In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams

Abstract

In the present study, the effect of in-plane thermal loading on vibrational behaviour of functionally graded (FG) nanobeams are carried out by presenting both Navier type solution and differential transform method. Classical and first order shear deformation beam theories are adopted to count for the effect of shear deformations. Thermo-mechanical properties of FG nanobeam are supposed to vary smoothly throughout the thickness based on powerlaw model and material properties are assumed to be temperature-dependent. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of FG nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of FG nanobeams based on Euler-Bernoulli and Timoshenko beam theories. According to the numerical results, it is revealed that the proposed modeling and semi analytical approach can provide accurate frequency results of the FG nanobeams as compared to analytical results and also some cases in the literature. In following a parametric study is accompanied to examine the effects of the several parameters such as temperature change, gradient indexes, small scale parameter, mode number and boundary conditions on the natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the vibration behaviour of a FG nanobeam are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

Current challenges in modelling vibrational fatigue and fracture of structures: a review

“…At high temperature, the materials displayed thermal relaxing and caused a reduction in compressive strength and increase in failure strain. Thermal effect on vibrating structure has been widely investigated [12,18,25,32,61,[180][181][182][183][184][185][186]. Cao et al [181] investigated numerically the thermal vibration and thermal contraction of single-wall carbon nanotubes (CNT).…”

“…In another paper, Ebrahimi and Salari [186] studied the vibration behaviour of functional graded (FG) nanobeams under the effects of in-plane thermal loading. The parametric study showed that change in temperature, mode shape and boundary conditions influenced the fundamental frequencies.…”

Free Vibration of Axially Functionally Graded Beam

“…In this field, Farzad Ebrahimi and Erfan Salari obtained outstanding achievements. Considering the thermal-mechanical effect and size-dependent thermo-electric effect, the buckling and vibration behavior of FGM nanobeams are studied [23][24][25][26]. Considering the concept of neutral axis, they [27] studied the free buckling and vibration of FGM nanobeams using semi-analytical differential transformation method.…”

Free vibration, bending and buckling of a FG-CNT reinforced composite beam

“…Small content of CNTs in polymer matrix can considerably improve the dynamic response of CNTRC beam. Several studies have been reported in literature to elaborate the linear (Alibeigloo and Emtehani, 2014;Brischetto and Carrera, 2012;Ebrahimi et al, 2015;Jam and Kiani, 2015;Lin and Xiang, 2014;Yas and Samadi, 2012) and nonlinear (Ansari et al, 2014;Ke et al, 2010;Mareishi et al, 2015;Shen and Xiang, 2013;Wu et al, 2016) vibration of CNTRC structures. It is observed that the content of CNTs is same in CNTRC structures; nevertheless the resultant frequencies of symmetric distribution are higher than unsymmetrical distribution of CNTs for both linear and nonlinear analysis.…”