کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
511397 865845 2012 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Homogeneous trees of second order Sturm–Liouville equations: A general theory and program
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Homogeneous trees of second order Sturm–Liouville equations: A general theory and program
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Structures - Volumes 104–105, August 2012, Pages 13–20
نویسندگان
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