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Finite element dynamic analysis of rotating tapered three dimensional Timoshenko beams

Finite element dynamic analysis of rotating tapered three dimensional Timoshenko beams
Finite element dynamic analysis of rotating tapered three dimensional Timoshenko beams

The equations of motion are derived for the three dimensional rotating tapered Timoshenko beam using a Lagrangian formulation in conjunction with the finite element technique. These equations include the effects of Coriolis forces, shear deformation and rotary inertia, hub radius, taper ratios and pre-cone and setting angle. A mixed set of generalized co-ordinates that accounts for inertia coupling between reference motions and local elastic deformations is employed. The shape functions of the three dimensional beam element are derived using Timoshenko beam theory. Explicit expressions of the element mass, stiffness, Coriolis and inertia terms matrices are derived in parametric form thus avoiding extensive numerical computations. The generalized eigenvalue problem is defined and cast into state space form using explicit expressions for the mass, stiffness and Coriolis matrices.

Modal transformations from the space of nodal co-ordinates to the space of modal co-ordinates are invoked to alleviate the problem of large dimensionality resulting from the finite element discretization. Both planar and complex modal transformations are presented and implemented to obtain a reduced order model. The reduced order model form of equations of motion is computer generated, integrated forward in time and the system dynamic response is evaluated for different types of external loading conditions.

Explicit expressions for Southwell coefficient for rotating tapered Timoshenko beams are obtained as a function of all parameter variations. The frequency spectrum of the forced time signal response is computed and plotted along with the response profiles for a wide range of parameter variation using the FFT algorithm.

University of Southampton
Bazoune, Abdelaziz
Bazoune, Abdelaziz

Bazoune, Abdelaziz (2002) Finite element dynamic analysis of rotating tapered three dimensional Timoshenko beams. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

The equations of motion are derived for the three dimensional rotating tapered Timoshenko beam using a Lagrangian formulation in conjunction with the finite element technique. These equations include the effects of Coriolis forces, shear deformation and rotary inertia, hub radius, taper ratios and pre-cone and setting angle. A mixed set of generalized co-ordinates that accounts for inertia coupling between reference motions and local elastic deformations is employed. The shape functions of the three dimensional beam element are derived using Timoshenko beam theory. Explicit expressions of the element mass, stiffness, Coriolis and inertia terms matrices are derived in parametric form thus avoiding extensive numerical computations. The generalized eigenvalue problem is defined and cast into state space form using explicit expressions for the mass, stiffness and Coriolis matrices.

Modal transformations from the space of nodal co-ordinates to the space of modal co-ordinates are invoked to alleviate the problem of large dimensionality resulting from the finite element discretization. Both planar and complex modal transformations are presented and implemented to obtain a reduced order model. The reduced order model form of equations of motion is computer generated, integrated forward in time and the system dynamic response is evaluated for different types of external loading conditions.

Explicit expressions for Southwell coefficient for rotating tapered Timoshenko beams are obtained as a function of all parameter variations. The frequency spectrum of the forced time signal response is computed and plotted along with the response profiles for a wide range of parameter variation using the FFT algorithm.

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Published date: 2002

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Local EPrints ID: 464965
URI: http://eprints.soton.ac.uk/id/eprint/464965
PURE UUID: 7f057a47-53e9-42a2-aeb9-37a8969f4621

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Date deposited: 05 Jul 2022 00:14
Last modified: 05 Jul 2022 03:47

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Contributors

Author: Abdelaziz Bazoune

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