Abstract: The vibration attenuation system includes a load bearing layer, a non-load bearing layer, and a rigid beam connector. The load bearing layer has a first density and a first stiffness. The non-load bearing layer has a second density and a second stiffness. The second density is lower than the first density. The rigid beam connector has a third density and a third stiffness. The rigid beam connector couples the load bearing layer to the non-load bearing layer. The coupling of the non-load bearing layer to the load bearing layer is enabled through the use of the rigid beam connector which provides a nonlocal connection to transfer energy from the load bearing layer to the non-load bearing layer.

Abstract: A method of using an acoustic resonator including receiving at a first stage of a resonator an incoming acoustic wave. The method further includes resonating the incoming wave with a flexible membrane, a taper of the flexible membrane, and a cavity of a first stage, thereby producing synergistic effect on a resulting acoustic resonance. Additionally, the method includes transforming an acoustic energy associated with the incoming acoustic wave into an elastic energy, wherein the elastic energy is channeled through the flexible membrane, thereby reducing an intensity of the incoming acoustic wave and resulting in a first reduced incoming acoustic wave. Further the method includes transferring the first reduced incoming acoustic wave through a hole of a neck of the flexible membrane. The method also includes transferring a first pressure wave caused by a perturbation in the flexible membrane into a second stage, thereby producing a second acoustic wave.

Abstract: A method of using an acoustic resonator including receiving at a first stage of a resonator an incoming acoustic wave. The method further includes resonating the incoming wave with a flexible membrane, a taper of the flexible membrane, and a cavity of a first stage, thereby producing synergistic effect on a resulting acoustic resonance. Additionally, the method includes transforming an acoustic energy associated with the incoming acoustic wave into an elastic energy, wherein the elastic energy is channeled through the flexible membrane, thereby reducing an intensity of the incoming acoustic wave and resulting in a first reduced incoming acoustic wave. Further the method includes transferring the first reduced incoming acoustic wave through a hole of a neck of the flexible membrane. The method also includes transferring a first pressure wave caused by a perturbation in the flexible membrane into a second stage, thereby producing a second acoustic wave.