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.
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