In this paper, buckling analysis of Functionally graded rectangular Nano-plates considering the surface effect is investigated. Also, to define the material properties the Mori-Tanaka scheme is used which according to this scheme the material properties change continuously along the thickness direction. Displacement field is obtained using modified shear deformation theories. In these theories, against classical plate theory, the effects of rotary inertia and transverse shear deformations are considered and various functions such as exponential, trigonometric, hyperbolic and parabolic functions are used to considering these effects along the thickness direction. To considering nonlocal and surface effects the nonlocal elasticity theory and surface elasticity theory are employed respectively. The governing equations of motion are obtained by Hamilton’s principle and the Galerkin method is used to solve these equations. To show the accuracy of the present formulations, the presented results in this thesis are compared with those reported in the literature. Finally, the effects of various parameters which is related to the surface parameters such as residual surface stress, surface elasticity constant and also other parameters such as thickness ratio, aspect ratio, material index and nonlocal parameter of Functionally graded nano-plate are investigated.

In the present study the free vibration analysis of Functionally graded composite rectangular nanoplates in thermal environment is investigated. The nonlocal elasticity theory based on the exponential shear deformation theory has been used to obtain the natural frequencies of the nanoplate. In exponential shear deformation theory an exponential functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. Nonlocal elasticity theory is employed to investigate effect of small scale on natural frequency of the Functionally graded rectangular nanoplate. The temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only. Material properties are assumed to be temperature dependent, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The govering equations are derived by implementing Hamilton’s principle. To show the accuracy of the formulations, present result’s inspecific cases are compared with available results in literature and good agreement are seen. Finally, the effect of various parameters such as nonlocal parameter, power law indexes, width to length ratio, the thickness to length ratio, and temperature fields on the natural frequencies of rectangular FG nanoplates are presented and discussed in detail.

In this study, the vibration behavior of Functional graded (FG) circular and annular nanoplate embedded in a Visco-Pasternak foundation and coupled with temperature change is studied. The effect of in-plane pre-load and temperature change are investigated on the vibration frequencies of FG circular and annular nanoplate. To obtain the vibration frequencies of the FG circular and annular nanoplate, two different size dependent theories are utilized. The material properties of the FGM nanoplates are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique. The FG circular and annular nanoplate is coupled by an enclosing viscoelastic medium which is simulated as a Visco- Pasternak foundation. By using the modified strain gradient theory (MSGT) and the modified couple stress theory (MCST), the governing equation is derived for FG circular and annular nanoplate. The differential quadrature method (DQM) and the Galerkin method (GM) are utilized to solve the governing equation to obtain the frequency vibration of FG circular and annular nanoplate. The results are subsequently compared with valid result reported in the literature. The effects of the size dependent, the in-plane pre-load, the temperature change, the power index parameter, the elastic medium and the boundary conditions on the natural frequencies are investigated. The results show that the size dependent parameter has an increasing effect on the vibration response of circular and annular nanoplate. The temperature change also play an important role in the mechanical behavior of the FG circular and annular nanoplate. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the nanoplate.

In this study, the vibration behavior of Functional graded (FG) circular and annular nanoplate embedded in a Visco-Pasternak foundation and coupled with temperature change is studied. It is assumed that a uniform radial magnetic field acts on the top surface of the plate and the magnetic permeability coefficient of the plate along its thickness are assumed to vary according to the volume distribution function. The effect of in-plane pre-load and temperature change are investigated on the vibration frequencies of FG circular and annular nanoplate. To obtain the vibration frequencies of the FG circular and annular nanoplate, two different size dependent theories are utilized. The material properties of the FGM nanoplates are assumed to vary in the thickness direction and are estimated through the Mori– Tanaka homogenization technique. The FG circular and annular nanoplate is coupled by an enclosing viscoelastic medium which is simulated as a Visco-Pasternak foundation. By using the modified strain gradient theory (MSGT) and the modified couple stress theory (MCST), the governing equation is derived for FG circular and annular nanoplate. The differential quadrature method (DQM) and the Galerkin method (GM) are utilized to solve the governing equation to obtain the frequency vibration of FG circular and annular nanoplate. The results are subsequently compared with valid result reported in the literature. The effects of the size dependent, the in-plane pre-load, the temperature change, the magnetic field, the power index parameter, the elastic medium and the boundary conditions on the natural frequencies are investigated. The results show that the size dependent parameter has an increasing effect on the vibration response of circular and annular nanoplate. Also, the temperature change play important role in the mechanical behavior of the FG circular and annular nanoplate. According to the results, the application of radial magnetic field to the top surface of the plate changes the state of stress in both tangential and radial direction. The present analysis results can be used for the design of the next generation of nano-devices that make use of the thermal vibration properties of the nanoplate.

In this paper a Functional graded material (FGM) thermal barrier coating (TBC) is prepared using Atmospheric Plasma Spraying (APS) method. The FGM layers were deposited by varying the feeding ratio of CYSZ/NiCrAlY and conventional CYSZ on a NiCrALY-coated Inconel 738 substrates. Hot corrosion behavior, bonding strength and the related failure mechanisms of a conventional TBC and a FGM TBC are investigated. Hot corrosion studies were conducted in presence of 45% Na2SO4+ 55% V2O5 molten salt at 1000 oC temperature. The as-sprayed coatings and heat-treated coatings were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). Exposing to hot corrosion test, the FGM TBC showed better chemical stability and higher life service in comparison to the conventional TBC. As a result, Functional graded material thermal barrier coating exhibited very promising potential as a novel TBC material.

Functionally graded materials are the novel class of advanced composite structures with variable properties in one or more directions. The mechanical properties of Functionally graded Materials (FGM) such as Poisson’s ratio, Young’s modulus of elasticity, material density and shear modulus of elasticity undergo changes gradually and continuously between two surfaces in a predetermined manner. FGM structures are often made of a combination of ceramics and metals in which the metal component provides strength and fracture resistance while ceramic component provides thermal resistance. Due to desirable properties, FGM materials are used in various fields of engineering such as optics, electronics, space vehicles, shipbuilding, mechanical, biomechanical and other engineering structures subjected to high thermal and residual stresses. Therefore, the analytical study of thermoelastodynamic problems is of great importance for the Functionally graded media. The use of potential functions to analyze three-dimensional elastic problems is one of the most effective methods. This method facilitates solving three-dimensional elastic problems by uncoupling the set of governing differential equations or at least simplifying them. In the present study, the displacement potential functions for solving thermoelastodynamic problems in the transversely isotropic media with Functionally graded materials are introduced. For this purpose, first, the three-dimensional kinematic and thermodynamic equations for the Functionally graded materials in the transversely isotropic materials are written and then using a systematic method to separate the equations, the displacement potential functions to solve thermoelastodynamic problems are obtained, which can be used further to solve problems of beams, plates, shells, and infinite and semi-infinite media. The obtained potential functions include two scalar functions F and χ; the scalar function F satisfies the sixth-order partial differential equation while the χ-scalar function satisfies the second-order partial differential equation. In addition, in the present study, the thermal potential functions for the specific state of the isotropic Functional graded media are presented.

In this paper, an analysis of free vibration in Functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesses according to a volume fraction power law distribution. The finite element method (FEM) is presented to model the Functionally graded nanoplate and solve mathematical equations accurately. The finite element formulation for HSDT nanoplate is also presented. Natural frequencies of FG nanoplate with various boundary conditions are compared with available results in the literature. At the end some numerical results are presented to evaluate the influence of different parameters, such as power law index, nonlocal parameter, aspect ratio and aspect of length to thickness of nanoplate. In addition, all combinations of simply supported and clamped boundary conditions are considered.

In this paper, axisymmetric free vibration analysis of a circular Nano-plate having variable thickness was studied. The variation in thickness of plate was considered as a linearly in radial direction. Nonlocal elasticity theory was utilized to take into account size-dependent effects. Ritz functions was utilized to obtain the frequency equations for simply supported and clamped boundary. To verify accuracy of Ritz method, differential transform method (DTM) also used to drive the size dependent natural frequencies of circular nano-plates. The validity of solutions was performed by comparing present results with those of the literature for both classical plate and nano plate. Effect of nonlocal parameter, mode number and taper parameter on the natural frequency are investigated. Results showed that taper parameter has significant effect on the non-dimensional frequency and its effects on the clamped boundary condition is more than simply support.

In the current study, the modified shear deformation theories are used for analyzing the electro-mechanical vibration of inhomogeneous piezoelectric nanoplates in conjunction with the nonlocal elasticity theory. These theories not only satisfy transverse shear traction-free conditions on the top and bottom surfaces of the plate but also consider exponential and trigonometric distributions for the transverse shear deformations. Heterogeneity of the structure is supposed to be in the thickness direction of the nanoplate and it is assumed that the simply supported Functionally graded piezoelectric nanoplate is subjected to a biaxial force and an external electric voltage. The governing equations of the vibrating Functionally graded piezoelectric nanoplate are obtained by using Hamilton’s principle, which are then solved by using Navier’s method to achieve the vibrational behavior of the structure. The detailed discussion is presented to explain the influences of the various parameters on the natural frequencies of Functionally graded piezoelectric nanoplates. It is concluded that increasing gradient index parameter, nonlocal parameter, thickness ratio and compressive forces lead to a decrease in natural frequencies while rising tensile forces and aspect ratio increase the natural frequencies.