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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 108
Edited by: J. Kruis, Y. Tsompanakis and B.H.V. Topping
Paper 106

Development of a Dynamic Stiffness Element for Free Vibration Analysis of a Moving Functionally Graded Beam

J.R. Banerjee1 and W.D. Gunawardana2

1School of Mathematics, Computer Sciences and Engineering, City University London, United Kingdom
2Open University, Romford, Essex, United Kingdom

Full Bibliographic Reference for this paper
J.R. Banerjee, W.D. Gunawardana, "Development of a Dynamic Stiffness Element for Free Vibration Analysis of a Moving Functionally Graded Beam", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 106, 2015. doi:10.4203/ccp.108.106
Keywords: free vibration, functionally graded beam, moving beam, dynamic stiffness method, Wittrick-Williams algorithm.

The dynamic stiffness matrix of a moving functionally graded beam is developed in this paper. The material properties of the beam are assumed to vary through the thickness of the beam from its bottom to top surface according to a power law. The formulation integrates independent dynamic stiffness theories developed earlier for a moving isotropic beam and a non-moving functionally graded beam. First the kinetic and potential energies of a moving functionally graded beam are established from which the governing differential equation of motion and natural boundary conditions are derived by applying Hamilton's principle. For harmonic oscillation, the differential equation is solved analytically and expressions for bending displacement and bending rotation are obtained in explicit algebraic form. The frequency dependent dynamic stiffness matrix is developed by applying boundary conditions to relate the amplitudes of the forces and displacements at the two ends of the harmonically vibrating functionally graded moving beam.

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