Synergistic acoustic metamaterial for soundproofing: Combining membrane and locally resonant structure

•The study proposes a new design for low-frequency and broadband sound insulation.•Locally resonant structure (LRS) and membrane enhance the sound transmission loss.•LRS- and membrane-induced anti-resonance realizes high dynamic effective density.•Effective impedance models are presented to estimate the dynamic effective density.•Soundproofing performance is experimentally verified using SSAM enclosure and plate.