Abstract In this paper, the thermal effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams subjected to various types of thermal loading is investigated by presenting a Navier type solution and employing a semi analytical differential transform method (DTM) for the first time. Two kinds of thermal loading, namely, linear temperature rise and nonlinear temperature rise are studied. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form and the material properties are assumed to be temperature-dependent. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton׳s principle and they are solved applying DTM. 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. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as thermal effect, material distribution profile, small scale effects, mode number and boundary conditions on the normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the vibration behaviour of a FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.
Highlights We study the thermo-mechanical vibration of FG nanobeams (FGNBs) under various B.C.s Various types of thermal loadings are examined. Numerical simulations show the effectiveness of analytical method and obtained results. Several significant parameters on thermo-vibrational behavior of FGNBs are discussed. Normalized frequencies of the temperature-dependent FGNBs are discussed in detail.
Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment
Acta Astronautica ; 113 ; 29-50
2015-03-27
22 pages
Article (Journal)
Electronic Resource
English
Three-dimensional vibration analysis of functionally graded material plates in thermal environment
Online Contents | 2009
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