The Nonlinear Thermo-Mechanical Vibration of an FGM Beam on Winkler-Pasternak Foundation via Perturbation Analysis Method - Mohammadi, Nader; Nasirshoaibi, Mehrdad (Journal of Applied Nonlinear Dynamics, 2026)
In this work, the perturbation analytical method is used to analyze the nonlinear free vibration of a functionally graded beam on the Winkler-Pasternak elastic basis exposed to mechanical and thermal loadings. The partial differential equation describing the beam's nonlinear motion is first developed under the assumption of the Euler-Bernoulli theory and with the aid of Von-strain-displacement Karman's relation. The Galerkin technique is then used to change the partial differential equation into a nonlinear ordinary differential equation. The ordinary differential equation is resolved using the analytical perturbation method. The effect of boundary conditions, the elastic foundation coefficients (including linear and nonlinear Winkler foundation moduli and elastic shear modulus foundation), axial force, and temperature on the nonlinear natural frequency of FG beams is studied. Results reveal that the presented analytical solution provides accurate predictions with minimum computational effort, as the first-order solution is enough to obtain results with the desired accuracy.