Derivation of the Dynamic Stiffness Matrix of a Functionally Graded Beam using Higher Order Shear Deformation Theory

Su, H. and Banerjee, R. (2015) Derivation of the Dynamic Stiffness Matrix of a Functionally Graded Beam using Higher Order Shear Deformation Theory. In: Kruis, J., Tsompanakis, Y. and Topping, B.H.V. (eds.) Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing :. CZE: Civil-Comp Proceedings. pp. 1-12.

Su_Huijuan_2015_Derivation_of_the_Dynamic_Stiffness_Matrix_of_a_Functionally_Graded_Beam_using_Higher_Orde ... (262kB)

Item Type:	Book Section
Abstract:	The dynamic stiffness matrix of a functionally graded beam (FGB) is developed using a higher order shear deformation theory. The material properties of the FGB are varied in the thickness direction based on a power-law. The kinetic and potential energies of the beam are formulated by accounting for a parabolic shear stress distribution. Hamilton’s principle is used to derive the governing differential equations of motion in free vibration. The analytical expressions for axial force, shear force, bending moment and higher order moment at any cross-section of the beam are obtained as a by-product of the Hamiltonian formulation. The differential equations are solved in closed analytical form for harmonic oscillation. The dynamic stiffness matrix of the FGB is then constructed by relating the amplitudes of forces and displacements at the ends of the beam. The Wittrick-Williams algorithm is applied to the dynamic stiffness matrix of the FGB to compute its natural frequencies and mode shapes in the usual way after solving the eigenvalue problem. Finally, some conclusions are drawn.
Uncontrolled Keywords:	Free vibration, functionally graded beams, dynamic stiffness method, Wittrick-Williams algorithm, parabolic shear deformation beam theory
Creators:	Su, Huijuan and Banerjee, Ranjan
Editors:	Kruis, J., Tsompanakis, Y. and Topping, B.H.V.
Publisher:	Civil-Comp Proceedings
Faculties, Divisions and Institutes:	Faculties > Faculty of Arts, Science & Technology > Engineering
Date:	14 May 2015
Date Type:	Publication
Page Range:	pp. 1-12
Title of Book:	Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing :
Event Title:	Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing
Event Dates:	2015-09-01 - 2015-09-04
Place of Publication:	CZE
Number of Pages:	12
Language:	English
ISBN:	978-1-905088-63-8
DOI:	https://doi.org/10.4203/ccp.108.105
Status:	Published / Disseminated
Refereed:	Yes
Related URLs:	https://pure.northampton.ac.uk/en/public...
URI:	http://nectar.northampton.ac.uk/id/eprint/13397

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