1720. Conversion of inhomogeneous robin boundary conditions into virtual sources for wave motions and heat conduction

In vibration engineering, the differential equations of wave motions and heat conduction are usually accompanied by inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents Hilbert space from being applied for modal decomposition....

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Bibliographic Details
Published inJournal of Vibroengineering pp. 2846 - 2857
Main Authors Hong, Boe-Shong, Su, Po-Jen
Format Journal Article
LanguageEnglish
Published JVE International Ltd 01.10.2015
Subjects
Boundary value problems
Conduction
Heat
Vibration research
Wave-motion, Theory of
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Summary:In vibration engineering, the differential equations of wave motions and heat conduction are usually accompanied by inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents Hilbert space from being applied for modal decomposition. To deal with this difficulty, this paper does not treat boundary inhomogeneity as a "condition", but almost converts it into a virtual source in conjunction with homogeneous boundary. This conversion counts mostly on the Laplace-Galerkin transform, a functional tool developed in previous works. We also explore boundary topology of this virtual-source conversion, and find that its strategy is to zero the environment and simultaneously create a spatially impulsive source on the homogeneous boundary, yielding almost the same solution. In one-dimensional region, such a boundary source takes the form of Dirac delta function usually combined by its derivatives. In a sense, this paper catches how Nature really handles boundary conditions.
ISSN:1392-8716