Nonlinear vibration analysis of piezoelectric functionally graded nanobeam exposed to combined hygro-magneto-electro-thermo-mechanical loading

The present study makes the first attempt to introduce a comprehensive non-classical model of nonlinear free vibration of piezoelectric functionally graded (P-FG) nanobeam exposed to hygromagneto-electro-thermal environment using the extended theory of piezoelectricity. Initially, by employing Von Karman geometric nonlinearity and Hamilton's principle, nonlinear governing equations and related boundary conditions are obtained. The Galerkin method combined with Ritz averaging technique is utilized in order to achieve the frequency response of nanobeams for various boundary conditions under different environmental conditions. The numerical results are first validated with well-known literature which are shown to be in complete agreement. Eventually, with the aid of several numerical examples, the effects of various parameters including power law index, nonlocal parameter, aspect ratio, voltage, temperature change, moisture and magnetic field are investigated.