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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.

Summary

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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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 108 PROCEEDINGS OF THE FIFTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING 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 doi:10.4203/ccp.108.106 purchase the full-text of this paper 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. Summary 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. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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