Acoustic wave propagation 1 Acoustics 1 Analytical models 1 Apparent elastic modulus 1 Deformation 1 Effective material property 1 Elastic waves 1 Finite-element approach 1 Mechanical deformation 1 Mechanical instabilities Metamaterials 1 Modulation 1 Modulation frequencies 1 Modulation wavelength 1 Stiffness 1 Stiffness modulation 1 article 1 modulation 1 rigidity 1