High-order accurate equations describing vibrations of thin bars
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 457-472
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A method for deriving one-dimensional wave propagation equations in thin inhomogeneous anisotropic bars based on the mathematical homogenization theory for periodic media is used to obtain equations governing the longitudinal and transverse vibrations of a homogeneous circular bar. The equations are derived up to $O(\varepsilon^8)$ terms and take into account variable body forces and surface loads. Here, $\varepsilon$ is the ratio of the bar's typical thickness to the typical wavelength.
@article{ZVMMF_2006_46_3_a9,
author = {N. S. Bakhvalov and M. \`E. \`Eglit},
title = {High-order accurate equations describing vibrations of thin bars},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {457--472},
publisher = {mathdoc},
volume = {46},
number = {3},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a9/}
}
TY - JOUR AU - N. S. Bakhvalov AU - M. È. Èglit TI - High-order accurate equations describing vibrations of thin bars JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2006 SP - 457 EP - 472 VL - 46 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a9/ LA - ru ID - ZVMMF_2006_46_3_a9 ER -
%0 Journal Article %A N. S. Bakhvalov %A M. È. Èglit %T High-order accurate equations describing vibrations of thin bars %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2006 %P 457-472 %V 46 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a9/ %G ru %F ZVMMF_2006_46_3_a9
N. S. Bakhvalov; M. È. Èglit. High-order accurate equations describing vibrations of thin bars. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 457-472. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a9/