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High-order accurate equations describing vibrations of thin bars

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Abstract

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(ε8) terms and take into account variable body forces and surface loads. Here, ε is the ratio of the bar’s typical thickness to the typical wavelength.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

    N. S. Bakhvalov & M. E. Eglit

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  1. N. S. Bakhvalov
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  2. M. E. Eglit
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Deceased.

Original Russian Text © N.S. Bakhvalov, M.E. Eglit, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 3, pp. 457–472.

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Bakhvalov, N.S., Eglit, M.E. High-order accurate equations describing vibrations of thin bars. Comput. Math. and Math. Phys. 46, 437–452 (2006). https://doi.org/10.1134/S0965542506030109

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