جستجوی مقالات مرتبط با کلیدواژه « بستر الاستیک » در نشریات گروه « مکانیک »

This article examines the effect of layer arrangement and fiber angles on the vibration behavior of cylindrical shell (FML) in GLARE and ARALL samples and on Pasternak elastic bed with different boundary conditions using 3D elasticity theory (composite/metal volume ratio is fixed in taken). The governing equations are obtained using the potential energy minimization principle. In order to ensure the accuracy and convergence of the results of this study, the numerical solution was done using the Finite Element Method (FEM). The results show that the layering has a great influence on the vibration behavior of the FML cylindrical shell. The results are in good agreement with other literature. The use of three-dimensional elasticity theory along with the analysis of different samples for the vibrations of reinforced FML shells, which is presented for the first time in this research, is one of the most important innovations of the current research, and these results can be used as a suitable criterion for analyzing and optimizing FML shells. It can be used with any number of metal and composite layers, any fiber placement angle and under any boundary conditions.

In this paper, the free vibrations of functionally graded porous beams with simple boundary conditions on an elastic foundation in a thermal environment were studied using the theory of third-order shear deformation. The properties of the material are temperature dependent and continuously change in the direction of the thickness of the beam and according to the power law distribution of the volume fraction of the material constituents. The uniform porosity distribution at the cross section is examined. Hamilton's principle was used to obtain the governing equations of motion. In order to discretize these equations, the generalized differential quadrature method has been used. Here, the effect of various parameters such as heat field type, temperature difference, power law index, porosity volume fraction, slenderness ratio and elastic foundation parameters on the natural frequencies of a functionally graded porous beam was studied for simple boundary conditions. The results, in addition to showing these effects on the thermomechanical behavior of the beam, also confirm the accuracy of the numerical method used.

In this study, the buckling of functionally graded graphene platelet-reinforced porous nanocomposite plates with various shapes such as rectangular, elliptical, and triangular ones embedded in an elastic medium is analyzed. To mathematically model the considered plate and elastic foundation, the first-order shear deformation plate theory, and the Winkler-Pasternak model are used, respectively. Three types of graphene nanoplatelet distribution and porous dispersion patterns through the thickness direction are considered for the nanocomposite plate. The effective material properties are obtained via a micromechanical model. By writing the energy functional of the system and using the analytical P-Ritz method, the influences of porosity coefficient, the weight fraction of graphene nanoplatelets, elastic foundation coefficients, and also the length-to-width and thickness ratios on the critical buckling loads are analyzed. It is illustrated that the plate with the non-uniform porosity distribution pattern of the first type and first type of graphene nanoplatelets due to the greater concentration of graphene nanoplatelets on the upper and lower surfaces of the plate and the increase in the stiffness of the plate, it has higher critical buckling load. Also, the maximum critical buckling load is related to shear loading and the minimum critical buckling load is related to biaxial buckling load. Also, by increasing the porosity coefficient, the critical buckling loads of the plate associated with all patterns of graphene nanoplatelets are reduced.

In this study, the free vibrations of functionally graded graphene platelet-reinforced porous nanocomposite plates with various shapes such as rectangular, elliptical, and triangular ones embedded on an elastic foundation are analyzed. To mathematically model the considered plate and elastic foundation, the first-order shear deformation plate theory, and Pasternak model are used, respectively. Three types of graphene nanoplatelet distribution patterns and porous dispersion types through the thickness are considered for the nanocomposite plate. To obtain the effective material properties of the considered nanocomposite, a micromechanical model is employed. Then, the energy functional of considered functionally graded graphene platelet-reinforced porous nanocomposite plates are expressed, and the analytical P-Ritz method is used to solve the vibration problem corresponding to different shapes and boundary conditions, the influences of porosity coefficient, the weight fraction of graphene nanoplatelets, elastic foundation coefficients and also the lengths-to-width and -thickness ratios on the natural frequency are analyzed. It is illustrated that the plate with non-uniform and symmetric of first type porosity distribution pattern and the first type graphene nanoplatelets has a higher natural frequency. Also, by increasing the porosity coefficient, the natural frequency of the plate associated with all patterns of graphene nanoplatelets is reduced.

The purpose of the present work was to study the dynamic instability of a three-layered sandwich beam with flexible core and simply supported boundary conditions subjected to a periodic axial load resting on elastic foundation. A higher-order theory was used for analysis of sandwich beams. In this theory, the classical theory was used for the face sheets and quadratic and cubic functions were assumed for the core, respectively. The elastic foundation was modeled as Winkler’s type. The dynamic instability regions were investigated for simply supported conditions by Bolotin’s method. The governing equations derived by the principle of minimum potential energy. The results showed that the responses of the dynamic instability of the system were influenced by the excitation frequency, the foundation modulus and the angle of the plies. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory.

The aim of the present work is to determine the transverse deflection of a plate on the granular material under the impact of a ball. Through the analytical solution, the granular bed is equivalent to the elastic bed. The granular materials behave elastically by with a damping reaction under the impact loading. There are suggestions by literatures for introducing these elastic and damping effects which are used in the present work. The impact force is an intensive short duration force which is considered as a function of time and impact position. The equations of motion are derived by Hamilton's principle and the stress and strain relations are written by the first order shear theory and the vibration response of the plate is derived. Moreover, an experimental apparatus is designed to measure the plate deflection. Experimental parameters include the plate type and thickness, ball speed, impact position and granular thickness. The experimental data are used to validate the theoretical evaluations. The comparison of the evaluated and measured data shows that the theoretical model is acceptably gives the plate deflection.

In this paper, an approximate solution based on the Rayleigh’s method is sought to analyze the vibration behavior of Euler-Bernoulli cracked beam resting on an elastic foundation. The modeling of the elastic foundation is implemented using the Winkler elastic spring theory and the stiffness factor of the elastic spring is specified corresponding to material characteristics of the elastic foundation. The Dirac’s delta function is used to apply the crack opening mode in the equation of the Rayleigh in which the factor of this function can be identified in terms of the stiffness factor of an equivalent rotational spring by considering material and geometric parameters of the crack. In the present analysis, explicit relationships are originally established to obtain the natural frequency in three boundary conditions of simply supported-simply supported, clamped-free and clamped-clamped. In this method, the natural frequency of the first mode is determined as the ratio of the maximum enriched potential energy and the maximum kinetic energy. Based on these relationships, the effects of the crack depth, the crack position and the elastic foundation on the response of natural frequency of the beam are investigated. The results of the analysis demonstrate that increasing the crack depth decreases the natural frequency of the beam containing the crack; while the elastic foundation increases the natural frequency of the cracked beam. The comparison of the results of proposed relationships with those of full modeling of the structure in Abaqus software shows a great accuracy of the present analysis.

This study explores the free vibration analysis of a functionally-graded rectangular plate which has been reinforced by carbon nanotubes (CNT) using the novel theory of trigonometric higher-order shear deformation. Carbon nano-tubes have been distributed through the thickness direction in a linear, symmetric and non-symmetric fashion. The foundation pertaining to Pasternak , or rather duo-parameter, has been utilized in the modeling; moreover, the new mixtures rule has been used for estimating the plate properties. The governing equations have been derived using the Hamilton’s principle, and the Navier’s solution has been used for dealing with a rectangular plate boundary conditions. Lastly, the effects of diverse parameters have been examined upon the vibrational behavior of the plate, such as the different distributions of CNT and the geometric properties of the plate. The results show that the amount of natural frequencies rise in proportion with an increase in the ratio of thickness to the width of the plate (h/b); a decrease in the ratio of length to the width of the plate (a/b); as well as an increase in the coefficients of the elastic foundation, such that the changes in the amounts of natural frequencies will be tremendously decreased in proportion with K> 10000 and K> 1000, and such changes will not be tangible.Furthermore, the highest amounts of frequencies will be pertinent to the X distribution, and the lowest amounts of frequencies will be pertinent to the O distribution

This research studies the effect of hydro-static pressure on the free vibration of a circular plate in contact with an inviscid and bounded fluid. The plate is in bottom of rigid cylindrical vessel with clamped boundary condition. At first, the potential energy of the plate on elastic foundation is performed by solving the governing equation on circular plate with clamped boundary condition. Next, the governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. The natural frequencies and mode shapes of the plate are determined by applying the Rayleigh-Ritz method on the total energy of the system. The effects of the parameters such as fluid height, fluid density, plate thickness to its radius ratio, and wave numbers on the natural frequencies and mode shapes are investigated. Comparison of analytically outcome of this study is made with results of the experimental modal test.

In this paper, free vibration of functionally graded carbon nanotube annular sector plates is studied. Distribution of carbon nanotubes is continuous and meaningful and gradual changes of materials in the direction of thickness are in the form of volume fraction. Annular sector plate is placed on the Winkler-Pasternak two parameters elastic foundation. The motion equations of plate are derived using the Hamilton principle and the refined plate theory. These coupled differential equations are transformed to ordinary equations using the trigonometric series expansion of space variation functions and then are solved with the help of differential quadrature method. The obtained results are compared with the other researcher’s results and an excellent agreement can be observed between them. Finally, the effects of different geometric parameters, different distributions of carbon nanotubes in the thickness direction, elastic foundation, and also different boundary conditions on the natural frequencies are investigated.

Free vibration characteristics of functionally graded materials cylindrical shells surrounded by elastic medium under axial force, lateral pressure and different boundary conditions using wave propagation method are investigated in this paper. The material properties of functionally graded materials are assumed to be graded in the thickness direction according to the power law. The elastic medium is assumed as two-parameter Pasternak elastic foundation. Governing equations based on the first order shear deformation theory of Sanders-Koiter for the cylindrical shell resting on elastic foundation under mechanical loads are derived by using Hamilton’s principle. By assuming displacement field in wave propagation form, governing equations are solved. Natural frequencies of cylindrical shell under various boundary conditions are obtained and compared with the results in the literature. It is seen that using displacement field in wave propagation form, acts as an effective and reliable method and gives the acceptable results for various boundary conditions. Although it is shown that for different boundary conditions and geometry dimensions, accuracy of the wave propagation approach is different. In addition, based on the developed theory the effects of different boundary conditions, axial force, lateral pressure and elastic foundation parameters on vibration behavior of functionally graded cylindrical shell are investigated.

The free vibration of a rotating Timoshenko nanobeam with a variable cross section on elastic foundation is investigated using the differential quadrature method. For more accuracy, the Timoshenko beam theory is applied where the effects of the shear deformation and rotary inertia are considered. First, the Eringen nonlocal elasticity theory is investigated briefly and the governing differential equations of motion of a Timoshenko nanobeam are derived considering the nonlocal scale parameter, variable cross section and rotation of the nanobeam. Then, by applying the nondimensional parameters, the equations are obtained in the nondimensional form and then, they are rewritten in the differential quadrature form. Finally, by solving these equations, the natural frequencies of the system are obtained. A number of parametric studies are conducted to assess the effects of the nonlocal scaling parameter, rotational speed, hub radius, and the stiffness coefficients of the elastic foundation on the natural frequencies of the system. By neglecting some parameters to reach a simpler model, the results are validated against those reported in the literature where a reasonably good agreement is observed.

The eccentrically stiffened cylindrical shells are one of the most important structures in aerospace industries. In this paper, semi-analytical method for eccentrically stiffened functionally graded (FG) cylindrical shells under external pressure and surrounded by an elastic medium is presented. The proposed model is based on Winkler and Pasternak elastic foundation parameters. According to the Von Karman nonlinear equations and the classical plate theory (CPT) of shells, strain displacement relations are obtained. The smeared stiffeners technique and Galerkin method, used for solving nonlinear dynamic problem. With considering three terms approximation for the deflection shape, the frequency-amplitude relation for non-linear vibrations obtained. The nonlinear dynamic response is obtained from fourth order Runge-Kutta method. The nonlinear dynamic buckling behavior of stiffened FGM shells is investigated based on the Budiansky-Roth criterion. The effect of parameters such as eccentrically stiffened, elastic foundation and excitation force on the frequency-amplitude curve of the nonlinear vibrations and parameters such as damping and loading speed on the nonlinear dynamic response of the FGM cylindrical shells have been investigated. The natural frequency, static and dynamic buckling load are analyzed, too.

In this research, the nonlinear buckling analysis of Functionally Graded (FG) nano-composite beam reinforced by various distributions of Boron Nitrid Nanotube (BNNT) is investigated under electro-thermodynamical loading with considering initial geometrical imperfection. The analysis is performed based on nonlocal elasticity theory and using the Finite Element Method (FEM). Various distributions of BNNT along the beam’s thickness are considered as uniform and decreasing-increasing functionally graded; and the extended mixture model is used to estimate the properties of nano-composite beam. The elastic medium around the smart nano-composite beam is modeled as elastic foundation. The governing equations of equilibrium are derived using energy method and nonlocal elasticity theory; and the critical buckling load is obtained for various boundary conditions such as simply-simply supported (S-S) and clamped-clamped (C-C) using the FEM. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of nano-composite beam increases and consequently the stability of the system increases. The effect of FG-X distribution type is more than uniform distributions. Also, the critical buckling load of nano-composite beam increases with an increase in the electric field and elastic foundation.

Exact and numerical solution of eccentrically stiffened panels in the industry is a major step forward in the design of these structures. This paper presents an analytical approach to investigate the nonlinear stability analysis of eccentrically stiffened thin FG cylindrical panels on elastic foundations subjected to hygro-thermo-mechanical loads. The stiffeners are assumed to be spiral-type. The panel has the initial geometrical imperfection. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution. The elastic foundation is considered based on Winkler and Pasternak proposed model. Governing equations are derived basing on the Lekhnitsky smeared stiffeners technique and classical shell theory incorporating Von Karman-Donnell geometrical type nonlinearity. Explicit relations of load–deflection curves for FG cylindrical panels are determined by applying stress function and Galerkin method. The effects of angel of stiffener, different dimensional parameters, volume fraction index, initial geometrical imperfection, the stiffness of elastic foundation and moisture concentration on the postbuckling of FG panel are investigated. Also effects of temperature gradient through the thickness and effects of different boundary conditions are investigated for thermo-mechanical loading. The obtained results are validated by comparing with those in the literature.

In this article, free vibration analysis of functionally graded cylindrical nanoshell on the basis of the modified couple stress theory is investigated. The nanoshell is embedded in an elastic Pasternak medium, which is obtained by adding a shear layer to the Winkler model. In addition, the boundary conditions at two ends of cylindrical nanoshell are simply supported. It is assumed that the functionally graded cylindrical nanoshell, is made of aluminum and ceramic, follows the volume fraction definition and law of mixtures, and its properties change as a power function through its thickness. Governing equations and boundary conditions are obtained by applying the Hamilton’s principle and are based on first-order shear deformation. Navier solution is used for predicting the natural frequencies of functionally graded cylindrical nanoshell. Finally, the effect of parameters such as material length scale, circumferential wave number, the length to radius ratio, shear correction factor, power low index and elastic foundation coefficients of Winkler and Pasternak on natural frequency of functionally graded cylindrical nanoshell are identified. The results show, there is a very good agreement between the results of molecular dynamics simulations by previous researchers with the results of this study.

In the present paper, buckling of multi-layer rectangular orthotropic composite plates with two longitudinal or transverse in-plane circular cutouts, on Winkler-Pasternak elastic foundation, is investigated. The analysis is accomplished through two steps. First, the in-plane pre-buckling stress components induced by the partial edge loads are determined and in the second stage, the Galerkin method is employed to develop the governing equations of the buckling. In this regard, the classical theory of plates, von Karman strain-displacement equations, Galerkin and energy approaches, and reduction of the problem to an eigenvalue problem are used. The buckling load is determined based on various relative locations of the cutouts and the: (1) uniform partial, (2) sinusoidal partial, and (3) concentrated edge loads, for the movable simply supported and clamped edge conditions. Furthermore, influence of the elastic foundation of the composite plate is investigated for different concentrated and partial loads. Results reveal that buckling of plates with holes or cutouts is dependent on opposite factors and may occur in local or global forms and the elastic foundation has pronounced effects of on the buckling load. This effect is more noticeable when the partial load is distributed on a larger length of the edge.

In this article, nonlinear buckling analysis of nonlocal boron nitride Timoshenko nano beam on elastic foundation based on Modified couple stress theory, nonlocal elasticity Eringen’s model, and Von karman nonlinear geometry theory are investigated. The governing equation of motion and boundary conditions based on Hamilton’s principle are obtained. To solve the governing equation of motion, the differential quadrature method (DQM) is used to obtain the critical buckling load for two edges simply supported
(S-S) and simply supported-clamped (S-C) boundary conditions. The results of this research are compared with the obtained results by Murmu et al. that there is a good agreement between them. Finally, the effects of various parameters such as nonlocal Eringen’s parameter, slenderness ratio of nano beam, elastic foundation constants, electric field, temperature changes and material length scale parameter on the nonlocal critical buckling load of Timoshenko nano beam are illustrated. The results show that with increasing nonlocal parameter, slenderness ratio, electric field, and temperature changes, the critical buckling load decreases, while this results vice versa for elastic foundation constants and material length scale parameter. The critical buckling load for S-S boundary condition is lower than that of for S-C boundary condition.

In this paper, buckling and free vibration analysis of cylindrical panel reinforced by various distributions of carbon nanotubes (CNTs) on elastic foundation for two cases including uniform distributed (UD) and functionally graded (FG) is studied. Based on the first order shear deformation theory (FSDT), the equilibrium equations of cylindrical panel reinforced by CNTs are derived using energy method and Hamilton’s principle. Then, using Navier’s type solution, the governing equations of equilibrium for cylindrical panel reinforced by various distributions of CNTs are solved. Using the mixture rule, the material properties of cylindrical panel reinforced by CNTs are estimated. In this study, the effects of volume fraction, various distributions of CNTs, elastic foundation parameters on the critical buckling load and natural frequency of cylindrical panel reinforced with CNTs are investigated. The obtained results of this research indicate that the trend of increasing natural frequency leads to increase in the percentage of CNTs and elastic modulus parameters which the maximum natural frequency occurs for FG-X case. Also increasing the percentage of CNTs and elastic modulus parameters leads to increase the critical buckling load which the maximum and minimum values of this load take place for FG-X and FG-O, respectively. On the other hands, it can conclude that with suitable selecting of CNTs distributions and volume fraction, the stiffness of structures increases and then the critical buckling load and natural frequencies enhance. Thus this point is noticeable to design the optimum of structures at nanoscale.

In this paper, Asymmetric buckling analysis of functionally graded (FG) Circular plates with temperature dependent property that subjected to the uniform radial compression and thermal loading is investigated. This plate is on an elastic medium that simulated by Winkler and Pasternak foundation. Mechanical properties of the plate are assumed to vary nonlinearly by temperature change. The equilibrium equations are obtained using the classical plate theory (CPT), Von Karman geometric nonlinearity and virtual displacement method. Existence of bifurcation buckling is examined and stability equations are obtained by means of the adjacent equilibrium criterion. The effects of elastic foundation coefficient, thickness to radius, power law index, and temperature-dependency of the material properties on critical buckling load of FG plates are presented. The results of the present work have been compared with the results of other investigator and the results of the comparison are very good. It is found that by increasing temperature, critical buckling load decreases. It is also concluded that the critical buckling load of (FG) Circular plates increases with an increase in the Winkler and Pasternak constants of elastic foundation.