Random Eigenvalue Analysis for the Free Vibration of Rotating Beams Using Inverse Problem Approach

2017 ◽  
Author(s):  
Korak Sarkar ◽  
Ranjan Ganguli ◽  
Debraj Ghosh
Keyword(s):  
Inverse Problem ◽  
Free Vibration ◽  
Eigenvalue Analysis ◽  
Rotating Beams ◽  
Random Eigenvalue

Dynamic model for free vibration and response analysis of rotating beams

2013 ◽  
Vol 332 (22) ◽  
pp. 5917-5928 ◽  
Author(s):  
Hyungrae Kim ◽  
Hong Hee Yoo ◽  
Jintai Chung
Keyword(s):  
Free Vibration ◽  
Dynamic Model ◽  
Response Analysis ◽  
Rotating Beams

A Hybrid Inverse Mode Problem for Fixed-Fixed Mass-Spring Models

1996 ◽  
Vol 118 (4) ◽  
pp. 641-648 ◽  
Author(s):  
Izuru Takewaki ◽  
Tsuneyoshi Nakamura ◽  
Yasumasa Arita
Keyword(s):  
Inverse Problem ◽  
Closed Form ◽  
Sufficient Conditions ◽  
Eigenvalue Analysis ◽  
Spring Model ◽  
Mass Spring Model ◽  
Left And Right ◽  
The Masses ◽  
Mass Spring ◽  
Lowest Eigenvalue

A hybrid inverse mode problem is formulated for a fixed-fixed mass-spring model. A problem of eigenvalue analysis and its inverse problem are combined in this hybrid inverse mode formulation. It is shown if all the masses and the mid-span stiffnesses of the model are prescribed, then the stiffnesses of the left and right spans (side-spans) can be found for a specified lowest eigenvalue and a specified set of lowest-mode drifts in the side-spans. Sufficient conditions are introduced and proved for a specified eigenvalue and a specified set of drifts in the side-spans to provide positive stiffnesses of the side-spans and to be those in the lowest eigenvibration. A set of solution stiffnesses in the side-spans is derived uniquely in closed form.

Random Eigenvalue Characterization for Free Vibration of Axially Loaded Euler–Bernoulli Beams

AIAA Journal ◽  
2018 ◽  
Vol 56 (9) ◽  
pp. 3757-3765 ◽  
Author(s):  
Korak Sarkar ◽  
Ranjan Ganguli ◽  
Debraj Ghosh ◽  
Isaac Elishakoff
Keyword(s):  
Free Vibration ◽  
Random Eigenvalue ◽  
Axially Loaded

scholarly journals Application of Adomian Modified Decomposition Method to Free Vibration Analysis of Rotating Beams

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qibo Mao
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Decomposition Method ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Rotating Beams ◽  
Arbitrary Boundary ◽  
Various Boundary Conditions ◽  
Governing Differential Equation

The Adomian modified decomposition method (AMDM) is employed in this paper for dynamic analysis of a rotating Euler-Bernoulli beam under various boundary conditions. Based on AMDM, the governing differential equation for the rotating beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions as well as different offset length and rotational speeds are presented. The accuracy is assured from the convergence and comparison published results. It is shown that the AMDM offers an accurate and effective method of free vibration analysis of rotating beams with arbitrary boundary conditions.

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