Vibration of a piezoelectric nanobeam with flexoelectric effects by Adomian decomposition method

This paper aims to reveal the effect of different elastic foundations on free vibrations of piezoelectric sandwich Euler nanobeam with flexoelectricity based on nonlocal strain gradient theory. Three different elastic foundations: constant, linear, and quadratic, are considered. Adomian decomposition method has been used to obtain the vibration frequencies for three different classical boundary conditions (S-S, C-S, and C-C). The piezoelectric and flexoelectric effects on vibration are also discussed in detail.