Hygrothermal Effects on Vibration Response of Porous FG Nanobeams Using Nonlocal Strain Gradient Theory Considering Thickness Effect

In this work, the thickness-dependent size effect on nonlinear free vibration response of a Porous Functionally Graded (PFG) nanobeam in a hygrothermal environment is examined via nonlocal strain gradient theory (NSGT). Through the depth of the beam, hygro-thermal loadings are uniformly distributed. The mechanical properties of the beam are assumed to vary continuously in the thickness direction according to the power law expression. The equations of motion are derived using Hamilton's principle with consideration of von-Karman nonlinearity. The nanobeam vibration responses are obtained with the aid of the Galerkin technique and the Hamiltonian approach. A vital point of this work is to explore the effects of power law index, slenderness ratio, porosity volume fraction, and hygrothermal changes on the vibration behavior of PFG nanobeams. The results indicate how the thickness effect and porosity volume fraction significantly change the size-dependent vibration response of the FG nanobeam under hygrothermal conditions. The paper findings can be applied to improve the mechanical performance of PFG nanobeams.