Static analysis of functionally graded composite shells on elastic foundations with nonlocal elasticity theory

2020 ◽  
Vol 20 (1) ◽  
Author(s):  
Mohammad Arefi ◽  
O. Civalek
Keyword(s):  
Elasticity Theory ◽  
Static Analysis ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Composite Shells ◽  
Elastic Foundations ◽  
Functionally Graded Composite

scholarly journals Free vibration characteristics of functionally graded Mindlin nanoplates resting on variable elastic foundations using the nonlocal elasticity theory

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881345 ◽  
Author(s):  
Ma’en S Sari ◽  
Mohammad Al-Rbai ◽  
Bashar R Qawasmeh
Keyword(s):  
Free Vibration ◽  
Elasticity Theory ◽  
Collocation Method ◽  
Nonlocal Elasticity ◽  
Natural Frequencies ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Elastic Foundations

In this research, free vibration behavior of thick functionally graded nanoplates is carried out using the Chebyshev spectral collocation method. It is assumed that the plates are resting on variable elastic foundations. Eringen’s nonlocal elasticity theory is used to capture the size effect, and Mindlin’s first-order shear deformation plate theory is employed to model the thick nanoplates. Hamilton’s principle along with the differential form of Eringen’s constitutive relations are utilized to obtain the governing partial differential equations of motion for the functionally graded nanoplates under consideration. A numerical solution is presented by applying the spectral collocation method and the natural frequencies are obtained. A parametric study is conducted to study the effects of several factors on the natural frequencies of the functionally graded nanoplates. It is found that the parameters of the variable elastic foundation (Winkler and shear moduli), thickness to length ratio, length to width ratio (aspect ratio), the nonlocal scale coefficient, the gradient index, the foundation type, and the boundary conditions have a remarkable influence on the free vibration characteristics of the functionally graded nanoplates.

Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory

2017 ◽  
Vol 24 (17) ◽  
pp. 3809-3818 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati ◽  
Parisa Haghi
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Wave Number ◽  
Graded Material ◽  
Fg Nanobeam

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc.

Size-dependent vibration of functionally graded rotating nanobeams with different boundary conditions based on nonlocal elasticity theory

2021 ◽  
pp. 095440622110380
Author(s):  
Jianshi Fang ◽  
Bo Yin ◽  
Xiaopeng Zhang ◽  
Bin Yang
Keyword(s):  
Angular Velocity ◽  
Boundary Conditions ◽  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Gradient Variation

The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework of Euler-Bernoulli and Timoshenko beam theories. The thickness-wise material gradient variation of the nanobeam is considered. By introducing a second-order axial shortening term into the displacement field, the governing equations of motion of the present new nonlocal model of rotating nanobeams are derived by the Hamilton’s principle. The nonlocal differential equations are solved through the Galerkin method. The present nonlocal models are validated through the convergence and comparison studies. Numerical results are presented to investigate the influences of the nonlocal parameter, angular velocity, material gradient variation together with slenderness ratio on the vibration of rotating FG nanobeams with different boundary conditions. Totally different from stationary nanobeams, the rotating nanobeams with relatively high angular velocity could produce larger fundamental frequencies than local counterparts. Additionally, the axial stretching-transverse bending coupled vibration is perfectly shown through the frequency loci veering and modal conversion.

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