Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity
The authors study surface effects, including surface elasticity, surface stress, and surface density as well as the piezoelectric field on the free vibrations of a functionally graded material (FGM) nanobeam using nonlocal elasticity. The simply supported FGM nanobeam is composed of two different materials at the top and the bottom surfaces integrated on each side of the bulk. The surface effects are investigated using the Euler-Bernoulli model and by considering the normal stress along the height of the nanobeam. A cubic variation of the normal stress is assumed, and the balance conditions between the nanobeam bulk and its surfaces are satisfied. Accordingly, the surface density is introduced into the governing equations of the nanobeam. The isotropy and constant piezoelectric properties are assumed, and any residual surface stresses in the bulk due to the surface tension are neglected. The bulk and surface elasticity moduli, mass density, and residual surface stress are assumed to vary in the thickness direction according to the power law distribution, whereas Poisson's ratio is taken to be constant. The variations of the normalized natural frequencies of the nanobeam versus various values of the gradient index, the voltage values of the piezoelectric field, the nanobeam length, and the mode number are obtained. It is concluded that the voltage values and the material properties are two main approaches to achieve the desired natural frequencies in the inverse dynamic problem.
scientific article; zbMATH DE number 6305999
scientific article