The vibration excitation transmission of the platform should be suppressed while ensuring the safe and reliable operation of equipment. Currently, most research on vibration reduction focuses on individual pedestals or pedestal-platform plate structures, with few studies comprehensively considering the relationship between equipment, pedestal, and platform bottom plate vibrations. The study taken a typical offshore platform equipment's long base as the research object and utilized impedance analysis and optimization design technology to control input power flow of the platform bottom plate in key frequency bands. Design variables such as mass and stiffness were optimized to improve base plate thickness while maintaining support strength and stiffness. A coupling vibration control model for "equipment-pedestal-platform" was established, using a particle swarm optimization algorithm with linear weight decline for optimization. Finite element method verification results show that this technical process is feasible, reducing optimized input power flow by 95.43% in low frequencies below 300 Hz and decreasing total response level of vibration acceleration by 18.1 dB.