On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory

Abstract This paper contains a nonlocal strain gradient theory to capture size effects in wave propagation analysis of compositionally graded smart nanoplates. Shear deformation influences are also covered employing a higher-order shear deformation plate theory. Furthermore, a power law function is used here to describe the material distribution across the thickness of functionally graded (FG) nanoplate. A combination of linear and cosine function is assumed to show the variations of electric and magnetic potentials through the thickness of nanoplate. The nonlocal governing equations of FG-MEE nanoplate have been derived utilizing Hamilton’s principle for MEEMs. Then, attained differential equations are solved by the means of an analytical solution incorporating with an exponential function. After that, wave frequency, phase velocity and escape frequency of FG-MEE nanoplates are derived for each natural mode. Influences of a large variety of parameters including wave number, nonlocal parameter, length scale parameter, electric voltage, magnetic potential and material distribution parameter has been illustrated separately and the results are exactly interpreted to obtain highlights of each figure.