nonlocal buckling and vibration analysis of triple-walled zno piezoelectric timoshenko nano-beam subjected to magneto-electro-thermo-mechanical loadings

In this study, using the nonlocal elasticity theory, the buckling and vibration analysis of triple walled zno piezoelectric timoshenko beam on elastic pasternak foundation is analytically investigated under magnetoelectrothermomechanical loadings. using the timoshenko beam free body diagram, the equilibrium equation of timoshenko nanobeam model is obtained and solved by navier’s method for a simplysupported nanobeam. the surrounding elastic mediums are simulated by winkler and pasternak models and interlayer forces are considered by lenardjones potential. the effects of various parameters including the elastic medium, small scale, length, thickness, van der waals force on the critical buckling load and nondimensional natural frequency of triple walled zno nanobeam 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 nonlocal critical buckling load and nondimensional natural frequency of timoshenko nanobeam are  smaller than the local critical buckling load and nondimensional natural frequency. the results can be useful for designing the smart nanobeam for mems and nems.