Nowadays, with the development in nanotechnology, functionally graded piezoelectric (FGP) nanostructures have also been employed in micro electro-mechanical systems (MEMS) and nano electro-mechanical systems (NEMS). Thus, establishing an accurate model of FGP nanobeams is a key issue for successful NEMS design. In the present study, thermo-electro-mechanical vibration characteristics of FGP nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a numerical type solution. Material properties of FGP nanobeam are supposed to vary continuously throughout the thickness based on power-law model. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion are obtained for the free vibration analysis of graded piezoelectric nanobeams including size effect. In following a parametric study is accompanied to examine the effects of the several parameters such as temperature change, electric voltage, power-law index and nonlocal parameter on the natural frequencies of me size-dependent FGP nanobeams in detail. Numerical results are presented to serve as benchmarks for the application and the design of nanogenerators, nano-oscillators, and atomic force microscopes (AFMs), in which nanobeams act as basic elements.
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