, this amplitude reduces drastically to 10. At an increased damping ratio of 2%, however, the damper system appears to be less effective in the resonance region. For the case of ζ = 2.5%, the undamped platform again exhibits higher amplitudes compared to the previous two cases. Nevertheless, with the inclusion of the damper system, the amplitude is considerably reduced. It is important to note that excessive damping may induce partial structural damage, which is why higher damping ratios are generally avoided. For a higher-damping scenario, the amplitudes unexpectedly increase at higher frequencies due to the greater influence of incident waves. Based on the analysis, 1.5% is identified as the most effective damping ratio, and thus represents the optimal choice for the damper configuration. Hence, from the above analysis, it is concluded that the novel damper system model for this platform has the optimized parameters of (2%) for both mass ratio and damping ratios. The same values are used in the numerical simulation.

3. Results and Discussion

The heave response ratio (HRR) is mathematically expressed as the ratio of the root mean square (RMS) value of the heave time history of the platform with a damper system to the corresponding RMS value without the damper system. It is necessary to tune this value for the optimum mass ratio to arrive at the desired control in heave. Table 7 summarizes the heave response ratio for different mass ratios.

Table 7

Heave response ratio.

Fig. 7(a) the heave response amplitude operator (RAO) gives the qualitative idea of the structure’s behavior in different frequency regions; the wave spectra considered in this study are depicted in Fig. 7 (b). The Fig. 7(c) shows the PSD of the heave response with and without a damper. Secondary peaks appear in the 0.2–0.8 frequency range, corresponding to the natural heave frequency of the undamped platform (= 0.3 rad/s). The maximum peak is reduced significantly with the inclusion of a passive damper, but is excited closer to its natural frequency; however, the heave response is mitigated significantly. While this is observed for a mass ratio of 2%, a further increase induces additional masses to the primary system, changing its frequency band. The heave time histories corresponding to a 2% mass ratio, for both the cases with and without the damper, are presented in Fig. 8. As seen, the response is symmetric, ensuring a perfect recentering in the heave motion, which is desirable. Initially, without any control system, the platform oscillated about a mean position of 1.67 m from the sea surface. With the addition of the control system, the mean position was shifted to 1.98 m, but there is a reduction in heave vibration. This may be due to extra energy being dissipated per cycle, so the amplitude of oscillation (heave displacement and velocity) is reduced and the system returns to its mean position faster (i.e., “settles”). This increased damping effect prevents the platform from recentering to its original mean position. Hence, the platform oscillates in new equilibrium positions. A preliminary check under calm-water conditions was thoroughly performed, and the calculated mooring stiffness was found to be within the acceptable range. The introduction of the damping system caused coupling between the pitch and heave motions, resulting in tensioning of one side of the mooring line while the opposite side became relatively slack. This coupling effect contributed to the overall reduction in the platform’s heave oscillations.

Fig. 7

Load-responses characteristics curves

Fig. 8

Heave time histories with damper and without damper

Fig. 9 compares the heave PSDs for all mass ratios considered in this study. As observed, a mass ratio of 2% causes effective control of heave motion.

Fig. 9

Comparison of Heave PSD for different mass ratios

To evaluate the comparative effectiveness of the proposed damper system, a numerical analysis was performed on the semisubmersible platform equipped with a heave plate of dimensions 35 m × 35 m × 0.2 m, corresponding to 2% of the displaced volume (1026.5 kg). The power spectral density (PSD) of the heave response is illustrated in Fig. 10. The results demonstrate that the heave plate offers a moderate reduction in heave motion, exhibiting intermediate performance between the uncontrolled configuration and the platform integrated with the novel damper system. Nevertheless, significant response peaks persist in both the resonance and wave-peak regions, indicating potential risks to the platform’s dynamic stability. Furthermore, the fabrication and installation of such large-mass heave plates present considerable practical challenges, accompanied by long-term maintenance difficulties.

Fig. 10

Comparison of Heave PSD for different control types

To evaluate the platform’s performance under realistic sea-state conditions and to examine the feasibility of the proposed damper system, a comparative study was carried out incorporating the wave load effects that include all nonlinear (second-order) components. Considering only the peak wave frequency and neglecting the secondary frequency components is insufficient, since in actual sea states, nonlinear hydrodynamic interactions induce additional low-frequency responses and slow-drift motions in the platform. These second-order effects play a significant role, where low wave frequencies with longer periods predominantly excite the softer degrees of freedom of the platform, while high wave frequencies with shorter periods tend to influence the stiffer or rigid degrees of freedom. Fig. 11 presents the comparative analysis between the first-order and second-order effects, verified against the uncontrolled (without-damper) condition. It is observed that, in the absence of control, the system exhibits a concentration of energy with multiple peaks near both the natural frequency region and the wave-peak frequency region. With the inclusion of second-order effects, there is a noticeable increase in the heave response amplitude; however, the magnitude remains lower compared to the uncontrolled condition. Moreover, a distinct change in trend is observed at higher frequency ranges, where the response tends to stabilize earlier. This behavior indicates that the second-order wave load components counteract the excitation in the rigid degrees of freedom, particularly affecting the heave motion, as discussed earlier.

Fig. 11

Comparison of Heave PSD for different wave load effects

It is observed that in the second-order analysis, the low-frequency behavior is not accurately captured. This may be attributed to coupling effects in the pitch degree of freedom, which tend to counteract motion in the low-frequency region. Even with extended simulation times of 3 h, as conducted in the present study, the low-frequency characteristics remain inadequately represented. The mooring stiffness was consistently checked for both analyses and was found to be within acceptable limits. Table 8 summarizes the detailed characteristics of the heave time histories for the various scenarios considered. The inclusion of both the damper and the second-order wave effects results in an upward shift in the mean position of the platform. Furthermore, when second-order effects are accounted for, the standard deviation (SD) and root mean square (RMS) values of the heave response increase compared to those obtained from the first-order analysis. This rise in SD and RMS values confirms the presence of additional nonlinear and irregular components arising from secondary wave frequencies. These components introduce more variability into the heave response, reflecting the inherently unpredictable and complex nature of real-sea conditions.

Table 8

statistical comparisons of the heave response for different wave load cases

Since the platform is anchored by mooring lines for station-keeping during drilling operations, it is essential to investigate the platform–mooring interaction. Before the commencement of drilling, the mooring lines are pre-tensioned to maintain the required positional accuracy of the platform. However, during drilling, the lines may experience slackening due to dynamic environmental forces. The introduction of the damper system can potentially influence the mooring line tensions. The mooring tensions before and after the application of the control system are summarized in Tables 9 and 10, respectively. The results indicate that, upon implementing the damper system, the left-side mooring groups (1 and 3) experienced a reduction in tension (slackening), whereas the right-side mooring groups (2 and 4) exhibited an increase in tension, as reflected by the higher values in Table 10. The variations in mooring line tensions for the cases of increased and decreased tension are presented in Figs. 12 and 13, respectively. Such behavior is attributed to the amplification of roll and pitch motions of the platform induced by the damper action. Consequently, to counteract the rolling tendency, the right-side mooring lines are subjected to higher tension, while the left-side lines experience partial slackening. It is well established that a partially submerged floating body, when ballasted, moves vertically downward under the action of the ballast load. However, during de-ballasting or when buoyancy increases, the structure does not rise vertically; instead, it follows a zigzag trajectory due to the combined effects of roll and pitch moments. A similar phenomenon is observed in the present study—without control, the platform remains in deeper submergence, whereas upon activation of the damper system, it experiences an upward displacement. As a result, the heave motion is effectively reduced, though accompanied by an increase in roll and pitch amplitudes. This induces higher tension in one set of mooring lines while partially slackening the others. Hence, continuous monitoring of mooring tensions is necessary to ensure they remain within their yield limits. Apart from this consideration, the platform demonstrates satisfactory dynamic performance under the action of the proposed damper system.

Table 9

Mooring tension variation without damper case

Table 10

Mooring tension variation with damper case

Fig. 12

Time histories for the critical mooring line 2a

Fig. 13

Time histories for the critical mooring line 3c

4. Conclusions

Semisubmersible HYSI-981, deployed for oil and gas exploration, exhibits a large heave motion, which requires mitigation for operational safety. Passive dampers are used to achieve the desired level of heave control and tuned over a wider frequency band. Detailed dynamic analysis is carried out to assess the heave mitigation under operational sea states. Parametric studies conducted for different mass ratios showed that a 2% mass ratio is optimal and the best performer. The proposed damper outperforms a conventional heave plate of the same size in controlling heave motion. Second-order analysis confirms its realistic behavior, showing an 8% increase in heave energy content. Mooring interactions reveal the platform’s true response, with left-side lines slackening and right-side lines tensioning due to roll moment variations induced by the damper. The results confirm the effectiveness of the passive damper for low and moderate sea states. As observed, the heave response is symmetric with the damper, ensuring a perfect recentering in the heave motion, which is desirable. The passive damper, though it excites the platform at a frequency closer to its natural frequency, does not induce any erratic motion. In addition, the damper system is activated on the buoyancy force produced due to its submergence, which is unique. No external power is required to activate control motion, but it is self-developed by platform motion. The proposed damper has not been examined for higher sea states, and its effectiveness in such conditions may be considered in future work.

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