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Analysis of Rotating Beam Problems using Meshless Methods and Finite Element Methods

Electronic Theses of Indian Institute of Science

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Title Analysis of Rotating Beam Problems using Meshless Methods and Finite Element Methods
 
Creator Panchore, Vijay
 
Subject Rotating Beam Problem
Differential Equations - Rotating Beams
Ordinary Differential Equations
Helicopter Dynamics
Finite Element in Space
Meshless Methods
Petrov-Galerkin Method
Rotating Beams
Timoshenko Beam
Euler-Bernoulli Beam
Rotating Blades
Rotor Blade
Aerospace Engineering
 
Description A partial differential equation in space and time represents the physics of rotating beams. Mostly, the numerical solution of such an equation is an available option as analytical solutions are not feasible even for a uniform rotating beam. Although the numerical solutions can be obtained with a number of combinations (in space and time), one tries to seek for a better alternative. In this work, various numerical techniques are applied to the rotating beam problems: finite element method, meshless methods, and B-spline finite element methods. These methods are applied to the governing differential equations of a rotating Euler-Bernoulli beam, rotating Timoshenko beam, rotating Rayleigh beam, and cracked Euler-Bernoulli beam. This work provides some elegant alternatives to the solutions available in the literature, which are more efficient than the existing methods: the p-version of finite element in time for obtaining the time response of periodic ordinary differential equations governing helicopter rotor blade dynamics, the symmetric matrix formulation for a rotating Euler-Bernoulli beam free vibration problem using the Galerkin method, and solution for the Timoshenko beam governing differential equation for free vibration using the meshless methods. Also, the cracked Euler-Bernoulli beam free vibration problem is solved where the importance of higher order polynomial approximation is shown. Finally, the overall response of rotating blades subjected to aerodynamic forcing is obtained in uncoupled trim where the response is independent of the overall helicopter configuration. Stability analysis for the rotor blade in hover and forward flight is also performed using Floquet theory for periodic differential equations.
 
Contributor Ganguli, Ranjan
 
Date 2018-03-01T15:27:19Z
2018-03-01T15:27:19Z
2018-03-01
2016
 
Type Thesis
 
Identifier http://hdl.handle.net/2005/3209
http://etd.ncsi.iisc.ernet.in/abstracts/4072/G28330-Abs.pdf
 
Language en_US
 
Relation G28330