Sharif Digital Repository

In the present study, an attempt is made to present the governing equations on the post-buckling of two-dimensional (2D) FGP beams and propose appropriate optimization procedure to achieve optimal post-buckling behavior and mass. To this end, Timoshenko beam theory, Von-Karman nonlinear relations, virtual work principle, and generalized differential quadrature method are considered to derive and solve governing equations and associated boundary condition (Hinged–Hinged) for an unknown 2D porosity distribution. Proposed method is validated using the papers in the literature. The optimization procedure including defining porosity distributions (interpolations), post-buckling function and... 

In this study, buckling and vibrational characteristics of a nanoshell reinforced with graphene nanoplatelets under uniform axial load are investigated. The material properties of the piece-wise graphene-reinforced composites (GPLRCs) are assumed to be graded in the thickness direction of a nanoshell and are estimated using a nanomechanical model. The effects of the small scale are analyzed based on nonlocal stress–strain gradient theory (NSGT). The governing equations and boundary conditions (BCs) are developed using Hamilton’s principle and are solved with assistance of the generalized differential quadrature method. The novelty of the current study is the consideration of GPLRC and size... 

In this article, vibrational behavior and critical voltage of a spinning cylindrical thick shell covered with piezoelectric actuator (PIAC) carrying spring-mass systems are investigated. It should be noted that, the installed sensors on the proposed systems are considered as a tip mass. This structure rotates about axial direction and the formulations include the Coriolis and centrifugal effects. In addition, various cases of thermal (uniform, linear, and nonlinear) distributions are studied. The modeled cylindrical thick shell covered with PIAC, its equations of motion, and boundary conditions are derived by the principle of minimum total potential energy and based on a new... 

In this study, a periodic beam-like structure consisting of the horizontal and inclined beam elements is proposed. Three models with three different angles of inclination are considered. The generalized differential quadrature (GDQ) and generalized differential quadrature rule (GDQR) methods are used to solve the differential equations of longitudinal and transverse vibrations, respectively. The effects of two geometrical parameters on the first three band gaps of each model are investigated, comprehensively. Results show that this periodic structure has wide band gaps at low frequency ranges. Furthermore, the band gaps can get close to each other by changing the geometrical parameters.... 

In this study, a periodic beam-like structure consisting of the horizontal and inclined beam elements is proposed. Three models with three different angles of inclination are considered. The generalized differential quadrature (GDQ) and generalized differential quadrature rule (GDQR) methods are used to solve the differential equations of longitudinal and transverse vibrations, respectively. The effects of two geometrical parameters on the first three band gaps of each model are investigated, comprehensively. Results show that this periodic structure has wide band gaps at low frequency ranges. Furthermore, the band gaps can get close to each other by changing the geometrical parameters.... 

Free vibration response of a joined shell system including cylindrical and spherical shells is analyzed in this research. It is assumed that the system of joined shell is made from a functionally graded material (FGM). Properties of the shells are assumed to be graded through the thickness. Both shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first-order shear deformation theory of shells is used. The Donnell type of kinematic assumptions is adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations is... 

This is the first research on the frequency analysis of a graphene nanoplatelet composite circular microplate in the framework of a numerical-based generalized differential quadrature method. Stresses and strains are obtained using the higher order shear deformation theory. The microstructure is surrounded by a viscoelastic foundation. Rule of the mixture is used to obtain varying mass density and Poisson’s ratio, whereas the module of elasticity is computed by a modified Halpin–Tsai model. Governing equations and boundary conditions of the graphene nanoplatelet composite circular microplate are obtained by implementing Hamilton’s principle. The results show that outer to inner radius ratio... 

Damping characteristics of three-layered sandwich cylindrical shells with the focus on mode switching phenomenon are investigated in the present study. All layers of the sandwich cylinder are formulated based on the first-order shear deformation theory. Considering the von Karman strain displacement relations, the nonlinear equations of motion are derived through Hamilton’s principle. By separating the displacement components into previbration and vibration states and substituting in the obtained nonlinear equations of motion, the previbration equilibrium equations and vibration equations of motion are obtained. The acquired equations are solved by applying the generalized differential... 

Due to the remarkable progress in the field of the manufacturing process, smart composites have become the desired target for high-tech engineering applications. Accordingly, for the first time, thermal buckling, critical voltage and vibration response of a thermally affected graphene nanoplatelet reinforced composite (GPLRC) microdisk in the thermal environment are explored with the aid of generalized differential quadrature method (GDQM). Also, the current microstructure is coupled with a piezoelectric actuator (PIAC). The extended form of Halpin-Tsai micromechanics is used to acquire the elasticity of the structure, whereas, the variation of thermal expansion, Poisson’s ratio, and density... 

This is the first research on the free vibration analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) viscoelastic annular plate resting on the visco-Pasternak foundation and subjected to the nonlinear temperature gradient and mechanical loading within the framework of higher-order shear deformation theory (HSDT). Hamilton's principle is employed to establish governing equations within the framework of HSDT. In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Generalized differential quadrature method (GDQM) is applied... 

This is the first research on the nonlinear frequency analysis of a multi-scale hybrid nanocomposite (MHC) disk (MHCD) resting on an elastic foundation subjected to nonlinear temperature gradient and mechanical loading is investigated. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. We present a modified Halpin–Tsai model to predict the effective properties of the MHCD. The displacement–strain of nonlinear vibration of multi-scale laminated disk via third-order shear deformation theory (TSDT) and using Von Karman nonlinear shell theory is obtained. Hamilton’s principle is employed to establish the governing... 

In this research, electrically characteristics of a graphene nanoplatelet (GPL)-reinforced composite (GPLRC) microdisk are explored using generalized differential quadrature method. Also, the current microstructure is coupled with a piezoelectric actuator (PIAC). The extended form of Halpin–Tsai micromechanics is used to acquire the elasticity of the structure, whereas the variation of thermal expansion, Poisson’s ratio, and density through the thickness direction is determined by the rule of mixtures. Hamilton’s principle is implemented to establish governing equations and associated boundary conditions of the GPLRC microdisk joint with PIAC. The compatibility conditions are satisfied by... 

This is a fundamental study on the nonlinear vibrations considering large amplitude in multi-sized hybrid Nano-composites (MHC) disk (MHCD) relying on nonlinear elastic media and located in an environment with gradually changed temperature feature. Carbon fibers (CF) or carbon nanotubes (CNTs) in the macro or nano sizes respectively are responsible for reinforcing the matrix. For prediction of the efficiency of the properties MHCD's modified Halpin-Tsai theory has been presented. The strain-displacement relation in multi-sized laminated disk's nonlinear dynamics through applying Von Karman nonlinear shell-theory and using third-order-shear-deformation-theory (TSDT) is determined. The energy... 

In this research, buckling and vibrational characteristics of a spinning cylindrical moderately thick shell covered with piezoelectric actuator carrying spring-mass systems are performed. This structure rotates about axial direction and the formulations include the Coriolis and centrifugal effects. In addition, various cases of thermal (uniform, linear, and nonlinear) distributions are studied. The modeled cylindrical moderately thick shell covered with piezoelectric actuator, its equations of motion, and boundary conditions are derived by the Hamilton's principle and based on a moderately cylindrical thick shell theory. For the first time in the present study, attached mass-spring systems... 

This paper presents a solution to the boundary stabilization of a FGM plate in free transverse vibration. The composite laminated plate dynamics is presented by a linear forth order partial differential equation (PDE). A linear control law is constructed to stabilize the plate. The control force consists of feedback of the velocity at the boundaries of plate. The novelty of this article is that it is possible to stabilize asymptotically a free transversely vibrating composite plate with simply supported or clamped boundary condition via boundary control without resorting to truncation of the model. © 2008 IEEE  

In this paper, a new linear theory for bending stress-strain analysis of a cracked beam has been developed. A displacement field has been suggested for the beam strain and stress calculations. The bending differential equation for the beam has been written using equilibrium equations. The required constant for this model is also obtained from fracture mechanics. The bending equation has been solved for a simply supported beam with rectangular cross-section and the results are compared with finite element and empirical results. There is an excellent agreement between theoretical results and those obtained by numerical and empirical methods. The model developed in this research is a simple and... 

A new meshless method called gradient reproducing kernel particle method (GRKPM) is proposed for numerical solutions of one-dimensional Burgers' equation with various values of viscosity and different initial and boundary conditions. Discretization is first done in the space via GRKPM, and subsequently, the reduced system of nonlinear ordinary differential equations is discretized in time by the Gear's method. Comparison with the exact solutions, which are only available for restricted initial conditions and values of viscosity, approves the efficacy of the proposed method. For challenging cases involving small viscosities, comparison with the results obtained using other numerical schemes... 

In this paper, the systematic error due to interpolation in CMOS deep sub micron folding and interpolating ADC is studied and a closed form equation is presented to calculate the error as a function of interpolation coefficient, input voltage range and the number of input differential pairs. The amount of INL due to interpolation error can be considered as the lower bound for attainable INL of a specific ADC architecture. A case study for an 8_bit ADC is treated under consideration of different folding and interpolating factors. The trade off between power dissipation and ADC performance is characterized according to input stage characteristics. ©2006 IEEE  

Due to the rapid development of process manufacturing, composite materials with graphene-reinforcement have obtained commercially notices in promoted engineering applications. For this regard, vibrational characteristics of a cylindrical nanoshell reinforced by graphene nanoplatelets (GPL) and coupled with piezoelectric actuator (PIAC) is investigated. Also, the nanostructure is embedded in a viscoelastic medium. The material properties of piece-wise graphene-reinforced composite (GPLRC) are assumed to be graded in the thickness direction of a cylindrical nanoshell and estimated through a nanomechanical model. For the first time in the current study is considering the effects of... 

This survey addresses the non-polynomial framework for bending responses of three-phase multi-scale hybrid laminated nanocomposite (MHLNC) reinforced circular/annular plates (MHLNCRCP/ MHLNCRAP) based upon the three-dimensional theory of elasticity for various sets of boundary conditions. The sandwich structure with two, three, five, and seven layers is modeled using compatibility conditions. The state-space based differential quadrature method (SS-DQM) is presented to examine the bending behavior of MHLNCRCP/ MHLNCRAP by considering various boundary conditions. Halpin–Tsai equations and fiber micromechanics are used in the hierarchy to predict the bulk material properties of the multi-scale...