Wave propagation characterization and design of two-dimensional elastic chiral metacomposite

In this work, a chiral metacomposite is proposed by integrating two-dimensional periodic chiral lattice with elastic metamaterial inclusions for low-frequency wave applications. The plane harmonic wave propagation in the proposed metacomposite is investigated through the finite element technique and Bloch's theorem. Band diagrams are obtained to illustrate wave properties of the chiral metacomposite. Effective dynamic properties of the chiral metacomposite are numerically calculated to explain low-frequency bandgap behavior in the chiral metacomposite. Interestingly doubly negative effective density and modulus of the chiral metacomposite are found in a specific frequency range, where a pass band with negative group velocity is observed. Tuning of the resulting low-frequency bandgaps is then discussed by adjusting microstructure parameters of the metamaterial inclusion and lattice geometry. Specifically design of a metacomposite beam structure for the broadband low-frequency vibration suppression is demonstrated.

[1]  V. Veselago The Electrodynamics of Substances with Simultaneously Negative Values of ∊ and μ , 1968 .

[2]  Graeme W Milton,et al.  On modifications of Newton's second law and linear continuum elastodynamics , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[3]  M D.J.,et al.  WAVE PROPAGATION IN CONTINUOUS PERIODIC STRUCTURES : RESEARCH CONTRIBUTIONS FROM SOUTHAMPTON , 1964 – 1995 , 2022 .

[4]  N. Fleck,et al.  Wave propagation in two-dimensional periodic lattices. , 2006, The Journal of the Acoustical Society of America.

[5]  M. Ashby,et al.  Cellular solids: Structure & properties , 1988 .

[6]  K. Bathe Finite Element Procedures , 1995 .

[7]  Ole Sigmund,et al.  Systematic design of phononic band–gap materials and structures by topology optimization , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[8]  Richard M. Christensen,et al.  Mechanics of cellular and other low-density materials , 2000 .

[9]  Massimo Ruzzene,et al.  Wave beaming effects in two-dimensional cellular structures , 2003 .

[10]  R. Lakes,et al.  Properties of a chiral honeycomb with a poisson's ratio of — 1 , 1997 .

[11]  C. Sun,et al.  Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density , 2009 .

[12]  Per-Gunnar Martinsson,et al.  VIBRATIONS OF LATTICE STRUCTURES AND PHONONIC BAND GAPS , 2003 .

[13]  Jensen Li,et al.  Double-negative acoustic metamaterial. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Alessandro Spadoni,et al.  Numerical and experimental analysis of the static compliance of chiral truss-core airfoils , 2007 .

[15]  Ahmed K. Noor,et al.  Continuum models for beam-like and plate-like lattice structures , 1978 .

[16]  Salvatore Torquato,et al.  Effective mechanical and transport properties of cellular solids , 1998 .

[17]  Stefano Gonella,et al.  Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting , 2009 .

[18]  Gengkai Hu,et al.  Analytic model of elastic metamaterials with local resonances , 2009 .

[19]  K. Saitou,et al.  Optimal synthesis of 2D phononic crystals for broadband frequency isolation , 2007 .

[20]  N. S. Bardell,et al.  The response of two-dimensional periodic structures to harmonic point loading : A theoretical and experimental study of a beam grillage , 1997 .

[21]  Willie J Padilla,et al.  Composite medium with simultaneously negative permeability and permittivity , 2000, Physical review letters.

[22]  Jakob Søndergaard Jensen,et al.  Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures , 2003 .

[23]  Massimo Ruzzene,et al.  Phononic properties of hexagonal chiral lattices , 2009 .

[24]  A. Spadoni Mechanics of Materials and Structures NUMERICAL AND EXPERIMENTAL ANALYSIS OF THE STATIC COMPLIANCE OF CHIRAL , 2007 .

[25]  John W. Hutchinson,et al.  Optimal truss plates , 2001 .

[26]  Melvin S. Anderson,et al.  Continuum Models for Beam- and Platelike Lattice Structures , 1978 .

[27]  Sheng,et al.  Locally resonant sonic materials , 2000, Science.

[28]  P. Sheng,et al.  Analytic model of phononic crystals with local resonances , 2005 .

[29]  L. Brillouin,et al.  Wave Propagation in Periodic Structures , 1946 .

[30]  M. Wolcott Cellular solids: Structure and properties , 1990 .

[31]  James G. Berryman,et al.  Long‐wavelength propagation in composite elastic media I. Spherical inclusions , 1980 .