[1] LIU Z, ZHANG X, MAO Y et al. Locally resonant sonic materials. Science, 289, 1734-1736(2000).

[2] HUSSEIN M I, LEAMY M J, RUZZENE M. Dynamics of phononic materials and structures： historical origins， recent progress， and future outlook. Applied Mechanics Reviews, 66(2014).

[3] GUO Z K, JIANG S, SHEN Y J et al. Nonlinear dynamic analysis and vibration reduction of two sandwich beams connected by a joint with clearance. Mechanical Systems and Signal Processing, 223, 111828(2025).

[4] GUO Z K, WEN J Q, YU D W et al. Widening the band gaps of hourglass lattice truss core sandwich structures for broadband vibration suppression. Journal of Vibration and Acoustics, 145(2023).

[5] CHEN X H, ZHANG C, CHEN M et al. Vibration bandgap characteristics of phononic crystals with fractal concave angle honeycomb structure. Journal of Synthetic Crystals, 51, 1343-1352+1360(2022).

[6] GUO Z K, WEI Y H, DONG T et al. Ultra-low-frequency vibration attenuation characteristics of multi-span metamaterial dual-beam structures. Mechanics of Solids, 59, 431-444(2024).

[7] HIRSEKORN M, DELSANTO P P, LEUNG A C et al. Elastic wave propagation in locally resonant sonic material： comparison between local interaction simulation approach and modal analysis. Journal of Applied Physics, 99, 124912(2006).

[8] WANG Y F, WANG Y Z, WU B et al. Tunable and active phononic crystals and metamaterials. Applied Mechanics Reviews, 72(2020).

[9] CHEN S, FAN Y C, FU Q H et al. A review of tunable acoustic metamaterials. Applied Sciences, 8, 1480(2018).

[10] SCHAEFFER M, RUZZENE M. Wave propagation in multistable magneto-elastic lattices. International Journal of Solids and Structures, 56, 78-95(2015).

[11] PAL R K, RIMOLI J, RUZZENE M. Effect of large deformation pre-loads on the wave properties of hexagonal lattices. Smart Materials and Structures, 25(2016).

[12] BERTOLDI K, BOYCE M C. Wave propagation and instabilities in monolithic and periodically structured elastomeric materials undergoing large deformations. Physical Review B, 78, 184107(2008).

[13] SHI J H, MOFATTEH H, MIRABOLGHASEMI A et al. Programmable multistable perforated shellular. Advanced Materials, 33, 2102423(2021).

[14] ZHANG H, WU J, FANG D N et al. Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation. Science Advances, 7, 1966(2021).

[15] RESTREPO V, GOSWAMI D et al. Exploiting mechanical instabilities in soft robotics： control， sensing， and actuation. Advanced Materials, 33, 2006939(2021).

[16] SHAN S C, KANG S H, RANEY J R et al. Multistable architected materials for trapping elastic strain energy. Advanced Materials, 27, 4296-4301(2015).

[17] AKSOY B, SHEA H. Multistable shape programming of variable-stiffness electromagnetic devices. Science Advances, 8, 543(2022).

[18] DENG B L, ZANATY M, FORTE A E et al. Topological solitons make metamaterials crawl. Physical Review Applied, 17(2022).

[19] CHEN T, PAULY M, REIS P M. A reprogrammable mechanical metamaterial with stable memory. Nature, 589, 386-390(2021).

[20] RANEY J R, NADKARNI N, DARAIO C et al. Stable propagation of mechanical signals in soft media using stored elastic energy. Proceedings of the National Academy of Sciences of the United States of America, 113, 9722-9727(2016).

[21] FRENZEL T, FINDEISEN C, KADIC M et al. Tailored buckling microlattices as reusable light-weight shock absorbers. Advanced Materials, 28, 5865-5870(2016).

[22] VASIOS N, DENG B L, GORISSEN B et al. Universally bistable shells with nonzero Gaussian curvature for two-way transition waves. Nature Communications, 12, 695(2021).

[23] PAN F, LI Y L, LI Z Y et al. 3D pixel mechanical metamaterials. Advanced Materials, 31, 1900548(2019).

[24] WU S, ZE Q J, DAI J Z et al. Stretchable origami robotic arm with omnidirectional bending and twisting. Proceedings of the National Academy of Sciences of the United States of America, 118(2021).

[25] WU L L, XI X Q, LI B et al. Multi-stable mechanical structural materials. Advanced Engineering Materials, 20, 1700599(2018).

[26] FABER J A, UDANI J P, RILEY K S et al. Dome-patterned metamaterial sheets. Advanced Science, 7, 2001955(2020).

[27] SONG Y P, PANAS R M, CHIZARI S et al. Additively manufacturable micro-mechanical logic gates. Nature Communications, 10, 882(2019).

[28] MAO J J, WANG S, TAN W et al. Modular multistable metamaterials with reprogrammable mechanical properties. Engineering Structures, 272, 114976(2022).

[29] AULD B A, GREEN R E. Acoustic fields and waves in solids： two volumes. Physics Today, 27, 63(1974).

[30] LI Z Y, MA T X, WANG Y Z et al. Vibration isolation by novel meta-design of pyramid-core lattice sandwich structures. Journal of Sound and Vibration, 480, 115377(2020).

[31] HUANG Z L. Study on low frequency vibration energy recovery based on defect state characteristics of acoustic metamaterials(2024).