## 1 Introduction  
The growing concern over environmental pollution and the depletion of fossil fuels has driven extensive research and development in the automotive industry, leading to a surge in electric vehicles. While EVs offer a promising solution for reducing emissions, their widespread adoption faces challenges such as range anxiety, long charging times, and limited charging infrastructure. To address these limitations, hybrid electric vehicles have emerged as a practical alternative, bridging the gap between conventional gasoline-powered vehicles and fully electric vehicles [1, 2]. HEVs, combining an internal combustion engine with an electric motor and battery system, offer improved fuel efficiency and reduced emissions compared to traditional vehicles. Among the various HEV configurations, the series hybrid electric vehicle stands out due to its unique powertrain architecture, where the ICE primarily charges the battery or ultra-capacitors, while the electric motor solely drives the wheels. This configuration allows for optimal operation of both the ICE and electric motor, maximizing efficiency and minimizing emissions [3]. This research delves into the intricacies of SHEVs, focusing on their operational principles, advantages, and the impact of load variations and road conditions on their performance. This study investigates the torsional vibration characteristics of the SHEV's electromechanical connection, a critical aspect influencing the vehicle's overall efficiency,reliability, and noise, vibration, and harshness behavior. This research aims to provide a comprehensive understanding of SHEV technology and its benefits; analyze the influence of load variations and road induced vibrations on the torsional vibration of the SHEV's powertrain [4,5]; and evaluate the amplitude-frequency response of the SHEV system under various operating conditions. The main findings of this research are as follows: The study reveals a significant correlation between load variations, road vibrations, rotational speed, and the torsional vibration experienced by the SHEV's electromechanical connection. The amplitude-frequency response curves provide valuable insights into the vibrational behavior of the SHEV system, paving the way for optimizing its design and performance. This research contributes to the growing body of knowledge on SHEVs, providing valuable insights for engineers and researchers to further enhance their efficiency, reliability, and overall performance [6]. However, the development of SHEVs also presents challenges that extend beyond the vehicle itself. One significant challenge lies in the design and implementation of intelligent controllers for HEVs, particularly for hardware-in-the-loop applications. Effective control strategies are crucial for optimizing the interaction between the ICE, electric motor, and battery system, ensuring seamless power delivery and maximizing energy efficiency [7]. Furthermore, the adoption of SHEVs necessitates a comprehensive understanding of their impact on travel behavior and urban planning. While electrification promises environmental benefits, it can also lead to unintended consequences such as increased travel demand and urban sprawl, known as the negative rebound effect. Therefore, it is essential to consider factors like technology adoption rates, trip generation, travel time, distance, mode shift, and urban development patterns when evaluating the overall impact of SHEV implementation [8]. The electrification of heavy goods vehicles introduces additional complexities due to their power demands and operational requirements. Various technologies are being explored for HGV electrification, including electric series with ultra-rapid DC charging, highway electrification with catenaries, and fuel cell systems. Each technology presents unique challenges in terms of power electronics, infrastructure requirements, and cost [9].