In this paper, firstly, the effective medium theory for the complex acoustic metamaterial structure is systematically developed, and the solution methods of the main effective parameters are deduced. Then, a universal applicable synergetic coupling metamaterial design method is proposed and a variety of lightweight thin-walled acoustic metamaterial structures are designed using this method to achieve low-frequency broadband strong isolation, low-frequency broadband strong sound absorption, broadband acoustic stealth, low-frequency broadband sub-diffraction and sub-wavelength acoustic focusing, low-frequency broadband multi-polarized elastic wave manipulation and ultra-light low-frequency vibration absorption. In addition to expanding the acoustic metamaterial structure system from a macro system to a macro-micro multi-scale system, it also systematically expanded the membrane-type acoustic metamaterial structure system to a plate-type and shell-type metamaterial system. Moreover, the low-frequency broadband strong sound insulation technology is realized by lightweight thin-wall acoustic metamaterial structures, and extended to large-scale applications. Finally, the low-frequency vibration absorption technology with the lightest additional weight is invented, and it is extended to the low-frequency vibration reduction application of airplanes.

Effective medium theory,Acoustic metamaterial,Synergetic coupling,Low-frequency noise and vibration attenuation,Sound focusing