Nanoelectromechanical systems (NEMS) play an important role in advancing high-precision sensing and high-speed computational applications due to their exceptional sensitivity and reduced size. This thesis explores the dynamic behaviors and vibrational properties of NEMS, focusing on coupled systems of molybdenum disulfide (MoS2) membrane and silicon nitride (SiNx) drumhead, and the effects of gas pressure on an MoS2 membrane resonator. Employing finite element simulations alongside theoretical modeling, the study thoroughly analyzes the coupling dynamics between MoS2 and SiNx resonators and investigates the vibrational responses of MoS2 membranes under pressure. Key achievements include the identification of vibrational modes, calculation of coupling constants, and comprehensive understanding of pressurized MoS2 membrane resonator behavior. These insights pave the way for enhancing NEMS applications in sensitive detection and resonant frequency modulation, significantly contributing to the field of nanotechnology and the development of advanced NEMS devices.