Dynamic stiffness for piecewise non‐uniform Timoshenko column by power series—part I: Conservative axial force

2001 ◽  
Vol 51 (5) ◽  
pp. 505-529 ◽  
Author(s):  
A. Y. T. Leung ◽  
W. E. Zhou ◽  
C. W. Lim ◽  
R. K. K. Yuen ◽  
U. Lee
Keyword(s):  
Power Series ◽  
Axial Force ◽  
Dynamic Stiffness ◽  
Timoshenko Column

Dynamic stiffness for piecewise non‐uniform Timoshenko column by power series—part II: Follower force

2001 ◽  
Vol 51 (5) ◽  
pp. 531-552 ◽  
Author(s):  
A. Y. T. Leung ◽  
W. E. Zhou ◽  
C. W. Lim ◽  
R. K. K. Yuen ◽  
U. Lee
Keyword(s):  
Power Series ◽  
Dynamic Stiffness ◽  
Follower Force ◽  
Timoshenko Column

scholarly journals Dynamic Stiffness Formulation for Free Vibration of Truncated Conical Shell and Its Combinations with Uniform Boundary Restraints

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Chunyu Zhang ◽  
Guoyong Jin ◽  
Zhihao Wang ◽  
Xuqin Qian ◽  
Linghua Tian
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Conical Shell ◽  
Dynamic Stiffness ◽  
Recursion Formula ◽  
Geometric Dimension ◽  
Mode Shapes ◽  
Elastic Boundary ◽  
Truncated Conical Shell ◽  
Boundary Lines

This paper presents a dynamic stiffness formulation for the free vibration analysis of truncated conical shell and its combinations with uniform boundary restraints. The displacement fields are expressed as power series, and the coefficients of the series are obtained as recursion formula by substituting the power series into the governing equations. Then, the general solutions can be replaced by an algebraic sum which contains eight base functions, which can diminish the number of degrees of freedom directly. The dynamic stiffness matrix is formulated based on the relationship between the force and displacement along the boundary lines. In the formulation, arbitrary elastic boundary restraints can be realized by introducing four sets of boundary springs along the displacement directions at the boundary lines. The modeling methodology can be easily extended to the combinations of conical shells with different thickness and semivertex angles. The convergence and accuracy of the present formulation are demonstrated by comparing with the finite element method using several numerical examples. Effects of the elastic boundary condition and geometric dimension on the free vibration characteristics are investigated, and several representative mode shapes are depicted for illustrative purposes.

The Software «MMI–calibration 3.0»

Metrologiya ◽  
2020 ◽  
pp. 16-24
Author(s):  
Alexandr D. Chikmarev
Keyword(s):  
Power Series ◽  
Data Processing ◽  
Statistical Treatment ◽  
Correction Function ◽  
Calibration Function ◽  
Measuring Instrument ◽  
Working Standard ◽  
Calibration Protocol ◽  
Error Probabilities ◽  
Continuous Power

A single program has been developed to ensure that the final result of the data processing of the measurement calibration protocol is obtained under normal conditions. The calibration result contains a calibration function or a correction function in the form of a continuous sedate series and a calibration chart based on typical additive error probabilities. Solved the problem of the statistical treatment of the calibration protocol measuring in normal conditions within a single program “MMI–calibration 3.0” that includes identification of the calibration function in a continuous power series of indications of a measuring instrument and chart calibration. An example of solving the problem of calibration of the thermometer by the working standard of the 3rd grade with the help of the “MMI-calibration 3.0” program.

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