## 1 Introduction
Other researchers such as [PERSON] et al. [16] designed a control system to mitigate the onset of parametric rolling in a real-time detection system. Using this tool and on-board measurements of the angular displacement and the velocity of the ship's roll, the system provides an early warning with sufficient time for the control system to respond and take the best action, avoiding an increase in the rolling amplitude. Previously, [PERSON] et al. [17] proposed signal-based methods to detect the onset of parametric roll in the time domain. [PERSON] et al. [18] also presented an innovative real-time detection method to predict the parametric roll in regular longitudinal waves. Other authors [10] proposed a decision support system to be used during the operation of fishing vessels in waves to improve vessel safety. After processing several parameters and measurements, this tool provides the ship master with the consequences of various ship-handling decisions. However, all these very interesting proposals, and other similar ones, have not been widely implemented in the world fleet, due to the difficulties associated with control system design as a consequence of the characteristics of wave-induced roll motion [9]. As some relevant research indicates [19], the safety of ship stability cannot only be ensured by measures taken during the design process of naval architects. What is more, it is essential that ship operators (ship master and officers on watch) assume a certain level of knowledge, skills, experience and prudence during ship operation to avoid dangerous situations for the ship's safety. Then, in some potentially dangerous operational situations, the officer on watch must have the knowledge to predict and make the most appropriate decision to reduce the risk level. This philosophy is included in the so-called operational measures of the SGISC framework, where operational limitations and operational guidance are provided to ship masters to support decision making on board and ensure the safety of navigation [20]. As a consequence of this IMO resolution, important works about operational guidance were published. Researchers such as [PERSON] et al. [21] were focused on rolling motion and proposed a new procedure to be easily implemented in a user's code to assess simplified operational guidance without the use of commercial software at any ship speed and heading. [PERSON] [22] proposed a new guideline which relies on a simplified numerical tool capable of assessing the rolling motion due to non-linear irregular wave effects in the time domain, keeping computational effort as low as possible. Regarding the operational limitation, according to MSC.1/Circ.1627 [20], it is possible to design a ship to be operated in a specific operational area. For example, [PERSON] et al. [23] carried out an interesting study on the design of a vessel taking into account the specific conditions that the ship will operate in, particularly with regards to parametric roll. Therefore, the importance of predicting excessive rolling motion is shown in other works such as [6], where excessive lateral acceleration was investigated in naval vessels in order to determine the agreement of their stability criteria with the new SGISC, although the SGISC do not refer to naval vessels. Although the synchronism phenomenon can be experienced with any wave influence direction with respect to the ship's heading, it is most likely to happen when the ship is sailing in pure beam seas. Moreover, a ship is most vulnerable to this undesirable phenomenon when it is in static condition, such as when a fishing vessel is engaged in fishing tasks, or when it has suffered engine failure. For this reason, the Level 2 criterion of SGISC considers a ship at zero speed in beam waves [21]. Therefore, in the present paper, as in other relevant research on parametric resonance [24], the influence of the most unfavourable condition for synchronous rolling was studied, i.e., receiving purely regular beam waves.