Modeling of Lamb wave propagation in plate with two-dimensional phononic crystal layer coated on uniform substrate using plane-wave-expansion method

We show that the conversional three-dimensional plane wave expansion method can be revised to investigate the lamb wave propagation in the plate with two-dimensional phononic crystal layer coated on uniform substrate. We find that an imaginary three-dimensional periodic system can be constructed by stacking the studied plates and vacuum layers alternately, and then the Fourier series expansion can be performed. The difference between our imaginary periodic system and the true three-dimensional one is that, in our system, the Bloch feature of the wave along the thickness direction is broken. Three different systems are investigated by the proposed method as examples. The principle and reliability of the method are also discussed.

[1]  Sylvain Ballandras,et al.  A full 3D plane-wave-expansion model for 1-3 piezoelectric composite structures. , 2002, The Journal of the Acoustical Society of America.

[2]  S Mohammadi,et al.  Complete band gaps in two-dimensional phononic crystal slabs. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  V Laude,et al.  Evidence for complete surface wave band gap in a piezoelectric phononic crystal. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Eleftherios N. Economou,et al.  Elastic and acoustic wave band structure , 1992 .

[5]  B. Djafari-Rouhani,et al.  Theory of acoustic band structure of periodic elastic composites. , 1994, Physical review. B, Condensed matter.

[6]  Z. Hou,et al.  Singularity of the Bloch theorem in the fluid/solid phononic crystal , 2006 .

[7]  B. Djafari-Rouhani,et al.  Acoustic band structure of periodic elastic composites. , 1993, Physical review letters.

[8]  B. Bonello,et al.  Lamb waves in plates covered by a two-dimensional phononic film , 2007 .

[9]  S. Tamura,et al.  SURFACE AND PSEUDOSURFACE ACOUSTIC WAVES IN SUPERLATTICES , 1998 .

[10]  S. Benchabane,et al.  Full band gap for surface acoustic waves in a piezoelectric phononic crystal. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Zhengyou Liu,et al.  Localized states of acoustic waves in three-dimensional periodic composites with point defects , 2003 .

[12]  B. Manzanares-Martínez,et al.  Surface elastic waves in solid composites of two-dimensional periodicity , 2003 .

[13]  Y. Tanaka,et al.  Watching ripples on crystals. , 2002, Physical review letters.

[14]  Eleftherios N. Economou,et al.  Elastic waves in plates with periodically placed inclusions , 1994 .

[15]  Yukihiro Tanaka,et al.  Surface acoustic waves in two-dimensional periodic elastic structures , 1998 .

[16]  B. Bonello,et al.  Propagation of guided elastic waves in 2D phononic crystals. , 2006, Ultrasonics.

[17]  Tsung-Tsong Wu,et al.  Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates , 2006 .

[18]  Emmanuel Lafond,et al.  Evidence of surface acoustic wave band gaps in the phononic crystals created on thin plates , 2006 .

[19]  Z. Hou,et al.  Convergence problem of plane-wave expansion method for phononic crystals , 2004 .

[20]  B. Auld,et al.  Acoustic fields and waves in solids , 1973 .

[21]  Jian-chun Cheng,et al.  Stopbands for lower-order Lamb waves in one-dimensional composite thin plates , 2006 .

[22]  R. Martínez-Sala,et al.  SOUND ATTENUATION BY A TWO-DIMENSIONAL ARRAY OF RIGID CYLINDERS , 1998 .