Nonlinear vibration analysis of electro-hygro-thermally actuated embedded nanobeams with various boundary conditions

In this manuscript, a non-classical beam model is proposed based on the Eringen’s nonlocal elasticity theory for nonlinear vibration analysis of magneto–electro–hygro–thermal piezoelectric functionally graded (PFG) nanobeams rested in elastic foundation. The Hamilton’s principle is employed to derive the nonlinear motion equation and related boundary conditions within the framework of Euler–Bernoulli beam model with von-Karman type nonlinearity. The power–law distribution model is utilized to explain the continuous variation of material properties through the thickness of FG nanobeam. The Galerkin-based method is employed to discretize the nonlinear partial differential motion equations into a set of time-dependent ordinary differential equations. The numerical results are given to investigate the influence of various parameters such as nonlocal parameter, amplitude ratio, aspect ratio, power–law index, external voltage, temperature change, magnetic field, moisture effect and Winkler–Pasternak elastic foundations on the nonlinear frequency ratio of PFG nanobeam for various boundary conditions. It is expressly shown that the nonlinear frequency ratio of PFG nanobeam is significantly influenced by these effects. Some of the numerical results are compared with well-known literature, which are proved to be in good agreement. The presented results can serve as benchmarks for future nonlinear analysis of PFG nanobeams.