scholarly journals Free vibrations analysis of a tree structure by the transfer influence coeffcient method. (1st report. Formulation for a two-dimensional tree structure).

1991 ◽  
Vol 57 (536) ◽  
pp. 1091-1098 ◽  
Author(s):  
Takahiro KONDOU ◽  
Atsuo SUEOKA ◽  
Yuji YASUDA ◽  
Deok Hong MOON
Keyword(s):  
Free Vibrations ◽  
Tree Structure ◽  
Two Dimensional

Comparison of Beam and Shell Theories for the Vibrations of Thin Turbomachinery Blades

1983 ◽  
Vol 105 (2) ◽  
pp. 383-392 ◽  
Author(s):  
A. W. Leissa ◽  
M. S. Ewing
Keyword(s):  
Shallow Shell ◽  
Shell Theory ◽  
Free Vibrations ◽  
Two Dimensional ◽  
Analysis Method ◽  
One Dimensional ◽  
Low Aspect Ratio ◽  
Turbomachinery Blades ◽  
Dimensional Analysis Method ◽  
Beam Theories

A great deal of published literature exists which analyzes the free vibrations of turbomachinery blades by means of one-dimensional beam theories. Recently, a more accurate, two-dimensional analysis method has been developed based upon shallow shell theory. The present paper summarizes the two types of theories and makes quantitative comparisons of frequencies obtained by them. Numerical results are presented for cambered and/or twisted blades of uniform thickness. Significant differences between the theories are found to occur, especially for low aspect ratio blades. The causes of these differences are discussed.

Space-Optimized Tree: A Connection+Enclosure Approach for the Visualization of Large Hierarchies

2003 ◽  
Vol 2 (1) ◽  
pp. 3-15 ◽  
Author(s):  
Quang Vinh Nguyen ◽  
Mao Lin Huang
Keyword(s):  
Hierarchical Structure ◽  
Dimensional Space ◽  
Tree Structure ◽  
Relational Data ◽  
Two Dimensional ◽  
Approach Space ◽  
Link Diagram ◽  
New Approach ◽  
Semantic Zooming ◽  
Tree Visualization

This paper describes a new approach, space-optimized tree, for the visualization and navigation of tree-structured relational data. This technique can be used especially for the display of very large hierarchies in a two-dimensional space. We discuss the advantages and limitations of current techniques of tree visualization. Our strategy is to optimize the drawing of trees in a geometrical plane and maximize the utilization of display space by allowing more nodes and links to be displayed at a limited screen resolution. Space-optimized tree is a connection+ enclosure visualization approach that recursively positions children of a subtree into polygon areas and still uses a node–link diagram to present the entire hierarchical structure. To be able to handle the navigation of large hierarchies, we use a new hybrid viewing technique that combines two viewing methods, the modified semantic zooming and a focus+ context technique. While the semantic zooming technique can enlarge a particular viewing area by filtering out the rest of tree structure from the visualization, the focus+context technique allows the user to interactively focus, view and browse the entire visual structure with a reasonable high-density display.

FREE VIBRATIONS OF COMBINED HEMISPHERICAL–CYLINDRICAL SHELLS OF REVOLUTION WITH A TOP OPENING

2013 ◽  
Vol 14 (01) ◽  
pp. 1350023 ◽  
Author(s):  
JAE-HOON KANG
Keyword(s):  
Present Method ◽  
Thin Shell ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Two Dimensional ◽  
Algebraic Polynomials ◽  
Shells Of Revolution

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of joined hemispherical–cylindrical shells of revolution with a top opening. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur, uθ and uz in the radial, circumferential, and axial directions, respectively, are taken to be periodic in θ and in time, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the joined shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. Natural frequencies are presented for different boundary conditions. The frequencies from the present 3D method are compared with those from 2D thin shell theories.

Minimal Query Algorithm of XML Document Based on Unconstrained Tree Pattern

2012 ◽  
Vol 430-432 ◽  
pp. 1677-1681
Author(s):  
Hua Bei Nie ◽  
Yi Wang
Keyword(s):  
Tree Structure ◽  
Two Dimensional ◽  
Structure Model ◽  
Document Structure ◽  
Tree Pattern ◽  
Xml Document ◽  
Query Tree ◽  
Query Algorithm ◽  
Query Patterns ◽  
Relational Table

XML document structure uses the tree structure to express the document structure model that is different from the traditional two-dimensional relational table structure and XML query patterns mainly for tree query. Tree pattern always divided into constrained type and unconstrained type. This paper based on unconstrained tree pattern query, provide a mini algorithm of unconstrained tree pattern query, and prove the correctness of algorithm theoretically.

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