Application of the WKB method to catenary-shaped slender structures
The purpose of this work is the derivation of closed form expressions for the linear vibration modes of catenary-shaped slender structures. The dynamic behaviour of the structure is described using the Euler-Bernoulli beam formulation with variable tension and angle terms. The desired expressions are obtained by treating the governing fourth-order partial differential equation of dynamic equilibrium using the WKB method [J. D. Logan, Applied Mathematics, second ed., Wiley Interscience, 1997]. (C) 2007 Elsevier Ltd. All rights reserved.
wkb slender structures catenary eigenvalues