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).

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.

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. 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.

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.

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.

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.

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.

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.