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Dynamic stiffness formulation and free vibration analysis of a moving timoshenko beam

Banerjee, J. R., Su, H. and Gunawardana, W. D. (2008) Dynamic stiffness formulation and free vibration analysis of a moving timoshenko beam. In: AIAA Meeting Papers on Disc ; Vol 13, No. 3 (Conference Proceeding series). American Institute of Aeronautics and Astronautics. 9781563479380.

Item Type: Conference Proceedings
Abstract: A moving Timoshenko beam is analyzed for its free vibration characteristics using the dynamic stiffness method. First the governing differential equations of motion in free vibration of a moving Timoshenko beam are derived using Hamilton’s principle. The derivation gives the expressions for shear force and bending moment from the natural boundary conditions which are consequential of the Hamiltonian formulation. Next the dynamic stiffness matrix is developed by solving the governing differential equations of motion and then eliminating the arbitrary constants from the general solution so as to form the force-displacement relationship of the harmonically vibrating moving Timoshenko beam. The resulting dynamic stiffness matrix, which turns out to be a Hermitian matrix, is used in conjunction with the Wittrick-Williams algorithm to determine the natural frequencies and mode shapes of some examples. In the analysis, simply supported, fixed-simply supported and fixed-fixed end conditions are considered. Results using the Timoshemko theory are compared and contrasted with the corresponding results obtained from the Bernoulli-Euler theory. The critical speeds for all three end conditions are illustrated. Representative mode shapes are presented for different moving speeds. Finally, some conclusions are drawn.
Additional Information: Full title of event: 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 16th AIAA/ASME/AHS Adaptive Structures Conference, 10th AIAA Non-Deterministic Approaches Conference, 9th AIAA Gossamer Spacecraft Forum, and the 4th AIAA Multidisciplinary Design Optimization Specialist Conference
Subjects: T Technology > TA Engineering (General). Civil engineering (General) > TA349 Mechanics of engineering. Applied mechanics > TA355 Vibration
Creators: Banerjee, J R, Su, Huijuan and Gunawardana, W D
Publisher: American Institute of Aeronautics and Astronautics
Faculties, Divisions and Institutes: University Faculties, Divisions and Research Centres - OLD > School of Applied Sciences (to 2009) > Engineering (to 2009)
Faculties > Faculty of Arts, Science & Technology > Engineering
Date: 2008
Date Type: Publication
Title of Book: AIAA Meeting Papers on Disc ; Vol 13, No. 3 (Conference Proceeding series)
Event Title: 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
Event Dates: 7-10 April 2008
Event Location: Schaumburg, USA
Event Type: Conference
Language: English
ISBN: 9781563479380
Media of Output: DVD-ROM
Status: Published / Disseminated

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