Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1972. ,
Elastodynamics and 780 resonances in elliptical geometry, Journal of Physics A: General Physics, vol.46, p.435204, 2013. ,
Acoustics of heterogeneous media: macroscopic behavior by homogenization, Current Topics in Acoustical Research, vol.1, pp.63-90, 1994. ,
Dynamique des compositesélastiques péri-785 odiques. (Dynamics of periodic elastic composites), Arch. Mech, vol.37, pp.269-284, 1985. ,
Long wavelength inner-resonance cut-off frequencies in elastic composite materials, International Journal of Solids and Structures, vol.49, pp.3269-3281, 2012. ,
Phononic bandgaps in linearized 790 elasticity. Comptes Rendus de l'Académie des Sciences I, vol.340, pp.933-938, 2005. ,
Homogenization of spectral problems in bounded domains with doubly high contrasts, Networks and Heterogeneous Media, vol.3, pp.413-436, 2008. ,
An active acoustic metamaterial with tunable effective density, 2010. ,
, ASME Journal of Vibration and Acoustics, vol.132, pp.410111-0410119
Résonances d ' objetsélastiques en géométries elliptique et sphéroidale (Resonance of elastic objects in elliptic and spheroidal geometries), 2014. ,
Asymptotic analysis for 800 periodic structures, 1978. ,
Accurate computation of Mathieu functions, 2013. ,
The Tabulation of Mathieu functions, Mathematical Tables and Other Aids to Computation, vol.1, pp.409-419, 1945. ,
Elastic metamaterials with inertial locally resonant structures: Application to lensing and localization, Physical Review B, vol.84, p.174303, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01281298
On the computation of Mathieu functions, Journal of Mathematics and Physics, vol.25, pp.1-20, 1946. ,
Dynamic mass density of resonant metamaterials with homogeneous inclusions, Journal of the Acoustical Society of America, vol.142, pp.890-901, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01574528
Inner resonance in media governed by hyperbolic and parabolic dynamic equations. Principle and exam-815 ples, pp.83-84, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01802862
Accurate calculation of the modified Mathieu functions of integer order, Quarterly of Applied Mathematics, vol.65, pp.1-23, 2007. ,
Mathieu functions, computational toolbox implemented in matlab, 2008. ,
Homogenization approach and Bloch-Floquet theory for band-gap prediction in 2D locally resonant metamaterials, Journal of Elasticity, vol.139, pp.61-90, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02146908
Coupling of substructures for dynamic analyses, AIAA Journal, vol.6, pp.1313-1319, 1968. ,
URL : https://hal.archives-ouvertes.fr/hal-01537654
High-frequency homogenization for periodic media, Proceedings of the Royal Society A, vol.466, pp.2341-2362, 2010. ,
The principal frequencies of vibrating systems with elliptic 830 boundaries, Quarterly Journal of Mechanics and Applied Mathematics, vol.8, pp.361-372, 1955. ,
, Elastodynamics, vol.2, 1978.
Algebraic methods to compute Mathieu functions, Journal of Physics A: General Physics, vol.34, pp.3541-3551, 2001. ,
Mathieu functions. Transactions of the Cambridge Philosophical Society, vol.23, pp.303-336, 1927. ,
Theory and numerical analysis of the Mathieu functions, 2008. ,
The transition matrix for acoustic and elastic wave scattering in prolate spheroidal coordinates, Journal of the Acoustical Society of America, vol.75, pp.35-45, 1984. ,
Locally resonant acoustic metamaterials with 2D anisotropic effective mass density, Philosophical Magazine, vol.91, pp.981-996, 2011. ,
Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young's modulus, Journal of the Acoustical Society of America, vol.132, pp.2887-2895, 2012. ,
Speed of sound in periodic elastic 850 composites, Physical Review Letters, vol.91, pp.2643021-2643024, 2003. ,
Acoustic metamaterial with negative density, Physical letters A, vol.373, pp.4464-4469, 2009. ,
, Locally resonant materials, vol.289, pp.1734-1736, 2000.
Le mouvement vibratoire d'une membrane de forme elliptique (Vibration of an elliptic membrane), Journal de Mathématiques Pures et Appliquées, vol.13, pp.137-203, 1868. ,
Mathieusche Funktionen and Spheroidfunktionen, 1954. ,
The theory of composites, 2002. ,
New metamaterials with macroscopic behavior outside that of continuum elastodynamics, New Journal of Physics, vol.9, p.359, 2007. ,
On modifications of Newton's second law and 865 linear continuum elastodynamics, Proceedings of the Royal Society A, vol.463, pp.855-880, 2007. ,
Methods of theoretical physics, 1953. ,
Scaling of membrane-870 type locally resonant acoustic metamaterial arrays, Journal of the Acoustical Society of America, vol.132, pp.2784-2792, 2012. ,
Willis elastodynamic homogenization theory revisited for periodic media, Journal of the Mechanics and Physics of Solids, vol.77, pp.158-178, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01112307
On asymptotic elastodynamic homogenization approaches for periodic media, Journal of the Mechanics and Physics of Solids, vol.88, pp.274-290, 2016. ,
Homogenization of periodic elastic composites and locally resonant materials, Physical 880 Review B, vol.83, p.104103, 2011. ,
Analytical formulation of three-dimensional dynamic homogenization for periodic elastic systems, Proceedings of the Royal Society A, vol.468, pp.1629-1651, 2012. ,
Determination of effective mass 885 density and modulus for resonant metamaterials, Journal of the Acoustical Society of America, vol.132, pp.2793-2799, 2012. ,
Dynamic homogenization in periodic fibre reinforced media. Quasi-static limit for SH waves, Wave Motion, vol.43, pp.474-498, 2006. ,
Asymptotic analysis of high-frequency 890 modulation in periodic systems. Analytical study of discrete and continuous structures, Journal of the Mechanics and Physics of Solids, vol.117, pp.123-156, 2018. ,
Metamaterials: How the subject started, Metamaterials, vol.1, pp.12-18, 2007. ,
Locally resonant sonic mate-895 rials, Physica B, vol.338, pp.201-205, 2003. ,
Non-local dynamic behavior of linear fiber reinforced materials, Mechanics of materials, vol.55, pp.16-32, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00943749
Homogenization of locally resonant acoustic metamaterials towards an emergent enriched continuum, 900 Computational Mechanics, vol.57, pp.423-435, 2016. ,
A general multiscale framework for the emergent effective elastodynamics of metamaterials, Journal of the Mechanics and Physics of Solids, vol.111, pp.414-433, 2018. ,
, Eigenfrequencies of an elliptic mem-905 brane. Mathematics of Computation, vol.27, pp.16-32, 1973.
Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media, Journal of Physics: Condensed matter, vol.10, pp.6051-6064, 1998. ,
The electrodynamics of substances with simultaneously negative values of and ?, Soviet Physics Uspekhi, vol.10, pp.509-514, 1968. ,
Variational principles for dynamic problems for inhomogeneous elastic media, Wave Motion, vol.3, pp.1-11, 1981. ,
Exact effective relations of s laminated body, Mechanics of 915 materials, vol.41, pp.385-393, 2009. ,
Eigenvalues of the laplacian on a elliptic domain, Computers and Mathematics with Applications, vol.55, pp.1129-1136, 2008. ,
Membrane-type acoustic metamaterial with negative dynamic mass, Physical Review Letters, pp.920-101, 2008. ,
Experimental study on negative effective mass in a 1D mass-spring system, New Journal of Physics, vol.10, p.43020, 2008. ,
Elastic metamaterials with local resonances: an overview. Theoretical and applied mechanics letters, vol.2, 2012. ,