Properties of a periodically stratified acoustic half-space and its relation to a Biot fluid

@article{citeulike:2354326, abstract = {The problem of the reflection of acoustic waves from a periodically layered acoustic half-space is solved exactly at all frequencies. Pass and stop bands and the associated complex slowness surfaces of propagation through the periodic medium are found. In the low-frequency limit, when the wavelength normal to the layering is much greater than one period, it is shown that there always exists a homogeneous ideal fluid with the same reflection properties as the layered medium. However, the effective acoustic medium that models transmission as well as reflection at low frequencies has a bulk modulus Keff given by K\&\#150;1\&\#150;1 where the brackets denote a volume weighted average, and, for the inertial density appearing in the equations of motion, the effective medium has a transverse isotropic density tensor with , the density component parallel to the layering, given by 1/\&\#150;1, and , the density component perpendicular to the layering given by . The range of wavespeeds speeds as a function of angle is shown to parallel the range of speeds in a Biot fluid as a function of the Biot coupling parameter. Normal propagation corresponds to full locking of the two phases in a Biot material and parallel propagation corresponds to the fully uncoupled case. The relation between the angle of propagation measured from the normal to the layering, and the corresponding Biot coupling parameter is that \&\#150;1 is proportional to cot2 .}, author = {Schoenberg, Michael and Sen, P. N. }, citeulike-article-id = {2354326}, doi = {10.1121/1.388724}, journal = {The Journal of the Acoustical Society of America}, keywords = {metamaterial, porous}, number = {1}, pages = {61--67}, posted-at = {2008-02-08 17:49:19}, priority = {2}, publisher = {ASA}, title = {Properties of a periodically stratified acoustic half-space and its relation to a Biot fluid}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=JASMAN000073000001000061000001\&idtype=cvips\&gifs=yes}, volume = {73}, year = {1983} }

TY - JOUR ID - citeulike:2354326 L3 - citeulike-article-id:2354326 TI - Properties of a periodically stratified acoustic half-space and its relation to a Biot fluid JF - The Journal of the Acoustical Society of America VL - 73 IS - 1 SP - 61 EP - 67 PB - ASA N2 - The problem of the reflection of acoustic waves from a periodically layered acoustic half-space is solved exactly at all frequencies. Pass and stop bands and the associated complex slowness surfaces of propagation through the periodic medium are found. In the low-frequency limit, when the wavelength normal to the layering is much greater than one period, it is shown that there always exists a homogeneous ideal fluid with the same reflection properties as the layered medium. However, the effective acoustic medium that models transmission as well as reflection at low frequencies has a bulk modulus Keff given by K–1–1 where the brackets denote a volume weighted average, and, for the inertial density appearing in the equations of motion, the effective medium has a transverse isotropic density tensor with , the density component parallel to the layering, given by 1/–1, and , the density component perpendicular to the layering given by . The range of wavespeeds speeds as a function of angle is shown to parallel the range of speeds in a Biot fluid as a function of the Biot coupling parameter. Normal propagation corresponds to full locking of the two phases in a Biot material and parallel propagation corresponds to the fully uncoupled case. The relation between the angle of propagation measured from the normal to the layering, and the corresponding Biot coupling parameter is that –1 is proportional to cot2 . KW - metamaterial KW - porous AU - Schoenberg, Michael AU - Sen, PN PY - 1983/// UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JASMAN000073000001000061000001&idtype=cvips&gifs=yes ER -