The increase of demand for offshore wind energy resulted in an increase of larger wind turbines. These turbines are often placed on top of a monopile (MP) substructure. The conventional method for installing these MPs uses a jack-up vessel. However, due to the local bathymetry and soil conditions. This method has its drawbacks, such as unavailability due to soil conditions, impracticality in excessively deep waters, or high costs. Heerema Marine Contractors (HMC) aims for the novelty of installing these MPs by using semi-submersible crane vessels (SSCV). Installing the MPs with a floating vessel is an attractive alternative due to its accessibility and speed. To counteract the extra motions of the floating vessel a Motion Compensated Gripper Frame (MCGF) is utilized. This gripper frame uses eight rollerboxes (RBs) equipped with polyurethane (PU) rollers to keep the MP in position, being able to install MPs from 7 up to 12.5 meters in diameter. During pile driving, vibrations will propagate through the MP, inducing vibrations within the RB. Existing pile driving models fall short in accurately describing the behavior of large diameter MPs. In large diameter MPs the effect of the so called ‘breathing’ of the MP is discarded as the radial coupling is neglected. In addition, the material properties of the PU rollers are undefined or uncertain. This thesis investigates the coupling between the MP and RB vibrations by using a numerical model derived with the Finite Difference Method (FDM). Three models were proposed: (1) the MP model, (2) the RB model and (3) the coupled model. Where the latter is coupled by incorporating a spring-dashpot system to simulate the behavior of the linearized PU rollers. The MP is considered behave axisymmetrically, simplifying the 3D wave equations to a 2D system of equations. The resulting motions from these models are directly compared to the motions obtained from a Finite Element Method (FEM) simulation in Abaqus. The MP model, in particular, exhibits good agreement with the Abaqus model. The RB model and coupled model predict higher accelerations than their FEM counterparts, aligning with expectations as the FDM model is computed by the 1D Euler-Lagrange beam equation, directing all stresses and forces directly into bending of the beam. Analysis of the dynamic stiffness in both the MP and RB reveals that the RB is vulnerable to excessive vibration when the roller stiffness aligns in such a way that the eigenfrequency of the RB intersects with the ring frequency of the MP. This susceptibility is particularly notable in the case of small-diameter MPs (7-7.7m), where the roller stiffness that causes excessive vibrations, is close to the assumed base value of 200 kN/mm. In the category of large diameter MPs, a roller stiffness exceeding 1650 kN/mm could produce a similar effect. As the roller stiffness is a critical parameter for the response of the RB, it is important to know its value during the design phase. To prevent or mitigate excessive vibrations, it is essential to choose a roller stiffness that avoids eigenfrequency intersections between the RB and the MP. This proactive step is vital for optimizing the performance and stability of the MCGF during pile driving operations. It is crucial to acknowledge that this thesis employs a simplified hammer input force for a 12.5m diameter MP, showcasing predominantly low frequencies. In reality, higher frequencies occur, which could result in more energy density, a significant consideration given that smaller diameter MPs result in higher ring frequencies. For future analyses, determining specific hammer forces corresponding to different diameters is therefore recommended. Furthermore, the comparison between the industry practice for calculating resulting stresses in the RB and those derived from the numerical model indicates higher stresses in the industry approach. However, it is noteworthy that the predominant contribution to maximum stresses originates from the prestress on the MP, constituting 93% of the total stress. As a consequence, the additional stresses attributed to accelerations are relatively negligible in comparison.