# Recent Advances in Non-Traditional Elastic Wave Manipulation by Macroscopic Artificial Structures
## 1 Introduction  
A metamaterial (MTM) is an artificial composite material or structure that has physical properties rarely found in nature. They are constructed by repeatedly arranging man-made micro-structures. Adjustments to the shape, size and arrangement of the micro-components can give unique characteristics such as negative parameters that cannot exist in conventional materials. The concept of MTMs was proposed by [PERSON] [1]; he predicted that a material that had simultaneous negative electric permittivity (\(\epsilon\)) and negative magnetic permeability (\(\mu\)) would have a negative refractive index (\(n\)). Subsequently, negative \(n\) was realized in electromagnetic metamaterials (EM-MTMs) [2] by embedding metallic structures appropriately to achieve effective negative \(\epsilon\) and \(\mu\). Since then, EM-MTMs have been applied to various fields such as super-resolution imaging [3; 4; 5], invisibility cloaking [6; 7; 8] and sensing [9; 10; 11; 12]. Acoustic metamaterials (AMTMs) can be also implemented by adjusting the effective density (\(\rho\)) and bulk modulus (\(B\)) [13]. \(\rho\) is analogous to \(\epsilon\), and compressibility (\(\kappa=1/B\)) is analogous to \(\mu\). More details can be found in [14] showing the exact duality of constitutive components in between two different fields at cylindrical coordinates. Studies of AMTMs that exploit the mechanisms used in EM-MTMs have also been conducted [15; 16]. Elastic metamaterials (EMTMs) can generate elastic waves with meta-characteristics, but this application is impeded by some special characteristics of elastic waves. Electromagnetic waves generally have two transverse modes (transverse electric (TE) and transverse magnetic (TM)), and acoustic waves have only one longitudinal mode. However, elastic waves propagate as vibrational motion of a solid medium, so they have both transverse and longitudinal modes concurrently to be considered. This coupling oftransverse and longitudinal modes does not occur in electromagnetic waves and acoustic waves in the linear approximation, so the techniques used in electromagnetism or acoustics cannot be applied directly to EMTMs. Therefore, relevant research on EMTMs has been conducted [17]. EMTMs can manipulate elastic waves by exploiting either Bragg scattering or local resonance. Bragg scattering causes a strong destructive effect on the propagation of scattered waves within a medium when the distance between two scatterers is one-half of the wavelength. At frequencies that meet this condition, a bandgap occurs, in which the real-valued wavevector is forbidden, so waves cannot propagate. Local resonances in a micro-structure can yield negative \(\rho\) or negative stiffness \(K\) if significant deformation is applied. Therefore, a local resonator within the micro-structure must be designed to suppress dynamic external behavior and prevent wave propagation. If a synthetic substance has either negative \(\rho\) or negative \(K\), then waves within that substance have an imaginary-valued velocity, so they attenuate rather than propagate or reflect. These novel characteristics of EMTMs lead to various applications such as passive vibration attenuation systems [18; 19; 20; 21; 22; 23; 24; 25], active vibration attenuation systems [26; 27; 28; 29], energy harvesters [30; 31; 32], energy dissipation systems [33; 34], seismic barriers [35; 36; 37; 38; 39; 40; 41; 42], viscoelastic systems [43; 44], non-reciprocal elastic wave propagation systems [45; 46; 47], gyroscopic metamaterials [48; 49] and elastic topological phononic crystals [50; 51]. In this review, we discuss the theoretical and experimental development of applications using EMTMs in five sections. In Section 2.1, we introduce representative studies of locally resonant EMTMs. In Section 2.2, we explain the gradient-index lens (GRIN) implemented by phononic crystals. In Section 2.3, we introduce super-resolution techniques that use EMTM hyperlenses. In Section 2.4, we provide the mechanism of elastic cloaking using MTMs.