Ultrasonic metamaterials with negative modulus

By Nicholas X. Fang, D. Xi, Jianyi Xu, M. Ambati, Werayut Srituravanich, Cheng Sun, Xiang Zhang. Nature Materials, 2006

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A Review of Acoustic Metamaterials and Phononic Crystals (2020, methodology): “[38] firstly proposed an acoustic metamaterial composed of a periodic one-dimensional Helmholtz resonator cavity with acoustic inductance and capacitance (see Figure 8).”
Anisotropic Complementary Acoustic Metamaterial for Canceling out Aberrating Layers (2014, background): “resonance which would inevitably occur in practice [31].”
Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction (2016, background): “acoustic or elastic (negative density and negative shear or bulk modulus) metamaterials (Craster and Guenneau, 2012; Deymier, 2013; Liu et al., 2000; Fang et al., 2006; Kadic et al., 2013).”
Elastic metamaterials and dynamic homogenization: a review (2014, background): “Negative modulus could be achieved through a periodic array of Helmholtz resonators [31,32], and the negative density could be achieved through an array of thin membranes [33].”
Sound transmission loss of metamaterial thin plates with periodic subwavelength arrays of shunted piezoelectric patches (2015, background): “Different types of local resonators have been proposed in the design of acoustic metamaterials, such as coated spheres (the coating is elastically soft material while the sphere is high density solid) [1], Helmholtz resonators [3], tensioned elastic membrane carrying mass blocks [7,8,10,14], soft ru”