Waves in wood: free vibrations of a wooden pole

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 di erential 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 e ective 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. c © 2001 Elsevier Science Ltd. All rights reserved.