• Advances in nano research
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• v.10 no.3
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• pp.271-280
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• 2021

The present work deals with an investigation on longitudinal wave propagation in nanobeams made of graphene sheets, for the first time. The nanobeam is modelled via a higher-order shear deformation theory accounts for both higher-order and thickness stretching terms. The general nonlocal strain gradient theory including nonlocality and strain gradient characteristics of size-dependency in order is used to examine the small-scale effects. This model has three-small scale coefficients in which two of them are for nonlocality and one of them applied for gradient effects. Hamilton supposition is applied to obtain the governing motion equation which is solved using a harmonic solution procedure. It is indicated that the longitudinal wave characteristics of the nanobeams are significantly influenced by the nonlocal parameters and strain gradient parameter. It is shown that higher nonlocal parameter is more efficient than lower nonlocal parameter to change longitudinal phase velocities, while the strain gradient parameter is the determining factor for their efficiency on the results.

• Steel and Composite Structures
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• v.49 no.6
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• pp.633-643
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• 2023

In this study, the natural frequencies of Functional Graded Materials (FGM) plates are predicted using Artificial Neural Network (ANN). A model based on Third-order Shear Deformation Theory (TSDT) and FEM is used to train the ANN model. Different training methods are tested to simulate input and output dependency. As this is a parametric model, several architectures and optimization algorithms were tested. The proposed model allows us to minimize the CPU time to evaluate candidate material properties for FGM plate material selection and demonstrate their influence on dynamic behavior. Consequently, the time required for the FGM design process (candidate materials for material selection) and the geometric optimization of the FGM structure would remain reasonable. The ANN model can help industries to produce FGM plates with good mechanical properties of the selected materials. I addition, this model can be used to directly predict vibration behavior by testing a large number of FGM plates, representing all possible combinations of metals and ceramics in today's industry, without having to solve any eigenvalue problems.

• Earthquakes and Structures
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• v.14 no.2
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• pp.103-115
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• 2018

In this work, a simple but accurate hyperbolic plate theory for the free vibration analysis of functionally graded material (FGM) sandwich plates is developed. The significant feature of this formulation is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the classical plate theory (CPT), instead of 5 as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM face sheet and the homogeneous core and the sandwich with the homogeneous face sheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. Numerical results of the present theory are compared with the CPT, FSDT, order shear deformation theories (HSDTs), and 3D solutions. Verification studies show that the proposed theory is not only accurate and simple in solving the free vibration behaviour of FGM sandwich plates, but also comparable with the higher-order shear deformation theories which contain more number of unknowns.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.573-583
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• 2010

In this paper, the existence of anti-periodic solutions for higher-order nonlinear ordinary differential equations is studied by using degree theory and some known results are improved to some extent.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.309-322
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• 2008

We prove the existence of infinitely many solutions of the nonlinear higher order elliptic equation with Dirichlet boundary condition $(-{\Delta})^mu=q(x,u)$ in ${\Omega}$, where $m{\geq}1$ is an integer and ${\Omega}{\subset}{R^n}$ is a bounded domain with smooth boundary, when q(x,u) satisfies some conditions.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.455-463
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• 2012

In this paper, by using degree theory, we consider a kind of higher-order Li$\acute{e}$enard type $p$-Laplacian differential equation as follows $$({\phi}_p(x^{(m)}))^{(m)}+f(x)x^{\prime}+g(t,x)=e(t)$$. Some new results on the existence of anti-periodic solutions for above equation are obtained.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• Steel and Composite Structures
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• v.24 no.5
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• pp.569-578
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• 2017

In this research work, a simple and accurate hyperbolic plate theory for the buckling analysis of functionally graded sandwich plates is presented. The main interest of this theory is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\not=}0$), the displacement field is composed only of 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 like in the well-known "higher order shear and normal deformation theories". Thus, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Governing equations are obtained by employing the principle of minimum total potential energy. Comparison studies are performed to verify the validity of present results. A numerical investigation has been conducted considering and neglecting the thickness stretching effects on the buckling of sandwich plates with functionally graded skins. It can be concluded that the present theory is not only accurate but also simple in predicting the buckling response of sandwich plates with functionally graded skins.

• Journal of Korean Society of Steel Construction
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• v.15 no.2
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• pp.97-107
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• 2003

To obtain a more accurate response from larninated composite structures, the effect of transverse shear deformation, transverse normal strain/stress, and nonlinear variation of in-plane displacements vis-$\\grave{a}$-vis the thickness coordinate should be considered in the analysis. The improved higher-order theory was used to determine the critical buckling load and natural frequencies of laminated composite structures. Solutions of simply supported laminated composite plates and sandwiches were obtained in closed form using Navier's technique, with the results compared with calculated results using the first order and other higher-order theories. Numerical results were presented for fiber-reinforced laminates, which show the effects of ply orientation, number of layers, side-toithickness ratio, and aspects ratio.

• Steel and Composite Structures
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• v.29 no.3
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• pp.349-362
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• 2018

Thermal buckling behavior of porous functionally graded nanobeam integrated with piezoelectric sensor and actuator based on the nonlocal higher-order shear deformation beam theory is investigated for the first time. Its material properties are assumed to be temperature-dependent and varying along the thickness direction according to the modified power-law rule. Note that the porosity with even type is considered herein. The equations of motion are obtained through Hamilton's principle. The influences of several parameters (such as type of temperature distribution, external electric voltage, material composition, porosity, small-scale effect, Ker foundation parameters, and beam thickness) on the thermal buckling of FG nanobeam are investigated in detail.