Two-dimensional elasticity solutions for free vibration of FGM beams resting on Winkler-Pasternak elastic foundations
PU Yu1，TENG Zhao-chun2
1. School of Civil Engineering，Lanzhou Institute of Technology，Lanzhou 730050，China；
2. College of Science, Lanzhou University of Technology, Lanzhou 730050, China
Abstract：Based on the two-dimension theory of linear elasticity, the free vibration differential equations for FGM beams resting on Winkler-Pasternak elastic foundations are derived. The material properties change continuously through the thickness of the beam and can vary according to power law distributions. Using differential quadrature method, the dimensionless frequencies of free vibration of FGM beams under four different boundary conditions are investigated. The formulations in this paper are validated by comparing the results with those available in the literature for homogeneous beams on Winkler-Pasternak elastic foundations. The influence of the boundary conditions, material graded index, length-to-thickness ratio and elastic coefficients of foundations on the non-dimensional frequency parameter of the FGM beans are considered.
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