Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions
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This paper deals with the semi-analytical nonlinear thermal vibration analysis of functionally graded (FG) nanoplates modeled by four-variable refined plate theory. The nanoplate is resting on a nonlinear hardening elastic medium and subjected to uniform and nonlinear temperature rises. Temperature-dependent gradient material properties of the nanoplate are described via simple power-law model. A closed-form expression for nonlinear frequency is presented using a novel Hamiltonian approach as well as He’s variational method. To the best of the author’s knowledge, the nonlinear governing equations and their solution for a refined four-variable nanoplate are very rare in the literature. It is seen that the nonlinear vibration frequency is affected by the uniform temperature rise, nonlinear temperature rise, scale parameter, maximum amplitude, material gradation, foundation parameters and temperature-dependency. The presented formulation and solution approaches can be used in future investigations on macro to nanoscale plates.
KeywordsNonlinear vibration Hamiltonian method Four-variable plate theory Nonlocal elasticity
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The authors declare that they have no conflict of interest.
- 10.Besseghier A, Houari MSA, Tounsi A, Mahmoud SR (2017) Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory. Smart Struct Syst 19(6):601–614Google Scholar
- 30.Barati MR, Shahverdi H (2016) An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position. Mech Adv Mater Struct 24:1–14Google Scholar
- 32.Ebrahimi F, Barati MR (2017) Vibration analysis of size-dependent flexoelectric nanoplates incorporating surface and thermal effects. Mech Adv Mater Struct 30:1Google Scholar
- 44.Ebrahimi F, Barati MR (2016) Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates. J Braz Soc Mech Sci Eng 39:1–21Google Scholar
- 57.Barati MR, Shahverdi H (2017) Nonlinear vibration of nonlocal four-variable graded plates with porosities implementing homotopy perturbation and Hamiltonian methods. Acta Mechanica. 1–20Google Scholar