Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear author, these are my comments abour this work:

Given the extensive structure of the ROV LARS 3D geometric model, the approach to addressing stability issues regarding horizontal impacts is not described.
The literature review of related works needs to be enriched with up-to-date references; it is suggested that a table be added to outline the contributions of existing studies and compare them with the metrics of the current work.
It is necessary to describe how structural integrity is ensured given that, under a longitudinal acceleration of 1g, the von Mises stress reaches a peak of 195.38 MPa.
The authors conduct a structural dynamics analysis for complex marine environments, but the specific level of environmental complexity applicable to real-world scenarios needs to be defined.
Point (2) of the conclusions states that under lateral and longitudinal accelerations of 1g, equivalent stresses reach 185.12 MPa and 195.38 MPa, yet the yield strength limit is not specified.
It is suggested that the references be arranged in order of appearance.

Best Regards

Author Response

Dear Reviewer 1,

We would like to express our sincere gratitude for your detailed review and constructive comments. Your insightful feedback has been invaluable in helping us improve the quality and clarity of our manuscript. Below, please find our point-by-point responses to your comments. For your convenience, all corresponding revisions made in the manuscript based on your suggestions have been explicitly highlighted in red.

Comments 1: Given the extensive structure of the ROV LARS 3D geometric model, the approach to addressing stability issues regarding horizontal impacts is not described.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have explicitly detailed this approach in Section 4 of the manuscript to ensure the methodology for horizontal stability is clear. [Page 18, Paragraph 4, Lines 620-628].

"By fundamentally altering the momentum transfer path, this approach directly addresses the dynamic instability issues observed in the original rigid frame under horizontal impacts. The viscoelastic elements provide necessary dynamic anti-sway stiffness to effectively curb destructive transient lateral and longitudinal displacements, thereby preventing global dynamic instability. Simultaneously, the viscous damping component acts as an efficient energy dissipator, converting high-frequency concentrated inertial impact kinetic energy into heat, which ensures the structural stability of the extensive LARS model under unpredictable extreme horizontal loads."

Comments 2: The literature review of related works needs to be enriched with up-to-date references; it is suggested that a table be added to outline the contributions of existing studies and compare them with the metrics of the current work.

Response 2: Thank you for this valuable suggestion. We strongly agree that enriching the literature review with up-to-date references strengthens the manuscript. We have carefully updated the reference list with recent studies regarding ROV transient dynamics and rigid frame dynamic modeling (e.g., Deng et al., 2024; Zhang et al., 2025). Regarding the suggestion to add a table, we carefully considered this approach. However, to maintain the narrative flow, we opted to integrate the comparative metrics directly into the textual analysis rather than using a rigid table. We have revised the Introduction section to better highlight our contributions compared to these recent works.[Page 3, Paragraph 2, Lines 125-135].

"Further expanding on the transient dynamic behavior of marine equipment, Deng et al. [34] developed a numerical model to predict wire tension spikes, known as snap loads, during the launch and recovery of a work-class ROV passing through the wave zone. In the context of large spatial rigid frame analysis, Zhang et al. [35] utilized the lumped mass method to systematically investigate the dynamic responses and line tension characteristics of a rigid truss structure under various operational conditions. Through a comprehensive review of the aforementioned research, a distinct viewpoint for this study is formed: relying solely on traditional structural hardening strategies to resist high-frequency transient impacts inevitably exposes obvious weight penalty limitations. Existing works predominantly focus on structural response analysis under quasi-static gravity loads or low-frequency wave excitations."

Comments 3: It is necessary to describe how structural integrity is ensured given that, under a longitudinal acceleration of 1g, the von Mises stress reaches a peak of 195.38 MPa.

Response 3: Thank you for pointing this out. We agree with this comment. Therefore, we have explicitly clarified in the manuscript that 195.38 MPa is the baseline stress of the original, unoptimized structure. Structural integrity is ensured by the implementation of our proposed viscoelastic damping strategy. After optimization, the peak stress under the exact same 1g longitudinal acceleration drops significantly to 119.25 MPa, which falls safely within the allowable yield strength limits of the material (275 MPa).

Comments 4: The authors conduct a structural dynamics analysis for complex marine environments, but the specific level of environmental complexity applicable to real-world scenarios needs to be defined.

Response 4: Agree. We have added a clearer definition mapping our simulated boundary conditions to real-world environmental complexities to contextualize the "extreme sea conditions" mentioned in the manuscript. We have revised Section 2.4 to provide this clarification [Page 11, Paragraph 1, Line 395-404].

"The structural dynamics analysis conducted in this study targets severe operational scenarios typically encountered in Sea State 5 to 6. Specifically, the low-frequency ±15° pitch and ±45° roll conditions represent the severe low-frequency motions of the mother ship induced by large-amplitude ocean waves. The 1g transient step acceleration conditions are designed to mathematically define the extreme, high-frequency impact loads caused by unpredictable wave slamming events, vessel transient heave, or the abrupt slack-to-tension snapping of the lifting cables during air-water interface crossing. To simulate these influences on the structure, swaying conditions and transient acceleration conditions are further defined in the model."

Comments 5: Point (2) of the conclusions states that under lateral and longitudinal accelerations of 1g, equivalent stresses reach 185.12 MPa and 195.38 MPa, yet the yield strength limit is not specified.

Response 5: Thank you for pointing this out. We agree with this comment. Similar to our clarification in Response 3, it is important to emphasize that the stresses of 185.12 MPa and 195.38 MPa represent the baseline results of the original structure before optimization. Therefore, we have modified the text in the conclusions to specify the yield strength limit of the material (275 MPa for TA2 titanium alloy) and explicitly added a reminder that these peak values belong to the unoptimized state. This provides a clear reference baseline for the readers to understand the severity of the initial frame.[Page 22, Paragraph 3, Line 760-766].

"Before optimization, the structure generates large transient deformations of 20.09 mm and 19.73 mm, respectively, while maximum equivalent stresses at critical nodes reach 185.12 MPa and 195.38 MPa. When compared to the 275 MPa nominal yield strength limit of the TA2 titanium alloy, this baseline result suggests that traditional rigid frames face obvious safety margin deficiencies and structural failure risks under high-frequency impact conditions."

Comments 6: It is suggested that the references be arranged in order of appearance.

Response 6: We have carefully checked the entire manuscript and rearranged all references to strictly follow the order of their appearance in the text.

Sincerely,

Leijie Hu 

Corresponding Author

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The proposed work lacks experimental validation and does not include a mesh convergence study.
The authors are requested to present the studies and results regarding sensitivity and uncertainty analysis.
Why are the models presented by the authors simplified?
The authors are requested to explain why the proposed approach does not consider plasticity, fatigue, and creep.
The authors are requested to provide further justification and a more detailed development of elements such as the gravity reduction coefficient and damping.
Why are wave action, high tide, and high-speed winds considered as dynamic loads in the proposed approach? The authors are requested to analyze and develop simulations of different scenarios to validate the proposed methodology.
Why does the proposed approach not consider simulating and modeling the joints, nor the possible alterations that may occur?

Author Response

Dear Reviewer 2,

We would like to express our sincere gratitude for your rigorous review and constructive comments. Your valuable feedback has significantly enhanced the theoretical depth and physical rigor of our manuscript. Below, please find our point-by-point responses to your comments. For your convenience, all corresponding revisions made in the manuscript based on your suggestions have been explicitly highlighted in blue.

Comments 1: The proposed work lacks experimental validation and does not include a mesh convergence study.

Response 1: We highly appreciate the reviewer's rigorous comment.

Regarding the experimental validation, due to the massive scale of the heavy-duty LARS and the extreme nature of the transient impacts being simulated, full-scale physical prototype testing is currently prohibitive. However, we have explicitly noted this limitation in the Conclusion section and plan to conduct scaled model testing in our future research.

Regarding the mesh convergence study, we have now explicitly added a discussion and a new comparative figure in Section 2.2 to visually and quantitatively verify the spatial discretization accuracy. Since the dynamic simulation relies on exporting Modal Neutral Files (.mnf) from the finite element solver to the multibody dynamics environment, the mesh independence verification was rigorously conducted in the static finite element domain prior to modal extraction. Specifically, the static storage condition was utilized to evaluate the high-stress gradient region at the middle bearing beam of the upper frame. By progressively scaling the local mesh size to 15 mm, 10 mm, and 8 mm, the corresponding peak von Mises stresses were recorded as 123.5 MPa, 116.0 MPa, and 116.5 MPa, respectively. It was observed that the stress variation stabilized at less than 0.5% (from 116.0 MPa to 116.5 MPa) once the local refinement reached our selected 10 mm, and the stress distribution profiles remained highly consistent. Consequently, this hierarchical discretization strategy reliably guarantees the mathematical accuracy of the exported matrices for subsequent dynamic analyses while maintaining optimal computational efficiency. Mention exactly where in the revised manuscript this change can be found – [Page 7, Paragraph 1, Lines 271-284].

"To ensure the numerical reliability of the subsequent dynamic analyses and eliminate the influence of grid size on the structural stiffness matrix, a mesh convergence study was conducted prior to modal extraction. The verification targeted the high-stress concentration area at the middle bearing beam of the upper frame under the static storage condition. As shown in Figure 2, when the local mesh size was progressively refined to 15 mm, 10 mm, and 8 mm, the resulting peak von Mises stresses were 111.8 MPa, 116.0 MPa, and 116.5 MPa, respectively. Because the relative variation in peak stress dropped to less than 0.5% when the mesh was refined from 10 mm to 8 mm, and the stress concentration profiles remained consistently stable, the 10 mm local refinement dimension was determined to be completely converged. This hierarchical discretization strategy was thus verified and adopted to maintain optimal computational efficiency while guaranteeing the solving accuracy of the spatial model.

Figure 2. Mesh convergence study under the static storage condition: equivalent stress distributions for local mesh sizes of (a) 15 mm; (b) 10 mm; (c) 8 mm."

Comments 2: The authors are requested to present the studies and results regarding sensitivity and uncertainty analysis.

Response 2: Thank you for pointing this out. We agree that sensitivity and uncertainty analyses are valuable for evaluating the robustness of the system against manufacturing tolerances and random environmental variations. However, the primary focus of this current study is to establish the ultimate physical safety boundaries of the LARS under deterministic, worst-case extreme loads (e.g., 1g transient step impacts). Therefore, a deterministic envelope approach was adopted to rigorously assess the maximum transient dynamic responses. We highly appreciate this insightful suggestion and have documented it as a crucial direction for our future probabilistic research framework.

Comments 3: Why are the models presented by the authors simplified?

Response 3: Thank you for pointing this out. The geometric simplifications (such as systematically eliminating non-load-bearing process chamfers, tiny sub-5mm assembly holes, and non-structural fasteners) were implemented strictly as a practical engineering treatment. In complex transient dynamic implicit integration, retaining these redundant microscopic features easily triggers severe mesh distortion, leading to stiffness matrix singularities and non-convergence. This geometric simplification strategy significantly optimizes computational efficiency and numerical stability, entirely without sacrificing the macroscopic mechanical equivalence and dynamic response accuracy of the main load-bearing framework.

Comments 4: The authors are requested to explain why the proposed approach does not consider plasticity, fatigue, and creep.

Response 4: Thank you for pointing this out. The proposed dynamic decoupled modeling approach specifically targets the structural responses under brief, high-frequency transient impacts (such as sudden snap loads during air-water interface crossing) rather than long-term cyclic accumulation or high-temperature operational environments. More importantly, as consistently demonstrated by our finite element results, the maximum peak von Mises stress of the optimized system is strictly suppressed at 119.25 MPa, which remains well below the 275 MPa yield strength limit of the TA2 titanium alloy material. Because the entire frame operates safely within the linear elastic domain during these transient events, material nonlinearities such as plastic deformation, high-cycle fatigue, and creep are fundamentally not triggered, making it physically reasonable to exclude them from the current modeling scope.

Comments 5: The authors are requested to provide further justification and a more detailed development of elements such as the gravity reduction coefficient and damping.

Response 5: We highly appreciate the reviewer’s rigorous suggestion. We agree that the quantitative rationale for configuring these specific parameters must be explicitly stated to ensure the physical fidelity of the model. Therefore, we have expanded the theoretical and empirical justifications in the manuscript. Specifically, we elucidated that the gravity reduction coefficient ( = 0.1) is determined based on the actual load-sharing distribution of the auxiliary deck mechanisms, retaining a 10% residual load to ensure a stable numerical pre-stress state. Furthermore, we detailed the parameterization criteria for the viscoelastic damping elements, which are calibrated to achieve an optimal critical damping ratio tailored to the structural clearance and impact kinetic energy. Mention exactly where in the revised manuscript this change can be found – [Section 2.3, Page 10, Paragraph 3, Lines 364-372; Section 4.1, Page 18, Paragraph 5, Lines 629-638].

"The specific value of the gravity reduction coefficient ( = 0.1) is determined based on the empirical load-sharing characteristics of the LARS under deck-secured conditions, where approximately 90% of the static vertical load is directly transferred to the hull base via auxiliary locking and supporting mechanisms. Retaining this 10% residual gravity is not arbitrary; mathematically, it introduces a continuous baseline pre-stress that characterizes the residual contact pressure on the guide rails. This effectively eliminates rigid-body singularities and guarantees the convergence of the nonlinear implicit integration during the initial impact phase."

"Regarding the specific numerical development of the viscoelastic elements, the parameters are calibrated based on the peak structural kinetic energy and permissible deformation limits. The equivalent stiffness coefficient k is quantified to strictly bound the maximum transient deformation within the geometric clearance of the anti-collision structures. Concurrently, the viscous damping coefficient C_d is parameterized to approach the critical damping ratio of the local collision mode. This specific quantitative matching inherently avoids secondary structural rebounds caused by under-damping and the excessive localized reaction forces induced by over-damping, thereby optimizing the energy dissipation efficiency during the millisecond-level impact window."

Comments 6: Why are wave action, high tide, and high-speed winds considered as dynamic loads in the proposed approach? The authors are requested to analyze and develop simulations of different scenarios to validate the proposed methodology.

Response 6: Thank you for pointing this out. We would like to clarify that wave action, high tide, and high-speed winds are not directly applied as fluid-dynamic or aerodynamic surface loads on the proposed model. Since the launch and recovery system is installed on the inner deck of the mother ship, it is inherently shielded from the direct impacts of these environmental factors. Instead, these extreme environmental conditions act indirectly upon the LARS by inducing severe multi-degree-of-freedom kinematic motions on the vessel deck. Therefore, in our practical modeling approach, the complex environmental effects of winds and waves are decoupled and accurately converted into the ultimate kinematic boundary excitations—specifically the ±15° pitch, ±45° roll, and the extreme 1g transient step accelerations transmitted through the deck base. The multiple scenarios simulated in our study effectively serve as the validation for these indirect, real-world dynamic loads.

Comments 7: Why does the proposed approach not consider simulating and modeling the joints, nor the possible alterations that may occur?

Response 7: Thank you for pointing this out. In our global system-level transient dynamics analysis, the connection areas between major sub-assemblies are modeled using ideal rigid constraints. This macroscopic approach successfully accounts for the load transmission and mass coupling of all structural components, which is highly effective and sufficient for evaluating the overall dynamic stability and global stress distribution of the extensive LARS frame. Modeling microscopic non-linear behaviors at the joints—such as micro-slip, thread yielding, or potential local alterations at the weld seams—requires highly refined sub-modeling techniques that fall outside the current scope of assessing macroscopic horizontal dynamic instability, but will undoubtedly be considered in our future localized component analyses.

Sincerely,

Leijie Hu 

Corresponding Author

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors explain and elaborate on each of the observations