To meet the low-frequency sound insulation requirements of electro-hydrostatic actuator systems, two types of petal-shaped membrane acoustic metamaterials (Membrane-type Acoustic Metamaterial, MAM) were designed. The finite element analysis of the sound pressure level, sound transmission loss, normal vibration displacement of the membrane, and structural modes of the designed membrane-type acoustic metamaterials was conducted using the acoustic-structure coupling module in COMSOL Multiphysics. The influence laws of the membrane thickness, membrane preload, and membrane elastic modulus on the sound transmission loss were also studied. The results show that the two designed MAMs have good sound insulation effects in the frequency range of 1541Hz. MAM1 can achieve a sound insulation bandwidth of 1620Hz, while MAM2 has a sound insulation bandwidth of 1620Hz and can achieve noise control in multiple characteristic frequency domains. For MAM1, increasing the membrane thickness and preload will increase the lower limit of the sound insulation bandwidth, the peak frequency of sound insulation, and the sound transmission loss, causing the sound transmission loss curve to shift towards the high-frequency band. For MAM2, increasing the membrane preload will initially increase and then decrease the sound transmission loss, while increasing the membrane thickness will increase both the frequency at which the sound insulation peak occurs and the sound transmission loss. The membrane elastic modulus will also broaden the sound insulation bandwidth of the MAM and increase the frequency at which the sound insulation peak occurs, but its influence on the lower limit of the sound insulation bandwidth and the maximum value of the sound insulation quantity is relatively small. The proposed two types of MAMs have good isolation effects on low-frequency noise and have reference significance for the control of low-frequency radiated noise.