Nonlocal Buckling and Vibration Analysis of Triple-Walled ZnO Piezoelectric Timoshenko Nano-beam Subjected to Magneto-Electro-Thermo-Mechanical Loadings

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In this study, using the non-local elasticity theory, the buckling and vibration analysis of triple- walled ZnO piezoelectric Timoshenko beam on elastic Pasternak foundation is analytically investigated under magneto-electro-thermo-mechanical loadings. Using the Timoshenko beam free body diagram, the equilibrium equation of Timoshenko nano-beam model is obtained and solved by Navier’s method for a simply-supported nano-beam. The surrounding elastic mediums are simulated by Winkler and Pasternak models and interlayer forces are considered by Lenard-Jones potential. The effects of various parameters including the elastic medium, small scale, length, thickness, van der Waals force on the critical buckling load and non-dimensional natural frequency of triple- walled ZnO nano-beam are investigated. The results of this study show that the critical buckling load reduces with increasing the temperature change, direct electric field, magnetic field, and length of nanotube, and vice versa for the thickness of nanotubes, and two parameters elastic foundations. Also, the non-local critical buckling load and non-dimensional natural frequency of Timoshenko nano-beam are  smaller than the local critical buckling load and non-dimensional natural frequency. The results can be useful for designing the smart nano-beam for MEMS and NEMS.