Chapter 19 Advanced Structured Composites as Novel Phononic Crystals and Acoustic Metamaterials Kathryn H. Matlack, Sebastian Kr€odel, Anton Bauhofer, and Chiara Daraio Abstract We design and test new periodic materials that can reflect and prohibit the propagation of structural vibrations. These materials are engineered as periodic structures with resonant elements. We rely on recent advances in additive manufacturing to 3-D print composite materials that combine periodically embedded metal resonators within a periodic, truss-like polycarbonate lattice structure, functioning as a support matrix. The polycarbonate lattice geometry allows the matrix to be ultra-low density yet loadbearing, and have tunable density and tunable effective elastic modulus. The high acoustic impedance mismatch between this lattice and the metal resonators opens the possibility to create materials with low frequency and wide band gaps, or frequencies where acoustic propagation is forbidden, using a combination of Bragg scattering effects with effects due to the presence of local resonators. Finite element modeling is used to analyze various lattice geometries, lattice densities, and resonator locations to show materials with tunable acoustic properties. Keywords Locally resonant acoustic metamaterial • Phononic crystals • Structural vibrations • Band gaps • 3D printing 19.1 Introduction The design of phononic crystals and acoustic metamaterials has received considerable attention in the past decade. Stemming from unprecedented properties found in photonic materials, similar Bragg scattering mechanisms have been shown to exist for elastic waves in periodic structures. Physically, periodicity in material properties causes destructive interference of elastic waves, which forbids some frequencies from propagating in certain directions within the structure. Dynamic properties of a multitude of periodic lattice geometries have been explored—ranging from square, triangular, Kagome, and hexagonal 2D structures [1], to complex 3D geometries such as pentamode structures [2, 3], and auxetic geometries [4, 5], to name a few examples. Locally resonant acoustic metamaterials contain resonators embedded in a matrix material. The advantage of locally resonant acoustic metamaterials is that wavelengths associated with resulting band gaps can be orders of magnitude longer than the periodicity of the metamaterial. So, small structures can be designed to absorb low frequency sound or vibrations, for applications such as passive frequency filters and acoustic shielding. Locally resonant acoustic metamaterials have been designed e.g. as materials of rigid inclusions surrounded by soft viscoelastic material that both acts as a soft spring against the inclusions and absorbs the vibration of the resonant modes of the inclusions to induce low frequency dips in the transmission spectrum [6, 7]. These systems have considered a variety of materials for inclusions (e.g. lead [6], gold [8], and tungsten [9], steel [7]), and in a variety of shapes and configurations [9, 10]. Other experimental designs have been explored, consisting of Helmholtz resonators [11], beams with periodic resonators [12, 13], embedded masses in a chiral lattice [14], among many others [15]. Low and wide frequency band gaps have been observed with the inertial amplification method studied in 2D [16] and 3D [17] mass-spring lattices. Local resonator concepts have also been utilized to engineer nanophononic metamaterials to reduce the thermal conductivity [18]. In this paper, we explore how to design locally resonant acoustic metamaterials that are coupled with periodic 3D geometric lattices. Instead of utilizing viscoelastic properties of coating material, we use the geometry of the structure to induce different locally resonant modes, considering structural modes within the designed materials. We study two representative 3D lattice geometries (square and auxetic) and investigate how these geometries can couple with local resonators to induce low frequency band gaps in structural vibrations. As a preliminary study, we consider quasi-1D latticeresonator chains, containing a 3D lattice but with lattice-resonator periodicity in one dimension. K.H. Matlack (*) • S. Kr€odel • A. Bauhofer • C. Daraio Department of Mechanical and Process Engineering, ETH Zu¨rich, Tannenstrasse 3, 8092 Zu¨rich, Switzerland e-mail: matlackk@ethz.ch The original version of this chapter was revised. An erratum to this chapter can be found at DOI 10.1007/978-3-319-21762-8_56 #The Society for Experimental Mechanics, Inc. 2016 C. Ralph et al. (eds.), Mechanics of Composite and Multi-functional Materials, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-21762-8_19 155
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