Transfer matrix method for natural vibration analysis of tree system
type: Item
instance of: scholarly article
title: Transfer matrix method for natural vibration analysis of tree system
zbMATH Open document ID: 1264.70048
DOI: 10.1155/2012/393204
author: Bin He
author: Huiling Zhang
author: Xiao-Ting Rui
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: The application of Transfer matrix method (TMM) ranges from linear/nonlinear vibration, composite structure, and multibody system to calculating static deformation, natural vibration, dynamical response, and damage identification. Generally TMM has two characteristics: (1) the TMM formulae share similarity to the chain mechanics model in terms of topology structure; then TMM often is selected as a powerful tool to analyze the chain system. (2) TMM is adopted to deal with the problems of the discrete system, continuous system, and especial discrete/continuous coupling system with the uniform matrix form. In this investigation, a novel TMM is proposed to analyze the natural vibration of the tree system. In order to make the TMM of the tree system have the two above advantages of the TMM of the chain system, the suitable state vectors and transfer matrices of the typical components of the tree system are constructed. Then the topology comparability between the mechanics model and its corresponding formulae of TMM can be adopted to assembling the transfer matrices and transfer equations of the global tree system. Two examples of natural vibration problems validating the method are given. The formulation of the proposed TMM is mathematically intuitive and can be held and applied by the engineers easily.
Mathematics Subject Classification ID: 70J50
Mathematics Subject Classification ID: 70H45
zbMATH DE Number: 6173247
Wikidata QID: Q58911520
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/393204
OpenAlex ID: W2002520137
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description: scientific article; zbMATH DE number 6173247