Abstract
In this paper, the nonlinear forced vibration of functionally graded (FG) Timoshenko microbeams under thermal effects and parametric excitation is studied using von Kármán nonlinear theory, Hamilton's principle and the modified couple stress theory. The coupled nonlinear differential equations of transverse vibration modes are obtained by the static condensation and Galerkin scheme. The nonlinear algebraic equations of steady-state responses are presented based on the method of multiple scales, and solved using Newton iterative method. Finally, the internal resonance and principal resonance are proposed, and the influence of system parameters, involving the material parameter, length scale parameter, frequency of parametric excitation and thermal loading on the frequency-response is investigated. The reliability of presented Timoshenko microbeam model is confirmed by comparison with previously published results.
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