Meeting growing global energy demand while reducing reliance on extensive onshore infrastructure has accelerated the deployment of offshore liquefied natural gas (LNG) facilities. Compared with conventional onshore terminals, offshore LNG systems offer reduced land use, lower environmental footprint, and greater flexibility in site selection (Banaszkiewicz et al., 2020; Semaskaite et al., 2022). Floating storage and regasification units (FSRUs) are widely adopted; however, their applicability is often limited by large motion responses, site-specific operability constraints, and stringent safety requirements under harsh environmental conditions (Giranza & Bergmann, 2018; Naveiro et al., 2021).

The buoyant leg storage and regasification platform (BLSRP) has been proposed as an alternative offshore LNG concept to overcome these limitations. The BLSRP adopts a form-dominant configuration in which a circular deck is supported by multiple buoyant legs hinged to the deck and restrained by taut mooring tethers. This hinged deck–leg arrangement provides partial kinematic isolation, enabling compliant behavior while maintaining global stability. Previous numerical and experimental studies have demonstrated favorable hydrostatic performance, acceptable Mathieu stability under eccentric loading, and reduced susceptibility to global resonance compared with conventional floating platforms (Chandrasekaran & Lognath, 2017a, 2017b; Chandrasekaran & Kiran, 2018). Despite these advantages, operational conditions such as eccentric topside loading during LNG transfer, degradation or malfunction of individual tethers, and severe environmental loading can induce excessive inward–outward radial motion of the buoyant legs. Due to the inherent kinematic coupling of the hinged system, this radial motion may cause secondary amplification of deck heave. Excessive heave can adversely affect offshore LNG transfer operations and platform safety under severe environmental conditions (Ji et al., 2023; Liang et al., 2022). Classification society guidelines similarly emphasize strict control of vertical motions to ensure safe LNG operations under combined environmental loading (ABS, 2018; DNV, 2022).

Passive control systems are attractive because of their simplicity, robustness, and independence from external power (Kandasamy et al., 2016; Zhang et al., 2023). Conventional tuned mass dampers (TMDs) and tuned liquid column dampers (TLCDs) generally act at deck level and require frequency tuning or auxiliary masses (Wu et al., 2016; You et al., 2022; Suja & Chandrasekaran, 2025). Semi-active MR dampers provide adaptive control but require power, sensors, and controllers (Arakkan & Chandrasekaran, 2026). These methods are less suited to the BLSRP, where heave is governed primarily by leg-level radial kinematics. Therefore, the present study proposes a passive LS-RCM that directly controls radial leg motion while preserving the compliant characteristics of the platform. The mechanism employs a centralized spring arrangement that exploits the unique geometry of the hinged deck–leg system to introduce additional restoring stiffness through radial control of the buoyant legs. This approach regulates radial leg motion and indirectly suppresses excessive deck heave without relying on frequency tuning, secondary masses, or active control inputs, while preserving the inherent compliance and hydrostatic characteristics of the BLSRP. Time-domain simulations are conducted using ANSYS AQWA under combined wave, current, and wind loading for moderate, high, and very high sea states. The study focuses on heave as the governing response parameter for offshore LNG operations and demonstrates the effectiveness of geometry-driven passive control in enhancing the dynamic stability of BLSRP-type platforms.

The essential components of the BLSRP considered in this study are illustrated in Fig. 1. The platform consists of a circular deck supported by symmetrically arranged buoyant legs hinged to the deck, allowing inward–outward radial motion while restricting moment transfer. The lower ends of the buoyant legs are restrained by taut-moored tethers that provide positional stability and restoring forces. The primary structural components of the BLSRP and the RCM are summarized in Table 1, while the corresponding geometric, mass, and hydrostatic properties are listed in Table 2. Structural and topside mass distributions, including deck mass eccentricity of (0.477, −0.440 m), are explicitly incorporated. Equivalent simplified geometries are adopted to preserve global mass, stiffness, and hydrostatic characteristics.

As a positively buoyant platform, the BLSRP exhibits high inherent stiffness in heave; however, its performance can deteriorate under eccentric topside loading or partial tether failure. Such conditions may induce pitch motion, leading to differential heave imbalance and reduced operational stability. To mitigate these effects, a centralized RCM is incorporated into the platform design. The proposed RCM is a passive linear spring system intended to regulate the radial motion of the buoyant legs. A central vertical shaft, aligned with the platform’s geometric axis, is fixed to the underside of the deck through a circular connecting plate (Fig. 2) and serves as the fastening point for the spring assemblies. Each buoyant leg is mechanically connected to the central shaft through a spring assembly consisting of a rigid connecting rod, a linear spring, and a movable piston rod. The hinged deck–leg connections permit rotation in the vertical plane and allow inward–outward radial displacement of the legs.

During outward radial motion, the piston rod extends and stretches the spring, storing elastic potential energy. The resulting restoring force retracts the buoyant leg toward its equilibrium position. Conversely, inward radial motion compresses the spring, which generates a restoring force opposing the displacement. Other platform degrees of freedom are restrained by the high-tension mooring system. The combined action of the spring-based RCM and the mooring system effectively controls radial leg motion, thereby suppressing excessive deck heave while preserving the inherent compliant behavior of the BLSRP.

The BLSRP is modeled using ANSYS Design Modeler, where the circular deck and buoyant legs are represented as solid and tubular elements, respectively. The buoyant legs are connected to the deck through hinged joints that allow inward–outward radial motion and symmetric rotation about the vertical axis. Each buoyant leg is anchored to the seabed by four inclined, taut mooring tethers that remain parallel within each group but vary in length due to mooring inclination. The static equilibrium of the platform, accounting for buoyancy, structural weight, tether pretension, and the RCM, is expressed as in Eq. (1)

where F_b is the buoyancy force, W is the platform weight without the RCM,W_RCM is the RCM weight, n is the number of buoyant legs, T₀ is the initial tether pretension, and θ is the tether inclination angle at the seabed. The RCM is designed as a nearly neutrally buoyant assembly, with its actual volumetric displacement closely matching the equivalent displacement required to compensate for its self-weight. Accordingly, the addition of the RCM does not significantly alter the hydrostatic equilibrium of the platform, and the tether pretension and metacentric height remain nearly identical for the BLSRP with and without the RCM. The adopted ballast location follows the optimum configuration previously established for the BLSRP (Arakkan & Chandrasekaran, 2025). The RCM connecting rod and piston are modeled as tubular elements, while the linear spring behavior is represented using a combined tether–fender formulation in ANSYS AQWA (2024 R2). The tether resists tensile forces and the fender accounts for compressive forces, together reproducing bidirectional elastic behavior. The spring force is defined as in Eq. (2)

where K_spring corresponds to the additional restoring stiffness introduced by the spring-based LS-RCM connecting the buoyant legs, L is the instantaneous separation between attachment points, andL₀ is the unstretched length. The selected spring stiffness was obtained through preliminary parametric studies to balance heave suppression and preservation of compliant behavior. The global dynamic behavior of the six-legged BLSRP system equipped with the passive LS-RCM is governed by the following equation of motion (3):

where M, C, and K represent the mass, damping, and hydrodynamic restoring stiffness matrices of the floating system, respectively; x denotes the generalized displacement vector, while ẋ and ẍ represent the generalized velocity and acceleration vectors, respectively; and F(t) represents the combined environmental excitation due to waves, current, and wind based on the sea condition adopted for each case. The passive LS-RCM enhances the restoring capability of the system by controlling the radial motion of the buoyant legs, thereby reducing excessive deck responses under environmental loading without requiring external power input.

Environmental conditions representative of offshore LNG operations are considered (Suja & Chandrasekaran, 2025). Three sea states—moderate, high, and very high—are defined using significant wave height (H_s), zero-crossing wave period (T_z), and mean wind speed at 10 m elevation, as listed in Table 3. These conditions represent operational, severe, and extreme offshore environments relevant to deepwater LNG systems. Two wave approach angles, 0° and 90°, are considered to capture critical directional effects and worst-case loading scenarios recommended by DNVGL-RP-C205 (DNV, 2019). Irregular waves are modeled using the JONSWAP spectrum to simulate realistic ocean conditions (Rasool et al., 2022). Ocean current effects are incorporated using a depth-varying current profile based on DNVGL-RP-C205 recommendations, as shown in Fig. 3. The profile considers a surface current velocity of 0.5 m/s decreasing linearly to 0.1 m/s below 90 m water depth, remaining nearly uniform at greater depths. Wave–current interaction is accounted for through Doppler-shifted encounter frequencies. Wind loading is evaluated using a power-law wind profile with gust effects. Three loading cases—C1 (wave only), C2 (wave with current), and C3 (combined wave, current, and wind)—are applied for all sea states, with and without the RCM.

The present study focuses on heave response control because heave governs the vertical stability of offshore LNG storage and regasification operations and is directly linked to allowable operational motion limits. The BLSRP exhibits high inherent stiffness in roll, pitch, and yaw due to its large metacentric height, symmetric buoyant-leg configuration, and taut-moored tether system. In addition, the hinged deck–leg connections filter bending moments, significantly reducing coupling between rotational and vertical deck motions. Although heave–pitch coupling can be significant in some compliant offshore platforms, free-decay tests and preliminary response assessments for the present BLSRP configuration show that pitch and roll responses remain negligible compared with heave across all examined sea states and wave approach angles. The hinged connections further eliminate moment transfer from the buoyant legs to the deck, significantly reducing the coupling between radial leg motion and deck rotations. Consequently, LNG operational safety is governed primarily by heave, justifying the focus of this study.

Free-decay results presented in Table 4 show that the passive LS-RCM primarily influences the heave response characteristics of the BLSRP, while the other translational and rotational modes remain only marginally affected. Slight variations in natural frequency, natural period, and damping ratio after incorporating the LS-RCM indicate that the mechanism modifies the global restoring behavior without significantly altering the inherent dynamic characteristics of the platform. This behavior is consistent with the stiffness-based operation of the LS-RCM, which redistributes dynamic response energy through controlled radial motion of the buoyant legs rather than through direct viscous damping. The LS-RCM temporarily stores and releases elastic strain energy, thereby modifying internal energy transfer paths and improving the dynamic stability of the platform under environmental excitation.

The power spectral density (PSD) results presented in Fig. 4 show that the dominant deck heave response energy is concentrated within the frequency range of approximately 0.33–0.36 rad/s, which remains well separated from the natural heave frequency of the BLSRP (approximately 0.171 rad/s). This confirms that the observed heave responses are primarily non-resonant and governed by wave-energy distribution and platform kinematic interaction effects. With the inclusion of the LS-RCM, peak PSD amplitudes are consistently reduced for all environmental loading cases, while the dominant response frequencies remain nearly unchanged. This demonstrates that heave mitigation is achieved mainly through the additional restoring stiffness introduced by radial leg control, without significant retuning of the overall system dynamics. The corresponding response amplitude operator (RAO) results in Fig. 5 further illustrate the frequency-dependent transfer characteristics of the platform under controlled and uncontrolled conditions. The RAO curves indicate that the LS-RCM reduces the overall response sensitivity near the dominant response frequencies for most loading cases. A slight increase in RAO observed in certain frequency regions after incorporating the LS-RCM is attributed to stiffness-induced redistribution of response energy and minor changes in the dynamic interaction between the buoyant legs and deck system. However, the combined PSD and RAO results confirm the effectiveness of the LS-RCM in mitigating deck heave responses under both moderate and high sea states for different wave approach angles, demonstrating stable and nearly direction-independent response control performance.

Although the dominant heave natural frequency does not coincide with the peak excitation frequency, significant heave responses may still occur under severe environmental loading due to broadband wave excitation and coupled platform kinematics. In the proposed BLSRP system, the radial deformation of the inclined compliant legs is dynamically coupled with the deck heave motion through the platform restoring mechanism. Inward motion of the buoyant legs lifts the deck upward, while outward motion causes downward deck movement, thereby contributing to coupled heave response. Excessive heave oscillations are controlled by the tether system, which provides restoring restraint and limits large displacement excursions. The LS-RCM further suppresses response variability while preserving the inherent compliant characteristics of the platform.

Recentering performance, evaluated using the heave phase plots, further confirms the improved dynamic stability achieved through the LS-RCM. Fig. 6 and Fig. 7 present the displacement–velocity trajectories of the deck under high and very high sea states for different environmental loading conditions and wave approach angles. The uncontrolled cases exhibit wider and more scattered trajectories, indicating larger oscillatory excursions, higher response energy, and reduced motion stability. This effect becomes more pronounced under very high sea states due to stronger environmental excitation. With the inclusion of the LS-RCM, the phase trajectories become more compact and concentrated around the equilibrium position, demonstrating improved recentering capability and reduced response spread. The smaller and smoother orbital patterns indicate lower displacement–velocity excursions and enhanced damping effectiveness, enabling the platform to return more efficiently to its equilibrium position after excitation. Although response amplitudes increase under severe sea states, the controlled cases remain significantly more stable than the uncontrolled configurations. Hence, the phase plot analysis confirms that the LS-RCM effectively improves platform stability, suppresses excessive heave motion, and enhances operational reliability under harsh environmental conditions.

Table 5 summarizes the normalized deck heave response statistics for moderate, high, and very high sea states at wave approach angles of 0° and 90° under different environmental loading cases, with and without the RCM. The reported heave values represent dynamic displacement relative to the calm-water equilibrium position of the deck. In general, inclusion of the RCM reduces the standard deviation (SD) of heave response, indicating improved motion stability and reduced response variability. This reduction becomes more significant under severe sea states. For example, in the very high sea state at 0° under wave-alone loading (C1), the SD decreases from 1.141 m to 0.621 m with the inclusion of the RCM.

The maximum and minimum heave amplitudes are also reduced in most loading conditions, resulting in a narrower response envelope and improved operational stability. The mean heave displacement remains close to zero for all cases, confirming that the RCM suppresses oscillatory motion without altering the static equilibrium position of the platform. The frequency corresponding to peak response shows negligible variation between controlled and uncontrolled cases, indicating stiffness-based mitigation rather than frequency retuning. Fig. 8 compares the maximum, minimum, and SD values presented in Table 5. From a design perspective, reductions in peak-to-peak heave and response variability increase the allowable operating window for LNG transfer and reduce cyclic demand on piping, loading systems, hinges, and tether components. However, the limited improvement observed in some combined-loading cases indicates that LS-RCM design should be based on the governing directional sea state rather than a single wave-only condition.

The deck–leg hinges are critical fatigue-sensitive components subjected to cyclic relative motion, bearing pressure, pin bending, local stress concentration, wear, and corrosion. Although heave–pitch coupling may increase hinge demand, the LS-RCM limits excessive radial leg motion and is therefore expected to reduce cyclic load ranges rather than rigidly restrain the joint. Life-cycle design should consider ultimate strength, fatigue damage using appropriate S–N curves, corrosion allowance, inspectability, replaceable pins or bearings, and scheduled maintenance. Detailed local hinge stress and long-term fatigue-life assessment require site-specific load histories and are beyond the scope of the present global-response study.

Because buoyant legs are the primary load-transferring members of the BLSRP, their radial responses directly influence deck motion, and overall structural performance. Therefore, their responses are examined to determine whether the LS-RCM suppresses or redistributes deformation among the legs. As shown in Table 6, for the 0° approach angle, the largest uncontrolled radial motions occur in BLS2 and BLS3, which are more directly exposed to the incoming waves, whereas BLS1 and BLS4 exhibit relatively smaller responses. The LS-RCM provides substantial peak reductions in BLS1 and BLS4, reaching approximately 73–78% across all sea states. Moderate reductions (7–12%) are observed for BLS2 and BLS3 under moderate and high sea states, while the effectiveness decreases under very high sea states. Slight increases in the peak responses of BLS5 and BLS6 suggest that the passive mechanism redistributes part of the response energy among the buoyant legs under severe environmental loading. Because tether forces are directly influenced by the radial motions of the buoyant legs, the observed reduction and redistribution of leg responses are expected to alter the distribution of tether demand. However, detailed tether load characterization under all environmental conditions is beyond the scope of the present study and warrants dedicated future investigation.

The radial responses of the buoyant legs for the 90° approach angle are summarized in Table 7. In this loading direction, the largest uncontrolled radial motions occur in BLS1 and BLS4, which are more directly aligned with the incoming waves, whereas the remaining legs exhibit comparatively lower responses. Under moderate sea states, the LS-RCM achieves noticeable peak reductions of approximately 13–24% in most buoyant legs. The effectiveness decreases under high sea states, with peak reductions generally limited to 2–12%, while a slight increase is observed in BLS4. Under very high sea states, the mechanism provides only marginal reductions in some legs (BLS1, BLS2, and BLS6) and slight increases in others (BLS3–BLS5), indicating redistribution of response energy among the buoyant legs under extreme environmental loading.

The time-history responses presented in Fig. 9 and Fig. 10 further demonstrate that the LS-RCM reduces oscillation amplitudes and produces smoother response patterns, particularly under moderate sea states. Although the reduction becomes less distinct as sea severity increases, the mechanism promotes a more balanced distribution of radial deformation and prevents excessive motion concentration in individual legs. Such redistribution is beneficial in reducing localized structural demand and enhancing the overall operational stability of the BLSRP without requiring external power input. Moreover, limiting excessive radial motion in individual buoyant legs can reduce stress concentration at the leg–deck connections and mitigate uneven load transfer to the tether system. The controlled responses also exhibit improved recentering characteristics, with oscillations remaining closer to the equilibrium position over time. These observations confirm that the LS-RCM not only suppresses peak responses but also contributes to a more uniform and predictable dynamic behavior of the floating platform under environmental loading.

This study presented a numerical investigation into the effectiveness of a passive RCM for mitigating heave motion of a BLSRP subjected to combined wave, current, and wind loading. The proposed RCM exploits the hinged leg–deck configuration by introducing additional restoring stiffness directly in the radial degree of freedom of the buoyant legs, thereby indirectly suppressing excessive vertical deck motion without altering the platform’s global hydrostatic equilibrium or inherent compliance. Free-decay analyses indicate only marginal changes in dynamic characteristics due to the elastic nature of the spring-based mechanism. Time- and frequency-domain results consistently demonstrate substantial reductions in heave response amplitudes. Power spectral density analyses across moderate, high, and very high sea states show clear peak suppression while maintaining separation between dominant response frequencies and the wave energy band, indicating reduced resonance risk. Phase-plot analyses confirm enhanced motion stability, with compact displacement–velocity trajectories observed under both operational and extreme conditions. Statistical measures further corroborate these findings, showing reduced response variability without shifting the mean heave position. The buoyant-leg response analyses further indicate that the LS-RCM not only mitigates deck heave but also promotes a more balanced distribution of radial deformation among the buoyant legs, thereby improving the overall operational robustness of the BLSRP. Overall, the results demonstrate that geometry-driven stiffness modulation at the buoyant-leg level provides an effective passive control strategy for compliant offshore LNG platforms.

The selected LS-RCM parameters were evaluated for the considered sea states and environmental conditions of the BLSRP. Although the LS-RCM effectively reduces response variability within the investigated range, its performance may vary under more extreme sea conditions or different wave characteristics, which may require further optimization of LS-RCM parameters.