Locally resonant bandgap and dynamic responses of meta-sandwich-like plate with L-shaped beam–mass resonators

Low-frequency vibration is quite harmful for our human being as it may influence machining accuracy and destroy our health. To solve the problems above in engineering, a novel physical model of locally resonant meta-sandwich-like plate is proposed, in which a L-shaped cantilever beam–mass system is used as resonator. In the resonator, one end of L-shaped beam is fixed at the center of the supporting rod, and a mass is attached at the free end of it. Furthermore, the supporting rods are bolted to the upper and lower faceplates. The resonator is equivalent to a spring–mass system by solving the equivalent spring stiffness and mass. Based on Hamilton's principle and the theory of thin plate, the dispersion equation of the novel metamaterial plate could be derived and a bandgap in a relatively low-frequency range which can realize low-frequency vibration isolation could be worked out. The validation of the present method and the theoretical result of bandgap range is conducted by the comparison studies. Then, the bandgap and dynamic response of locally resonant acoustic metamaterial plate are analyzed at length, and the influences of several geometric parameters of the resonator and faceplates, damping and boundary condition on the bandgap characteristics are presented.