Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct A lightweight adaptive hybrid laminate metamaterial with higher design freedom for wave attenuation X. Xiao a , Z.C. He a,c, ⁎ , Eric Li b, ⁎ , B. Zhou a,c , X.K. Li a a State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China b School of Science, Engineering & Design, Teesside University, Middlesbrough, UK c The State Key Hunan Provincial Key Laboratory of Vehicle Power and Transmission System, Xiangtan, China ARTICLE INFO Keywords: Lightweight adaptive hybrid laminate metamaterials Local resonant bandgap Electro-mechanical coupling ABSTRACT In this paper, we design a lightweight adaptive hybrid laminate metamaterial with higher design freedom for wave attenuation. The adaptive hybrid laminate acoustic metamaterials are composed of carbon-fiber-reinforced polymer (CFRP) and a periodic array of piezoelectric shunting patches attached to the laminate. A compre- hensive analytical model is first developed to reveal the tunable wave attenuation capability in regard to the equivalent bending stiffness of lightweight adaptive hybrid laminate metamaterial. The tunable wave attenua- tion behavior has been confirmed through finite element modeling (FEM). Numerical results demonstrate that the lightweight adaptive hybrid laminate metamaterial with the shunting circuits can remarkably suppress wave propagation compared to the un-shunted case. In addition, the effects of the laminate’s parameters as well as the shunting circuits on the bandgap’s location and bandwidth are discussed. By introducing the negative capaci- tance shunting circuit into the piezoelectric patches, the bandwidth can be enlarged significantly. 1. Introduction Acoustic metamaterials are artificially periodic composites that can exhibit some unique properties not available in nature, such as negative mass density and negative bulk modulus. Over the past decade, the attention and efforts made to investigate the theory and application of acoustic metamaterial have increased dramatically. However, the paper published in 2000 firstly laid the foundation for the theory of acoustic metamaterials, in which Liu [1] proposed local resonance acoustic metamaterials (LRAMs). The concept of LRAMs breaks the limitation of Brag-scattering metamaterials and provides a new approach for the manipulation of acoustic/elastic waves propagation in low frequency regions. Due to its unique ability, the acoustic metamaterials are only transparent to acoustic/elastic waves in a certain frequency range and become opaque in the band gap where wave propagation is prohibited, which has great potential for application in structural design of low- frequency vibration attenuation. For example, Liu et al. [1] took the lead to prove that the LRAMs can generate a bandgap between 400 Hz and 600 Hz by embedding rubber-coated lead spheres in an epoxy matrix. The in-depth research [2] found that a negative equivalent mass density that do not exist in nature can be achieved through dipolar resonance. Furthermore, Lee et al. [3] proposed an acoustic metamaterial that exhibits a negative equivalent modulus over a fre- quency range of 0 to 450 Hz, in which the acoustic wave propagation is forbidden. Similar works by Ding [4] show that multi-frequency band of negative equivalent modulus can be realized by embedding different sized split hollow spheres (SHSs) inside a sponge matrix. Based on these concepts, many acoustic/elastic metamaterials with resonant units are designed to achieve a wider bandgap at subwavelength scale, for emerging application such as acoustic cloaking [5–9], low frequency vibration suppression [10–13] and low frequency sound wave isolation [14–17]. Owing to the combination of the mass-spring system and the en- gineering structures to represent the LRAMs, the band gap as well as the negative mass density can also be realized numerically and experi- mentally [18–21]. However, the relatively narrow bandgaps near the local resonant frequency remain a significant challenge for the further development of LRAMs and engineering applications. It is well known that multiple resonant units can achieve local resonance at multiple frequencies. Hence, in order to improve the ability of LRAMs to obtain wider bandwidth, a metamaterial composed of multiple spring-mass system may be a better solution [22]. Unfortunately, the problem that arises is that low frequency bandgap may be accompanied with ex- cessive size and weight of attaching mass-spring system. The first effort https://doi.org/10.1016/j.compstruct.2020.112230 Received 21 October 2019; Received in revised form 7 February 2020; Accepted 16 March 2020 ⁎ Corresponding authors at: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China (Z.C. He). E-mail addresses: hezhicheng815@hnu.edu.cn (Z.C. He), q.li@tees.ac.uk (E. Li). Composite Structures 243 (2020) 112230 Available online 19 March 2020 0263-8223/ © 2020 Published by Elsevier Ltd. T