Due to rapid development of process manufacturing, composite materials with porosity have attracted commercial attention in promoting engineering applications. For this regard, in this research wave propagation-thermal characteristics of a size-dependent graphene nanoplatelet-reinforced composite (GNPRC) porous cylindrical nanoshell in thermal environment are investigated. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT). The governing equations of the laminated composite cylindrical nanoshell in thermal environment have been evolved using Hamilton’s principle and solved with the assistance of the analytical method. For the first time, wave propagation-thermal behavior of a GNPRC porous cylindrical nanoshell in thermal environment based on NSGT is examined. The results show that by increasing the thickness, the effect of porosity on the phase velocity decreases. Another important result is that by increasing the value of the radius, the difference between the minimum and maximum values of the phase velocity increases. Finally, influence of temperature change, wave number, angular velocity and different types of porosity distribution on phase velocity are investigated using the mentioned continuum mechanics theory. As a useful suggestion, for designing of a GPLRC nanostructure should be attention to the GNP weight function and radius, simultaneously.

On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell

In the present work the dynamic analysis of the functionally graded rectangular nanoplates is studied. The theory of nonlocal elasticity based on the quasi 3D high shear deformation theory (quasi 3D HSDT) has been employed to determine the natural frequencies of the nanosize FG plate. In HSDT a cubic function is employed in terms of thickness coordinate to introduce the influence of transverse shear deformation and stretching thickness. The theory of nonlocal elasticity is utilized to examine the impact of the small scale on the natural frequency of the FG rectangular nanoplate. The equations of motion are deduced by implementing Hamilton\'s principle. To demonstrate the accuracy of the proposed method, the calculated results in specific cases are compared and examined with available results in the literature and a good agreement is observed. Finally, the influence of the various parameters such as the nonlocal coefficient, the material indexes, the aspect ratio, and the thickness to length ratio on the dynamic properties of the FG nanoplates is illustrated and discussed in detail.

Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT

Application of the Rayleigh-Ritz method for the vibration problem of a porous multi-scale hybrid nanocomposite graphene oxide powder (GOP)/carbon fiber (CF)-reinforced beam is shown here for the first time on the basis of a new refined higher-order shear deformation beam theory. The structure consists of an initial matrix which is strengthened via both macro- and nano-scale reinforcements. Herein, GOPs and CFs are selected to be dispersed inside the resin. Moreover, the influences of porosity are included, too. The governing equations of the problem are achieved in the framework of a new refined higher-order beam model. Afterward, the Rayleigh-Ritz well-known finite-element method (FEM) is implemented to solve the problem for various boundary conditions (BCs). The validity of the presented formulation is checked by comparing the results of the employed FEM with those achieved from the Navier solution. it is shown that hybrid nanocomposites are able to support higher natural frequencies in comparison with either conventional fiber-reinforced composites or common two-phase GOP-reinforced nanocomposites.

Vibration analysis of graphene oxide powder-/carbon fiber-reinforced multi-scale porous nanocomposite beams: A finite-element study

Surface and size-dependent effects on the free vibration analysis of cylindrical shell based on Gurtin-Murdoch and nonlocal strain gradient theories

In present paper, a novel two variable shear deformation beam theories are developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. The advantage of this theory relies on its two-unknown displacement field as the Euler-Bernoulli beam theory, and it is capable of accurately capturing shear deformation effects, instead of three as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton’s principle. Analytical solutions for the bending and buckling analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending buckling of nanobeams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory. The results obtained are found to be accurate. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and buckling behaviour of nanobeams, but also comparable with the other shear deformation theories which contain more number of unknowns

A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams

In this paper, based on nonlocal Euler- Bernoulli beam model with arbitrary boundary conditions a simulation method called the Differential Transform Method (DTM) is employed to predict and to analysis the vibration of a single-walled carbon nanotube embedded in an elastic medium under thermal effect. A Winkler type elastic foundation is employed to model the interaction of carbon nanotube and the surrounding elastic medium. Ferstly, the Differential Transform Method is introduced. The research work reveals the significance of the small-scale coefficient, the vibrational mode number and the elastic medium on the non-dimensional natural frequency.

Vibration Analysis of Nano Beam Using Differential Transform Method Including Thermal Effect

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Vibration Analysis of Nano Beam Using Differential Transform Method Including Thermal Effect