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

Huijuan Su, Ranjan Banerjee

Research output: Contribution to Book/ReportConference Contributionpeer-review

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.
Original languageEnglish
Title of host publicationProceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing
EditorsJ. Kruis, Y. Tsompanakis , B.H.V. Topping
PublisherCivil-Comp Proceedings
Pages1-12
Number of pages12
ISBN (Print)978-1-905088-63-8
DOIs
Publication statusPublished - 14 May 2015
EventFifteenth International Conference on Civil, Structural and Environmental Engineering Computing - Prague, Czech Republic
Duration: 1 Sep 20154 Sep 2015

Conference

ConferenceFifteenth International Conference on Civil, Structural and Environmental Engineering Computing
CountryCzech Republic
CityPrague
Period1/09/154/09/15

Keywords

  • Free vibration
  • functionally graded beams
  • dynamic stiffness method
  • Wittrick-Williams algorithm
  • parabolic shear deformation beam theory

Fingerprint Dive into the research topics of 'Derivation of the Dynamic Stiffness Matrix of a Functionally Graded Beam using Higher Order Shear Deformation Theory'. Together they form a unique fingerprint.

Cite this