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Exact Analysis of Structures With Periodicity Using U-Transformation by H. C. Chan

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Published by World Scientific Publishing Company .
Written in English

Subjects:

  • Structural engineering,
  • Technology & Industrial Arts,
  • Engineering - Mechanical,
  • Technology,
  • Science/Mathematics,
  • Engineering - Civil

Book details:

The Physical Object
FormatHardcover
Number of Pages340
ID Numbers
Open LibraryOL9626849M
ISBN 109810236425
ISBN 109789810236427

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This text introduces the U-transformation method, used for the exact analysis of structures with the periodic property. The physical meaning of U-transformation is fully explained and the application of this technique to derive exact analytical solutions is thoroughly illustrated. By using the U-transformation method, it is possible to uncouple linear simultaneous equations with cyclic periodicity. This text discusses how to apply U-transformation twice to uncouple the two sets of unknown variables in a doubly periodic structure to achieve an analytical exact solution.   By using the U-transformation method, it is possible to uncouple linear simultaneous equations, either algebraic or differential, with cyclic periodicity. This book presents a procedure for applying the U-transformation technique twice to uncouple the two sets of unknown variables in a doubly periodic structure to achieve an analytical exact. Buy (ebook) Exact Analysis Of Structures With Periodicity Using U-transformation by Chan Hon Chuen Chan, Cai C W Cai, Cheung Y K Cheung, eBook format, from the Dymocks online bookstore.

  In order to derive the frequency equation for localized modes, the U-transformation must be used twice. In the present study, two-dimensional bi-periodic mass–spring systems having one disorder are considered. In order to uncouple the governing equation of the bi-periodic systems, the double U-transformation needs to be used twice. 2. In this paper, eigenvalues and eigenvectors of the specific types of structural matrices are studied, and a simple method is presented for calculating their eigenvalues. First, the required formulation to diagonalize circulant and block circulant matrices is presented by using U-matrix transformation. Then utilizing the method of this paper, matrices with non-circulant forms are converted into. Exact analysis of structures with periodicity using U-transformation. Singapore: World Scientific; Exact analysis of structures with periodicity using U-transformation.   Exact analysis of localized modes in bi-periodic mono-coupled mass–spring systems with a single disorder. If the U-transformation method is applied to this single periodic system as illustrated in the book Exact Analysis of Structures with Periodicity using U-transformation, World Scientific, Singapore () Google Scholar.

The U-transformation technique has been applied successfully to the analysis of periodic structures and nearly periodic structures. In this study the technique will be extended to the analysis of bi-periodic structures under static loading or natural vibration, since it is possible to uncouple the governing equation by applying the U-transformation twice.   By using the U-transformation method, it is possible to uncouple linear simultaneous equations, either algebraic or differential, with cyclic periodicity. This text presents a procedure for applying the U-transformation technique twice to uncouple the two sets of unknown variables in a doubly periodic structure to achieve an analytical exact. As such, in this paper, the mathematical exact solutions of spline finite strips in the plate analysis are derived using a unitary transformation approach (abbreviated as the U-transformation.   While all existing damage severity estimation methods that utilize modal data are either employing an iterative solution procedure or requiring spatially complete information, the SPE method is an exact, noniterative solution method and only requires substructure modal data.