Hygro-Thermal Vibrations of Porous FG Nano-Beams Based on Local/Nonlocal Stress Gradient Theory of Elasticity

Abstract

In this manuscript the dynamic response of porous functionally-graded (FG) Bernoulli–Euler nano-beams subjected to hygro-thermal environments is investigated by the local/nonlocal stress gradient theory of elasticity. In particular, the influence of several parameters on both the thermo-elastic material properties and the structural response of the FG nano-beams, such as material gradient index, porosity volume fraction, nonlocal parameter, gradient length parameter, mixture parameter is examined. It is shown how the proposed approach is able to capture the dynamic behavior of porous functionally graded Bernoulli–Euler nano-beams under hygro-thermal loads and leads to well-posed structural problems of nano-mechanics.

Application of the Higher-Order Hamilton Approach to the Nonlinear Free Vibrations Analysis of Porous FG Nano-Beams in a Hygrothermal Environment Based on a Local/Nonlocal Stress Gradient Model of Elasticity

“…Considering a porous functionally graded (FG) nano-beam with length "L" made of a ceramic (Si 3 N 4 )/metal (SuS 3 O 4 ) material and subjected to hygrothermal loadings as shown in Figure 1, in which y' and z' are the principal axes of the geometric inertia originating at the geometric center O of its rectangular cross-section, Σ(x), having thickness "h" and width "b". As already shown in [46], the effective value of the FG material generic property, f (z ), can be obtained as a combination of the corresponding thermo-elastic and physical properties of ceramic, f c , and metal, f m , by using the following rule of mixture equation…”

“…Table 1. Characteristic values of thermo-elastic properties ( f c , f m ) of ceramic (Si 3 N 4 ) and metal (SuS 3 O 4 ) [46].…”

“…Recent studies were developed using innovative L/NStrainG and/or the L/NstressG theories. In detail, the bending response and the free linear vibration of porous FG nanobeams under hygrothermal environments were analyzed by the same authors of this paper in [45,46]. Moreover, the dynamic response of Bernoulli-Euler multilayered polymer functionally graded carbon nanotubes-reinforced composite nano-beams subjected to hygro-thermal environments was investigated in [47].…”

Dynamic Response of Multilayered Polymer Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) Nano-Beams in Hygro-Thermal Environment

“…The ill-posedness of Lim’s NStrainGT can be advantageously circumvented using the variationally consistent nonlocal gradient formulations, such as local/nonlocal strain-driven gradient (L/NStrainG) and local/nonlocal stress-driven gradient (L/NStressG) theories, conceived by Barretta et al in [ 52 , 53 ] for both the static and dynamics problems. These novel constitutive formulations lead to well-posed static [ 54 ] and dynamic problems [ 55 ] of nanomechanics.…”

“…The main aim of this work is to study the dynamic response of multilayered polymer functionally graded carbon nanotubes-reinforced composite nano-beams subjected to hygro-thermal environments by using the aforementioned novel consistent nonlocal gradient formulations [ 54 , 55 ].…”