Free Vibration Analysis of a Functionally Graded Magneto-Piezo-Thermoelastic Ceramic-Metal Nanobeam Using Modified Nonlocal State-Space Strain Gradient Theory

This work studies how the variable nonlocal parameter is related to the material variations across a functionally graded (FG) nanobeam. Hamilton’s principle is used to derive the governing motion equations for a FG nanobeam within the refined higher-order state-space strain gradient theory. The presented formulation is tested numerically via Navier’s solution for a simply supported FG nanobeam. A comparison with the existing published findings is performed to show the precision of results. Furthermore, the effects of the nonlocal parameters of the ceramic and metal parts, as well as temperature, magnetic potential, and electric voltage on the free vibration response are investigated.