Waves in wood: free vibrations of a wooden pole

Published Date
May 2001, Vol.49(5):1155–1178, doi:10.1016/S0022-5096(00)00068-5

Author 

P.A. Martin ^a,,

J.R. Berger ^b

aDepartment of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401-1887, USA

bDivision of Engineering, Colorado School of Mines, Golden, CO 80401-1887, USA

Received 26 May 2000. Accepted 1 July 2000. Available online 27 April 2001. 

Abstract

Elastic waves in materials with cylindrical orthotropy are considered, this being a plausible model for a wooden pole. For time-harmonic motions, the problem is reduced to some coupled ordinary differential equations. Previously, these have been solved using the method of Frobenius (power-series expansions). Here, Neumann series (expansions in Bessel functions of various orders) are used, motivated by the known classical solutions for homogeneous isotropic solids. This is shown to give an effective and natural method for wave propagation in cylindrically orthotropic materials. As an example, the frequencies of free vibration of a wooden pole are computed. The problem itself arose from a study of ultrasonic devices as used in the detection of rotten regions inside wooden telegraph (utility) poles and trees; some background to these applications is given.

Keywords

Wood

Cylindrical orthotropy

Wave propagation

Neumann series

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