On nonlocal characteristics of curved inhomogeneous Euler–Bernoulli nanobeams under different temperature distributions

Ebrahimi, Farzad; Barati, Mohammad Reza

doi:10.1007/s00339-016-0399-7

Cited by 40 publications

(6 citation statements)

References 37 publications

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“…Also, the general solutions of Eq. (38), which satisfy the boundary conditions (33) and initial conditions (34), can be presented in the following form…”

Section: Equations Of Motionmentioning

confidence: 99%

“…The size-dependent governing motion equations of curved nanobeams are derived in these works according to the first-order shear deformation model of Timoshenko and are solved by using the Navier method. Ebrahimi and Barati [34,35] presented the analytical studies on the size-dependent vibrational behavior of curved nanobeams with different boundary conditions. The mechanical and thermal vibrations of curved nanobeams are studied in these researches based on the classical Euler-Bernoulli model and nonlocal strain gradient theory.…”

Section: Introductionmentioning

confidence: 99%

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Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory

Babaei

Eslami

2021

Eur. Phys. J. Plus

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A nonlocal strain gradient theory is developed in this paper to study the large amplitude vibrations of arches made of functionally graded (FG) porous material. The case of shallow arches resting on nonlinear elastic foundation is modeled via a general higherorder shear deformation theory. The third-order model of Reddy, the first-order model of Timoshenko, and the classical model of Euler-Bernoulli are analyzed. Thermomechanical properties of the arch exposed to the uniform thermal field are assumed to be temperature dependent. The nonlinear motion equations of the arch are established by employing Hamilton's principle and the von Kármán type of geometric nonlinearity. The two-step perturbation technique and the Galerkin method are utilized to solve the nonlinear governing equations. The size-dependent linear and nonlinear frequencies of the arch are obtained for the immovable pinned-pinned boundary conditions. The comparison studies are performed to verify the present solution method with the provided data in the literature, and a good agreement is observed. The novel parametric studies covered in this research include the effects of several parameters such as elastic foundation, nonlocal and length scale parameters, porosity, temperature field, power law index, and geometrical parameters on the frequencies of FG porous arches in detail.

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“…Also, the general solutions of Eq. (38), which satisfy the boundary conditions (33) and initial conditions (34), can be presented in the following form…”

Section: Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory

Babaei

Eslami

2021

Eur. Phys. J. Plus

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“…The thermal bending of pinned thin FG beams was studied by Levyakov (2013). The buckling and vibration analysis of curved FG beams and viscoelastic FG beams was presented by Ebrahimi and Barati (2016a, 2017).…”

Section: Introductionmentioning

confidence: 99%

Analysis of thick beams with temperature-dependent material properties under thermomechanical loads

Zhong

Zhou

et al. 2020

Advances in Structural Engineering

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This study focuses on the thermoelastic behavior of simply supported thick beams with temperature-dependent material properties under thermomechanical loads. The heat conduction analysis is based on the one-dimensional Fourier’s law, and the displacement and stress analysis is based on the two-dimensional thermoelasticity theory. The solution of temperature field across the thickness is obtained. By dividing the beam into a series of thin slices, the temperature and the material properties in each slice are considered to be uniform. The state space method is used to give the displacements and stresses for every slice. The transfer-matrix method is used to give the displacements and stresses for the beam. Finally, an example is conducted to analyze the temperature, displacement, and stress fields in a carbon steel beam. The example reveals that the temperature not only produces displacements and stresses itself but also affects the displacements and stresses induced by the mechanical load.

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“…Implementing a semianalytical approach, Niknam and Aghdam 34 discussed vibrational behavior of Euler-Bernoulli graded nanobeams. Most recently, Ebrahimi and Barati and Ebrahimi et al [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] explored thermal and hygrothermal effects on nonlocal behavior of nonhomogeneous nanoscale beams and plates. Ebrahimi and Barati 51 applied Reddy beam model for vibrational analysis of graded nanosize beams.…”

Section: Introductionmentioning

confidence: 99%

Influence of neutral surface position on dynamic characteristics of in-homogeneous piezo-magnetically actuated nanoscale plates

Ebrahimi

Barati

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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Based on exact position of neutral surface, vibrational behavior of smart nanoplates made of magneto-electro-elastic functionally graded materials is examined by implementing a Galerkin method for the first time. Magneto-electro-elastic properties of nanoplate vary in transverse direction via power-law model. The nonlocal governing equations of functionally graded plate under magneto-electrical field are formulated through Hamilton’s principle and nonlocal elasticity theory based on a four-variable refined plate theory, which avoids the use of shear correction factors by capturing shear deformation influences. Importance of various parameters including magnetic potential, electric voltage, various boundary conditions, nonlocality, material distribution, and plate thickness on natural frequencies of the magneto-electro-elastic functionally graded nanoplate are explored. It is elucidated that these parameters play significant roles on the dynamic behavior of magneto-electro-elastic functionally graded nanoplates.

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On nonlocal characteristics of curved inhomogeneous Euler–Bernoulli nanobeams under different temperature distributions

Cited by 40 publications

References 37 publications

Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory

Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory

Analysis of thick beams with temperature-dependent material properties under thermomechanical loads

Influence of neutral surface position on dynamic characteristics of in-homogeneous piezo-magnetically actuated nanoscale plates

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