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Title: Homogeneous trees of second order Sturm-Liouville equations: a general theory and program
Authors: Howson, W.P.
Watson, Andrew
Keywords: Quantum graphs
Sturm-Liouville equation
Transcendental eigenvalue problem
Dynamic stiffness matrix
Wittrick-Williams algorithm
Negative eigen values
Issue Date: 2012
Publisher: © Civil-Comp and Elsevier Ltd.
Citation: HOWSON, A.P. and WATSON, A., 2012. Homogeneous trees of second order Sturm-Liouville equations: a general theory and program. Computers and Structures, 104-105, pp. 13 - 20.
Abstract: Quantum graph problems occur in many disciplines of science and engineering and they can be solved by viewing the problem as a structural engineering one. The Sturm–Liouville operator acting on a tree is an example of a quantum graph and the structural engineering analogy is the axial vibration of an assembly of bars connected together with a tree topology. Using the dynamic stiffness matrix method the natural frequencies of the system can be determined which are analogous to the eigenvalues of the quantum graph. Theory is presented that yields exact solutions to the Sturm–Liouville problem on homogeneous trees. This is accompanied by an extremely efficient and compact computer program that implements the theory. An understanding of the former is enhanced by recourse to a structural mechanics analogy, while the latter program is fully annotated and explained for those who might wish to extend its capability. In addition, the use of the program as a ‘black box’ is fully described and a small parametric study is undertaken to confirm the accuracy of the approach and indicate its range of application including the computation of negative eigenvalues.
Description: This is the submitted version of an article that has been subsequently published in the journal, Computers and Structures [© Civil-Comp and Elsevier Ltd.] The definitive version is available at: http://dx.doi.org/10.1016/j.compstruc.2012.03.001.
Version: Submitted for publication
DOI: 10.1016/j.compstruc.2012.03.001
URI: https://dspace.lboro.ac.uk/2134/17510
Publisher Link: http://dx.doi.org/10.1016/j.compstruc.2012.03.001
ISSN: 0045-7949
Appears in Collections:Published Articles (Aeronautical and Automotive Engineering)

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