Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams

Ebrahimi, Farzad; Salari, Erfan

doi:10.1080/15376494.2015.1091524

Cited by 119 publications

(21 citation statements)

References 40 publications

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“…Excessive stresses due to intense temperature gradients make the engineering structures susceptible to failure [1]. Also, structures composed of functionally graded (FG) materials may be exposed to various thermo-mechanical loadings.…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position

Barati

Shahverdi

2016

Mechanics of Advanced Materials and Structures

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In this paper, an analytical method is presented for thermo-mechanical vibration analysis of functionally graded (FG) nanoplates with different boundary conditions under various thermal loadings including uniform, linear and non-linear temperature rise via a four-variable plate theory considering neutral surface position. The temperature-dependent material properties of FG nanoplate vary gradually along the thickness according to Mori-Tanaka homogenization scheme. The exactness of solution is confirmed by comparing obtained results with those provided in literature. A parametric study is performed investigating the effects of nonlocal parameter, temperature fields, gradient index and boundary conditions on vibration behavior of FG nanoplates.

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Section: Introductionmentioning

confidence: 99%

An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position

Barati

Shahverdi

2016

Mechanics of Advanced Materials and Structures

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“…Based on nonlocal beam theory: In Ref. [85] thermomechanical modeling of nanobeams for nonlinear frequencies and buckling was developed, effects of different thermal changes on vibration of FGM nanobeams studied in [86], and third-order Timoshenko beam theory subjected thermal loading was developed in [87][88][89] to investigate vibration and buckling responses.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent thermo-mechanical free vibration analysis of functionally graded porous microbeams based on modified strain gradient theory

Zanoosi

2020

J Braz. Soc. Mech. Sci. Eng.

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In present study, vibration analysis of functionally graded (FG) porous microbeam under thermal effects is investigated considering modified strain gradient theory (MSGT) of elasticity. As the main novelty of this study, in order to effectively acquire the effects of size of size-dependent porous structures, MSGT is employed (considers three material length scale parameters) rather than modified couple stress theory (MCST) (considers one material length scale parameter). The nonlinear governing equation of microbeam based on MSGT is derived from Hamilton's principle and to determine the natural frequency of the system under simply supports, Navier solution is employed. Numerical results presented for different beam models and theories and are compared with those available in previous studies. The obtained results show that frequencies from MSGT are higher than those from MCST and also classical theory (CT), especially when the microbeam thickness is comparable to the microbeam length scale parameter. Also, increases in the temperature of microbeam working environment, lead to decrease of microbeam natural frequency. Finally, parametric study is performed on natural frequency of FG microbeams to indicate the effects of: temperature changes, length scale parameter, slender ratio, and gradient index and porosity volume fraction.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Axially Functionally Graded Beam

Cao¹,

Wang²,

Hu³

et al. 2020

Mechanics of Functionally Graded Materials and Structures

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Axially functionally graded (AFG) beam is a special kind of nonhomogeneous functionally gradient material structure, whose material properties vary continuously along the axial direction of the beam by a given distribution form. There are several numerical methods that have been used to analyze the vibration characteristics of AFG beams, but it is difficult to obtain precise solutions for AFG beams because of the variable coefficients of the governing equation. In this topic, the free vibration of AFG beam using analytical method based on the perturbation theory and Meijer G-Function are studied, respectively. First, a detailed review of the existing literatures is summarized. Then, based on the governing equation of the AFG Euler-Bernoulli beam, the detailed analytic equations are derived on basis of the perturbation theory and Meijer G-function, where the nature frequencies are demonstrated. Subsequently, the numerical results are calculated and compared, meanwhile, the analytical results are also confirmed by finite element method and the published references. The results show that the proposed two analytical methods are simple and efficient and can be used to conveniently analyze free vibration of AFG beam.

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Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams

Cited by 119 publications

References 40 publications

An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position

An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position

Size-dependent thermo-mechanical free vibration analysis of functionally graded porous microbeams based on modified strain gradient theory

Free Vibration of Axially Functionally Graded Beam

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