فهرست مطالب اکبر علی بیگلو

Due to important role of composite materials in broad spectrum of applications, this paper focused on bending of a functionally graded graphene platelet reinforced composite porous circular/annular plates with various boundary conditions by employing state-space differential quadrature method (DQM). Equations of motion are established within the framework of theory of elasticity and are formulated along the thickness direction in the form of state-space. Applying DQM along the radial direction provides a semi-analytical solution to bending of the plate. The results of applying present approach are validated by comparing them with those reported in the literature. A thorough parametric investigation is conducted on the effects of different GPLs distributions integrated with various distribution patterns of internal porosity, thickness to radius ratio, graphene platelets (GPLs) weight fraction, porosity coefficient and edge boundary conditions on the bending behavior of FG-GPLRC circular/annular plates. The results reveal a very useful practical designing hint that locating more GPLs in the vicinity of the upper and bottom surfaces of the circular/annular plates with lower outer radius to thickness.

This paper analyzes the size-dependent vibration of nanoscale beams with simultaneously longitudinal and rotational motions based on nonlocal theory for the optimum design of nanoscale surgical robots. Also, for the first time, a parametric study is performed to explain the surface effects, viscoelastic-Pasternak foundations characteristics, thermal loads, geometric properties, symmetric and asymmetric cross-sections, axial and follower loads on the dynamics and stability of the system. Adopting the Galerkin discretization approach, the reduced-order dynamic model of the system is acquired. Also, analytical and numerical methods are exploited. To ensure the accuracy of the proposed model and method, the present study results are compared and validated with those of published articles. Stability maps and Campbell diagrams are drawn for different working conditions. The results showed that increasing the surface elastic modulus and residual stress improves the vibration frequencies and dynamic instability threshold. It is also found that with increasing system thickness/length, the axial velocity of static instability decreases/increases. In addition, it is observed that the system performance improves with increasing the elastic and shear coefficients of the foundation. The results of the present study significantly help designers and engineers control the vibration of bi-gyroscopic nanoscale robots.

The vibration of axially graded Rayleigh and Euler-Bernoulli micro-beams under a moving load on Pasternak foundation is studied numerically and analytically. Accurate mathematical modeling is acquired to analyze the effect of various parameters such as longitudinal gradient parameter of material, whirling inertia factor, the stiffness of Pasternak foundation, and strain gradient parameter on the critical velocity, and cancellation mechanism and the maximum amplitude of vibrations. Natural frequencies are obtained and compared with available results in the technical literature. Closed-form expressions are extracted for dynamic magnification coefficient and maximum amplitude of free vibration. The changes in material characteristics of the system have inverse influences on the amplitude of free and forced vibrations for lower and higher values of the critical gradient parameters. It is concluded that in comparison with homogenous Euler-Bernoulli beams, in the axially graded Rayleigh micro-beams surrounded by shear Pasternak foundation. It can be controlled the cancellation and maximum free vibration phenomenon, by choosing the accurate values of gradient parameter, whirling inertia coefficient, the stiffness of foundation, and strain gradient parameter. Also, the results of the present study can be used as a criterion for the optimal design of heterogeneous structures under the moving loads.

For the first time, in this work, Vibrations of the axially graded Rayleigh moving beams are studied. It is supposed that the material characteristics of the system change linearly or exponentially in longitudinal direction continuously. By using Galerkin method and eigenvalue problem, the natural frequencies and divergence of the system are computed numerically. In addition, the analytical relations are extracted for the critical velocity of the system. Critical velocity contours and stability maps are investigated for different distributions of material. As indicated, exponential and linear changes lead to a more stable system in the variable state of density and elastic modulus, respectively. Also, the results indicated that increasing the elastic modulus gradient parameter or decreasing the density gradient parameter results in an increase in the natural frequency of the system and a development in the stability. Hence, alteration in the density and elastic modulus gradient parameters has an opposite role in the dynamic behavior of the system. The results of this study can be useful for designing and optimizing high speed non-homogeneous axial movable structures.

This paper is carried out the free vibrational behavior of functionally graded polymer composite annular and circular plates reinforced with graphene nanoplatelets (GPLs) using three-dimensional elasticity theory. The weight fraction differs gradually across the thickness direction. Effective elasticity modulus of the nanocomposite has been estimated by the modified Halpin-Tsai model. Five different GPLs distribution patterns within the polymer matrix are considered.  State space first order differential equation by employing the equation of motion and constitutive relation within the framework of three-dimensional elasticity theory across the thickness direction is derived. Present approach is validated by comparing the numerical results with those reported in the literature. Influence of outer radius to thickness ratio, different GPL distribution patterns, GPLs loading and edge boundary conditions on the vibrational behavior of GPLs reinforced composite (GPLRC) circular/annular plates are studied. The results implied that GPLs with a low content can have an excellent influence on the natural frequencies of the circular and annular plate.

In this paper, in order to improve the efficiency of the moving systems, vibrations and stability of axially functionally graded Rayleigh moving micro-beams are studied. Also, to clarify the influences of various parameters such as axially functionally graded, the length of the material characteristics, and the whirling inertia on the stability boundaries of Rayleigh and Euler-Bernoulli beams, a detailed parametric study is done. It is assumed that the material characteristics of the system change linearly or exponentially in longitudinal direction continuously. To calculate the natural frequencies, dynamics configuration, and divergence and flutter instability thresholds of the system, the strain gradient theory, Galerkin discretization method, and an eigenvalue problem are utilized. In addition, the analytical relations are extracted for the critical velocity of the system. Critical velocity contours and stability maps are examined for different distributions. It is demonstrated that the exponential and linear changes lead to a more stable system in the variable state of density and elastic modulus, respectively. Also, the results indicated that increasing the elastic modulus gradient parameter or decreasing the density gradient parameter results in an increase in the natural frequency of the system and a development in the stability regions. Hence, the alteration in the density and elastic modulus gradient parameters has an opposite role in the dynamic behavior of the system.

In this paper thermoelastic behavior of a functionally graded material (FGM) conical shell with clamped edges condition is investigated. Material properties vary according to power law along the thickness direction. Thermo elastic properties of the shell are assumed to vary along the thickness by a power law distribution with Poisson ratio is held to be constant. By using first order shear deformation theory، strain-displacement relations and constitutive equations، governing differential equations can be derived in term of mid radius displacements and rotation. By using the differential quadrature method (DQM) the obtained governing equations can be solved. To validate the accuracy of the present procedure، numerical results were compared with those available in published literature. Finally the effect of gradient index، geometry dimension and thermo mechanical load on the bending behavior of conical shell is considered.

Conventional Ritz and Galerkin methods based on local theory of elasticity employ polynomials as their approximating functions, however these methods are not convenient to use in three-dimensional nonlocal analysis. In the present study, to conquer this difficulty, a type of weighted residual approach with a set of trigonometric approximating functions were developed. By using appropriate trigonometric approximating functions, it is possible to consider the effect of various edges boundary condition on frequency behavior of nanoplate. Validation of present formulation is carried out by comparing numerical result with the published results. It is concluded that the effect of nonlocal parameter on natural frequencies is significant especially in higher modes due to the lower wavelength of the mode. The research shows that in nonlocal elasticity there are distinct discrepancies between behaviors of two and three-dimensional results. In addition, the difference between the two- and three-dimensional results in local elasticity is not as noticeable as in nonlocal elasticity. Furthermore, the effects of length to thickness ratio, aspect ratio, nonlocal parameter and different boundary conditions on fundamental natural frequency of nanoplates were studied. This benchmark solution can be used to assess the accuracy of conventional two-dimensional theories.

In this research, dynamic behavior of non-linear finite element model of a drillstring is investigated. By considering total length of drillstring, a three-dimensional timoshenko beam element is employed. In addition the geometric stiffening effect, the added fluid mass and the contact between different parts of the drillstring and the borehole wall has been considered, with a complete model the effects of these factors have been analyzed separately. The equation of motion obtained and full order equations are used to drive the results. For the first time, a domain of drillstring that contact more possibility to occur in this domain is identified. The natural frequencies of the drillstring are evaluated and compared with the available commercial software results and recorded results for the actual drillstring. Coupling of vibrations of model is tested and the effect of linear and non-linear model in analysis of dynamic behavior and vibration of drillstring, especially in contact with the borehole wall and the effect of weight on bit change on the contact at stabilizers are analyzed and for the first time the contact time in each of stabilizers have been evaluated.

In this article, an improved 3D finite element (FE) model of low velocity transverse impact on armchair and zigzag single-walled carbon nanotubes (SWNTs) has been developed. Numerical examples for estimating the Young’s modulus of nanotubes are presented based on explicit and implicit analysis to illustrate the accuracy of this simulation technique. Based on explicit finite element model, the maximum dynamic deflections of single-walled carbon nanotubes with different boundary conditions, geometries as well as chiralities are obtained and then compared with theory investigation. Impact of a mass on simply supported and clamped nanobeams are investigated by using nonlocal Euler–Bernoulli and Timoshenko beam theory. The simulation results demonstrated good agreement with analytical results based on Euler–Bernoulli and Timoshenko nonlocal theory. When the aspect ratio is increased, the maximum dynamic deflection at the center of the beam is increased for both of the simply supported and the clamped-clamped nanobeams. The inclusion of the nonlocal effect increases the magnitudes of dynamic deflections. The dynamic deflections predicted by the classical theory are always smaller than those predicted by the nonlocal theory due to the nonlocal effects.

In this study, static and free vibration behaviors of two type of sandwich plates based on the three dimensional theory of elasticity are investigated. The core layer of one type is functionally graded (FG) with the homogeneous face sheets where as in second type the core layer is isotropic with the face sheets FG material. Plate is under uniform pressure at the top surface and free from traction in the bottom surface. The effective material properties of FG layers are estimated to vary continuously through the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. State space differential equations are obtained from equilibrium equations and constitutive relations. The obtained governing differential equations are solved by using Fourier series expansion along the in plane directions and state space technique across the thickness direction. Accuracy and exactness of the present approach is validated by comparing the numerical results with the published results. Furthermore it is possible to validate the exactness of the conventional two dimensional theories. Finally the influences of volume fraction, width-to-thickness ratios and aspect ratio on the vibration and static behaviors of plate are investigated.

In this paper، an analytical method is presented to study thermo-elastic behavior of nanoscale spherical shell subjected to thermal shock based on nonlocal elasticity theory. The shell is considered as elastic، homogeneous and isotropic solid. The nonlocal differential equation of motion is derived in terms of radial displacement. The analytical solution of equation of motion is obtained by Laplace transform and differential transform method (DTM). Mechanical boundary conditions are used to obtain unknown parameters that get in recurrence equation in Laplace domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform method (FLIT). Accuracy of obtained results is evaluated by well-known similar articles. The results have a good agreement in comparison with published data in pervious literatures. Also، the effects of nonlocal parameter and wall thickness of shell on the dynamic characteristics of nanoscale spherical shell are studied in various points across the thickness of shell under thermal shock. The present analytical method provides an appropriate field for analysis of times histories of radial and hoop stresses in a nanoscale shells subjected to various time dependent thermo-mechanical loads.

In this paper، the thermoelastic behavior of cylindrical sandwich shell with functionally graded (FGM) core under thermal shock is presented. Thermo mechanical properties of FGM layer are assumed to be independent of temperature and also، very continuously and smoothly functions in the radial direction as a nonlinear power function. The analytical solutions of governing partial differential equations for each layer of cylinder are solved by using Laplace transform and power series method. Mechanical boundary conditions and continuity equations for interfaces are used to obtain unknown parameters that get in recurrence equations for each layer of cylinder. The results in Laplace domain transferred to time domain by employing the fast inverse Laplace transform method (FLIT). The effects of FGM’s power on the dynamic characteristics of the FG thick sandwich cylindrical shell are studied in various points across the thickness of cylinder. The analytical presented method provides an appropriate field for analysis of transient radial and hoop stresses in a cylinder on various thermo mechanical load. Accuracy of gained equations is evaluated by similar articles. The results have a good agreement with published data in pervious researches.

In this paper, the vibration of composite cylindrical shell with piezoelectric layers in the interior and exterior surfaces is investigated. The composite shell without piezoelectric layers can be studied and compared the results with the results of other researchers, the cylindrical shell laminated with layers of piezoelectric vibration checked. The result is a three-dimensional elasticity equations relationships because they do not apply any approximate gain are quite analytical. Shells intended, is closed and has restricted the mainstays in the end it was simple, and the results for the ratio of the radius and the radius of the different thickness are obtained.

In this paper, the vibration characteristics of multi-layer shell that internal and external surfaces with a layer of piezoelectric sensor and actuator is investigated. The backrest shell laminated with simple analytical method to evaluate and the results were compared with results obtained by other researchers. The numerical solution methods (GDQ) for shells with piezoelectric layers and plain bearings, compared with analytical solution and then a variety of boundary conditions is studied. Using the equations of motion, the fundamental equations and relations Krnsh- displacement, State-space equations derived the equations using approximate separate layer, State-space equations with constant coefficients will become. These equations can be solved using natural frequencies in the backrest shell simple to obtain. If the abutments are not simple, solving equations differentials State-space analysis is not possible and should be used numerical methods. A fourth difference method numerical method common with the small number of sample points can be exact to achieve. By dq, State-space differential equations are solved and the non-traction conditions by applying high and low levels, can be found at the natural frequency. The direct and inverse piezoelectric effect, piezoelectric layer and composite layer thickness ratio of the radius of the middle of a thick crust on the vibrational behavior is studied.