Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method

Thermo-mechanical vibration analysis of functionally graded (FG) beams and functionally graded sandwich (FGSW) beams are presented. The functionally graded material (FGM) beams are considered to be resting on variable (i) Winkler foundation and (ii) two-parameter elastic foundation. The material properties of these beams are assumed to be varying in the thickness direction. The governing differential equations for beam vibration are being solved using the modified differential quadrature method (MDQM). The applied kinematic boundary conditions are implemented using the modified weighting coefficient matrix (MWCM). The weighting coefficients are generated from the Chebyshev basis function. Present results for the vibration of isotropic beam with variable Winkler foundation are in good agreement with those reported in the literature. Parametric study on the vibration response of FG beams and FGSW beams are being investigated. These parameters include (i) temperature distributions, (ii) power-law index, (iii) variable Winkler foundation modulus, (iv) two-parameter elastic foundation modulus and (v) normalized core thickness of FGSW beams.