Free vibration of porous FG nonlocal modified couple nanobeams via a modified porosity model

This paper explores the size–dependent vibration response of porous functionally graded (FG) micro/nanobeams based on an integrated nonlocal-couple stress continuum model (NLCS). The mutual effect of the microstructure local rotation and nonlocality are modelled using the modified couple stress theory and Eringen nonlocal elasticity theory, respectively, into the classical Euler–Bernoulli beam model. All the material properties of the bulk continuum including the microstructure material length scale parameter (MLSP) are assumed to be graded along the thickness according to a power law. For the first time, the effect of the porosity and voids on the modulus of elasticity and MLSP is taken as a ratio of the mass density with porosity-to-that without porosity. Accounting for the physical neutral axis concept and generalized elasticity theory, Hamilton's principle is utilized to formulate the equations of motion and boundary conditions for the FG porous micro/nanobeams. The analytical solution using Navier method is applied to solve the governing equations and obtain the results. The impact of different parameters such as the gradation index, porosity pattern, porosity parameter, nonlocal parameter, and MLSP on the free vibration characteristics of simply supported FG nanobeams are presented discussed in detail. The current model is efficient in many applications used porous FGM, such as aerospace, nuclear, power plane sheller, and marine structures.