A method and apparatus for attenuating acoustic waves is provided. A lattice is formed with a plurality of support struts. A plurality of resonating struts are formed extending between the support struts, wherein the resonating struts are configured to attenuate acoustic waves within a predetermined range of frequencies while allowing acoustic waves outside the predetermined range of frequencies to pass through the resonant structure unattenuated. The resonant structure is interposed between two bodies to isolate one body from acoustic waves from the other body over the predetermined range of frequencies.