Nonlocal state-space strain gradient wave propagation of magneto thermo piezoelectric functionally graded nanobeam

In this work, the state -space nonlocal strain gradient theory is used for the vibration analysis of magneto thermo piezoelectric functionally graded material (FGM) nanobeam. An analysis of FGM constituent properties is stated by using the power law relations. The refined higher order beam theory and Hamilton's principle have been used to obtain the motion equations. Besides, the governing equations of the magneto thermo piezoelectric nanobeam are extracted by developed nonlocal state-space theory. And to solve the wave propagation problems, the analytical wave dispersion method is used. The effect of magnetic potential, temperature gradient, and electric voltage in variant parameters are presented in graph.