Techno Press
Techno Press

Structural Engineering and Mechanics   Volume 20, Number 4, July10 2005, pages 465-476
DOI: http://dx.doi.org/10.12989/sem.2005.20.4.465
 
Free vibration of orthotropic functionally graded beams with various end conditions
Chao-Feng Lu and W. Q. Chen

 
Abstract     [Full Text]
    Free vibration of orthotropic functionally graded beams, whose material properties can vary arbitrarily along the thickness direction, is investigated based on the two-dimensional theory of elasticity. A hybrid state-space/differential quadrature method is employed along with an approximate laminate model, which allows us to obtain the semi-analytical solution easily. With the introduction of continuity conditions at each fictitious interface and boundary conditions at the top and bottom surfaces, the frequency equation for an inhomogeneous beam is derived. A completely exact solution of an FGM beam with material constants varying in exponential way through the thickness is also presented, which serves a benchmark to verify the present method. Numerical results are performed and discussed.
 
Key Words
    functionally graded beams; differential quadrature; state space method; approximate laminate model; exact solution.
 
Address
Chao-Feng Lu; Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P. R. China
W. Q. Chen; State Key Lab of CAD & CG, Zhejiang University, Hangzhou 310027, P. R. China
Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P. R. China
 

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