References
- Kutsenko AA, Shuvalov AL, Norris AN. Evaluation of the effective speed of sound in phononic crystals by the monodromy matrix method (L). J Acoust Soc Am. 2011;130:3553–3557.
- Zhao J, Pan Y, Zhong Z. Theoretical study of shear horizontal wave propagation in periodically layered piezoelectric structure. J Appl Phys. 2012;111:064906.
- Gao F, Wu Z, Li F, et al. Numerical and experimental analysis of the vibration and band-gap properties of elastic beams with periodically variable cross sections. Waves Random Complex Media. 2019;29:299–316.
- Kushwaha MS, Halevi P, Martínez G, et al. Theory of acoustic band-structure of periodic elastic composites. Phys Rev B Condens Matter. 1994;49:2313–2322.
- Del Vescovo D, Giorgio I. Dynamic problems for metamaterials: review of existing models and ideas for further research. Int J Eng Sci. 2014;80:153–172.
- Zhu R, Huang GL, Hu GK. Effective dynamic properties and multi-resonant design of acoustic metamaterials. J Vib Acoust. 2012;134:031006.
- Huang HH, Sun CT, Huang GL. On the negative effective mass density in acoustic metamaterials. Int J Eng Sci. 2009;47:610–617.
- Bergamini A, Delpero T, De Simoni L, et al. Phononic crystal with adaptive connectivity. Adv Mater. 2014;26:1343–1347.
- Zhang P, Parnell WJ. Band gap formation and tunability in stretchable serpentine interconnects. J Appl Mech. 2017;84:091007.
- Liu M, Zhu WD. Modeling and analysis of nonlinear wave propagation in one-dimensional phononic structures. J Vib Acoust. 2018;140:061010.
- Li FL, Wang YS, Zhang CZ. A BEM for band structure and elastic wave transmission analysis of 2D phononic crystals with different interface conditions. Int J Mech Sci. 2018;144:110–117.
- Ma Y, Zhang K, Deng Z. Wave component solutions of free vibration and mode damping loss factor of finite length periodic beam structure with damping material. Compos Struct. 2018;201:740–746.
- Zhou XQ, Yu DY, Shao X, et al. Band gap characteristics of periodically stiffened-thin-plate based on center-finite-difference-method. Thin-Walled Struct. 2014;82:115–123.
- Liu ZY, Zhang X, Mao Y, et al. Locally resonant sonic materials. Science. 2000;289:1734–1736.
- Tsu R, Fiddy MA. Waves in man-made materials: superlattice to metamaterials. Waves Random Complex Media. 2014;24:250–263.
- Wen J, Wang G, Yu D, et al. Theoretical and experimental investigation of flexural wave propagation in straight beams with periodic structures: application to a vibration isolation structure. J Appl Phys. 2005;97:114907.
- Liu L, Hussein MI. Wave motion in periodic flexural beams and characterization of the transition between Bragg scattering and local resonance. J Appl Mech. 2012;79:011003.
- Chang IL, Liang ZX, Kao HW, et al. The wave attenuation mechanism of the periodic local resonant metamaterial. J Sound Vib. 2018;412:349–359.
- Zhu R, Liu XN, Hu GK, et al. A chiral elastic metamaterial beam for broadband vibration suppression. J Sound Vib. 2014;333:2759–2773.
- Yu D, Liu Y, Wang G, et al. Flexural vibration band gaps in Timoshenko beams with locally resonant structures. J Appl Phys. 2006;100:124901.
- Fang X, Wen J, Bonello B, et al. Wave propagation in one-dimensional nonlinear acoustic metamaterials. New J Phys. 2017;19:053007.
- Casadei F, Delpero T, Bergamini A, et al. Piezoelectric resonator arrays for tunable acoustic waveguides and metamaterials. J Appl Phys. 2012;112:064902.
- Liu XN, Hu GK, Huang GL, et al. An elastic metamaterial with simultaneously negative mass density and bulk modulus. Appl Phys Lett. 2011;98:251907.
- Hu G, Tang L, Das R, et al. Acoustic metamaterials with coupled local resonators for broadband vibration suppression. AIP Adv. 2017;7(2):025211.
- Lee S, Ahn CH, Lee JW. Vibro-acoustic metamaterial for longitudinal vibration suppression in a low frequency range. Int J Mech Sci. 2018;144:223–234.
- Li ZN, Wang YZ, Wang YS. Nonreciprocal phenomenon in nonlinear elastic wave metamaterials with continuous properties. Int J Solids Struct. 2018;150:125–134.
- Li ZN, Yuan B, Wang YZ, et al. Diode behavior and nonreciprocal transmission in nonlinear elastic wave metamaterial. Mech Mater. 2019;133:85–101.
- Wang YZ, Wang YS. Active control of elastic wave propagation in nonlinear phononic crystals consisting of diatomic lattice chain. Wave Motion. 2018;78:1–8.
- Ning L, Wang YZ, Wang YS. Active control of elastic metamaterials consisting of symmetric double Helmholtz resonator cavities. Int J Mech Sci. 2019;153–154:287–298.
- Barnhart MV, Xu X, Chen Y, et al. Experimental demonstration of a dissipative multi-resonator metamaterial for broadband elastic wave attenuation. J Sound Vib. 2019;438:1–12.
- Miranda EJP, Nobrega ED, Ferreira AHR, et al. Flexural wave band gaps in a multi-resonator elastic metamaterial plate using Kirchhoff-Love theory. Mech Syst Signal Process. 2019;116:480–504.
- Zouari S, Brocail J, Génevaux JM. Flexural wave band gaps in metamaterial plates: A numerical and experimental study from infinite to finite models. J Sound Vib. 2018;435:246–263.
- Wu ZJ, Wang YZ, Li FM. Analysis on band gap properties of periodic structures of bar system using the spectral element method. Waves Random Complex Media. 2013;23(4):349–372.
- Wu ZJ, Li FM. Spectral element method and its application in analysing the vibration band gap properties of two-dimensional square lattices. J Vib Control. 2016;22(3):710–721.
- Wen SR, Wu ZJ, Lu NL. High-precision solution to the moving load problem using an improved spectral element method. Acta Mech Sin. 2018;34(1):68–81.
- Hutchinson JR. Shear coefficients for Timoshenko beam theory. J Appl Mech. 2001;68:87–92.
- Li F, Zhang C, Liu C. Active tuning of vibration and wave propagation in elastic beams with periodically placed piezoelectric actuator/sensor pairs. J Sound Vib. 2017;393:14–29.