فهرس المقالات Circular plate

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  1 - Effects of Viscosity on a Thick Circular Plate in Thermoelastic Diffusion Medium
  R Kumar Sh Devi
  10.22034/jsm.2019.667247
  The problem treated here is to determinethe viscosity effect on stresses, temperature change and chemical potential in a circular plate. The mathematical formulation is applied to two theories of thermoelastic diffusion developed by Sherief et al. [27] with one relaxati أکثر

  The problem treated here is to determinethe viscosity effect on stresses, temperature change and chemical potential in a circular plate. The mathematical formulation is applied to two theories of thermoelastic diffusion developed by Sherief et al. [27] with one relaxation time and Kumar and Kansal [9]with two relaxation times. Laplace and Hankel transform techniques are used to obtain the expression for the displacement components, stresses, temperature change and chemical potential. The resulting quantities are computed numerically and depicted graphically by using numerical inversion technique for a particular model. Effect of viscosity is shown in the normal stress, tangential stress, temperature change and chemical potential. Some particular cases of interest are also deduced. Viscoelastic materials play an important role in many branches of engineering, technology and, in recent years, biomechanics. Viscoelastic materials, such as amorphous polymers, semicrystalline polymers, and biopolymers, can be modelled in order to determine their stress or strain interactions as well as their temporal dependencies. تفاصيل المقالة
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  2 - Effect of Winkler Foundation on Radially Symmetric Vibrations of Bi-Directional FGM Non-Uniform Mindlin’s Circular Plate Subjected to In-Plane Peripheral Loading
  N Ahlawat R Lal
  10.22034/jsm.2019.1873720.1466
  An analysis has been presented of the effect of elastic foundation and uniform in-plane peripheral loading on the natural frequencies and mode shapes of circular plates of varying thickness exhibiting bi-directional functionally graded characteristics, on the basis of f أکثر

  An analysis has been presented of the effect of elastic foundation and uniform in-plane peripheral loading on the natural frequencies and mode shapes of circular plates of varying thickness exhibiting bi-directional functionally graded characteristics, on the basis of first order shear deformation theory. The material properties of the plate are varying following a power-law in both the radial and transverse directions. The numerical solutions of the coupled differential equations leading the motion of simply supported and clamped plates acquired by using Hamilton’s principle, is attained by harmonic differential quadrature method. The effect of different plate parameters namely gradient index, heterogeneity parameter, density parameter, taper parameter and thickness parameter is illustrated on the vibration characteristics for the first three modes of vibration for various values of in-plane peripheral loading parameter together with foundation parameter. Critical buckling loads in compression are calculated for both the boundary conditions by putting the frequencies to zero. The reliability of the present technique is confirmed by comparing the results with exact values and results of published work. تفاصيل المقالة
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  3 - Nonlinear Investigation of Magnetic Influence on Dynamic Behaviour of Non-Homogeneous Varying Thickness Circular Plates Resting on Elastic Foundations
  S.A Salawu G.M Sobamowo O.M Sadiq
  10.22034/jsm.2021.1912143.1650
  In this work, a nonlinear investigation of non-homogeneous varying thickness circular plates resting on elastic foundations under the influence of the magnetic fieldis investigated. The non-homogeneity of the circular plates’ material is presumed to occur due to l أکثر

  In this work, a nonlinear investigation of non-homogeneous varying thickness circular plates resting on elastic foundations under the influence of the magnetic fieldis investigated. The non-homogeneity of the circular plates’ material is presumed to occur due to linear and parabolic changes in Young’s modulus likewise the density along the radial direction in a unique manner. The geometric Von Kármán equations are used in modelling the governing differential equations. The transverse deflection is approximated using an assumed single term mode shape while the central deflection in form of Duffing’s equation is obtained using the Galerkin method. Subsequently, the semi-analytical solutions are provided using the Optimal Homotopy Asymptotic Method (OHAM), the analytical solutions are used for parametric investigation. The results in this work are in good harmony with past results in the literature. From the results, it is realized that the nonlinear frequency of the circular plate increases with an increase in the linear elastic foundation. Also, the results showed that clamped edge and simply supported edge condition produced the same hardening nonlinearity. However, varying taper and non-homogeneity lower the nonlinear frequency ratio. Also, maximum deflection occurs when excitation force is zero, and attenuation of deflection is observed due to the presence of a magnetic field, varying thickness, homogeneity, and elastic foundation. It is anticipated that the discoveries from this research will boost the design of structures subjected to vibration. تفاصيل المقالة
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  4 - A Problem of Axisymmetric Vibration of Nonlocal Microstretch Thermoelastic Circular Plate with Thermomechanical Sources
  R Kumar R Rani A Miglani
  10.22034/jsm.2019.664213
  In the present manuscript, we investigated a two dimensional axisymmetric problem of nonlocal microstretch thermoelastic circular plate subjected to thermomechanical sources. An eigenvalue approach is proposed to analyze the problem. Laplace and Hankel transforms are us أکثر

  In the present manuscript, we investigated a two dimensional axisymmetric problem of nonlocal microstretch thermoelastic circular plate subjected to thermomechanical sources. An eigenvalue approach is proposed to analyze the problem. Laplace and Hankel transforms are used to obtain the transformed solutions for the displacements, microrotation, microstretch, temperature distribution and stresses. The results are obtained in the physical domain by applying the numerical inversion technique of transforms. The results of the physical quantities have been obtained numerically and illustrated graphically. The results show the effect of nonlocal in the cases of Lord Shulman (LS), Green Lindsay (GL) and coupled thermoelasticity (CT) on all the physical quantities. تفاصيل المقالة
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  5 - Elastic Buckling of Moderately Thick Homogeneous Circular Plates of Variable Thickness
  S.K Jalali M.H Naei
  In this study, the buckling response of homogeneous circular plates with variable thickness subjected to radial compression based on the first-order shear deformation plate theory in conjunction with von-Karman nonlinear strain-displacement relations is investigated. Fu أکثر

  In this study, the buckling response of homogeneous circular plates with variable thickness subjected to radial compression based on the first-order shear deformation plate theory in conjunction with von-Karman nonlinear strain-displacement relations is investigated. Furthermore, optimal thickness distribution over the plate with respect to buckling is presented. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, employing the pseudospectral method that makes use of Chebyshev polynomials, the stability equations are solved. The influence of the boundary conditions, the thickness variation profile and aspect ratio on the buckling behavior is examined. The comparison shows that the results derived, using the current method, compare very well with those available in the literature. تفاصيل المقالة
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  6 - Vibration Analysis for Rectangular Plate Having a Circular Central Hole with Point Support by Rayleigh-Ritz Method
  K Torabi A.R Azadi
  In this paper, the transverse vibrations of rectangular plate with circular central hole have been investigated and the natural frequencies of the mentioned plate with point supported by Rayleigh-Ritz Method have been obtained. In this research, the effect of the hole i أکثر

  In this paper, the transverse vibrations of rectangular plate with circular central hole have been investigated and the natural frequencies of the mentioned plate with point supported by Rayleigh-Ritz Method have been obtained. In this research, the effect of the hole is taken into account by subtracting the energies of the hole domain from the total energies of the whole plate. To determine the kinetic and potential energies of plate, admissible functions for rectangular plate are considered as beam functions and it has been tried that the functions of the deflection of plate, in the form of polynomial functionsproportionate with finite degrees, to be replaced by Bessel function, which is used in the analysis of the vibrations of a circular plate. Consideration for a variety of edge conditions is given through a combination of simply supported, clamped and free boundary conditions. In this study, the effects of increasing the diameter of the hole and the effects of number of point supported on the natural frequencies were investigated and the optimum radius of the circular hole for different boundary conditions are obtained. The method has been verified with many known solutions. Furthermore, the convergence is very fast with any desirable accuracy to exact known natural frequencies. تفاصيل المقالة
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  7 - Transverse Vibration of Clamped and Simply Supported Circular Plates with an Eccentric Circular Perforation and Attached Concentrated Mass
  S.M Mirkhalaf Valashani
  In this investigation Rayleigh-Ritz variational method has been applied to determine the least natural frequency coefficient for the title problem. Classical plate theory assumptions have been used to calculate strain energy and kinetic energy. Coordinate functions are أکثر

  In this investigation Rayleigh-Ritz variational method has been applied to determine the least natural frequency coefficient for the title problem. Classical plate theory assumptions have been used to calculate strain energy and kinetic energy. Coordinate functions are combination of polynomials which satisfy boundary conditions at the outer boundary and trigonometric terms. In the second part of this study ABAQUS software is used to compute vibration natural frequency for some special combinations of geometrical and mechanical parameters. Then results of Rayleigh-Ritz method have been obtained for the mentioned special cases. It can be seen that the agreement between them is acceptable. تفاصيل المقالة
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  8 - A Semi-Analytical Solution for Free Vibration and Modal Stress Analyses of Circular Plates Resting on Two-Parameter Elastic Foundations
  M.M Alipour M Shariyat M Shaban
  In the present research, free vibration and modal stress analyses of thin circular plates with arbitrary edge conditions, resting on two-parameter elastic foundations are investigated. Both Pasternak and Winkler parameters are adopted to model the elastic foundation. Th أکثر

  In the present research, free vibration and modal stress analyses of thin circular plates with arbitrary edge conditions, resting on two-parameter elastic foundations are investigated. Both Pasternak and Winkler parameters are adopted to model the elastic foundation. The differential transform method (DTM) is used to solve the eigenvalue equation yielding the natural frequencies and mode shapes of the circular plates. Accuracy of obtained results is evaluated by comparing the results with those available in the well-known references. Furthermore, effects of the foundation stiffness parameters and the edge conditions on the natural frequencies, mode shapes, and distribution of the maximum in-plane modal stresses are investigated. تفاصيل المقالة
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  9 - Thermo-Elastic Analysis of Non-Uniform Functionally Graded Circular Plate Resting on a Gradient Elastic Foundation
  A Behravan Rad
  Present paper is devoted to stress and deformation analyses of heated variable thickness functionally graded (FG) circular plate with clamped supported, embedded on a gradient elastic foundation and subjected to non-uniform transverse load. The plate is coupled by an el أکثر

  Present paper is devoted to stress and deformation analyses of heated variable thickness functionally graded (FG) circular plate with clamped supported, embedded on a gradient elastic foundation and subjected to non-uniform transverse load. The plate is coupled by an elastic medium which is simulated as a Winkler- Pasternak foundation with gradient coefficients in the radial and circumferential directions during the plate deformation. The temperature distribution is assumed to be a function of the thickness direction. The governing state equations are derived in terms of displacements and temperature based on the 3D theory of thermo-elasticity. These equations are solved using a semi-analytical method to evaluate the deformation and stress components in the plate. Material properties of the plate except the Poisson's ratio are assumed to be graded continuously along the thickness direction according to an exponential distribution. A parametric study is accomplished to evaluate the effects of material heterogeneity indices, foundation parameters, temperature difference between the top and bottom surfaces of the plate and thickness to radius ratio on displacements and stresses. The results are reported for the first time and the new results can be used as a benchmark solution for the future researches. تفاصيل المقالة
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  10 - A Power Series Solution for Free Vibration of Variable Thickness Mindlin Circular Plates with Two-Directional Material Heterogeneity and Elastic Foundations
  M.M Alipour M Shariyat
  In the present paper, a semi-analytical solution is presented for free vibration analysis of circular plates with complex combinations of the geometric parameters, edge-conditions, material heterogeneity, and elastic foundation coefficients. The presented solution cover أکثر

  In the present paper, a semi-analytical solution is presented for free vibration analysis of circular plates with complex combinations of the geometric parameters, edge-conditions, material heterogeneity, and elastic foundation coefficients. The presented solution covers many engineering applications. The plate is assumed to have a variable thickness and made of a heterogeneous material whose properties vary in both radial and transverse directions. While the edge is simply-supported, clamped, or free; the bottom surface of the plate is resting on a two-parameter (Winkler-Pasternak) elastic foundation. A comprehensive sensitivity analysis including evaluating effects of various parameters is carries out. Mindlin theory is employed for derivation of the governing equations whereas the differential transform method is used to solve the resulted equations. In this regard, both the in-plane and rotary inertia are considered. Results show that degradations caused by a group of the factors (e.g., the geometric parameters) in the global behavior of the structure may be compensated by another group of factors of different nature (e.g, the material heterogeneity parameters). Moreover, employing the elastic foundation leads to higher natural frequencies and postponing the resonances. تفاصيل المقالة
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  11 - Stress Analysis of Two-directional FGM Moderately Thick Constrained Circular Plates with Non-uniform Load and Substrate Stiffness Distributions
  M.M Alipour M Shariyat
  In the present paper, bending and stress analyses of two-directional functionally graded (FG) circular plates resting on non-uniform two-parameter foundations (Winkler-Pasternak foundations) are investigated using a first-order shear-deformation theory. To enhance the a أکثر

  In the present paper, bending and stress analyses of two-directional functionally graded (FG) circular plates resting on non-uniform two-parameter foundations (Winkler-Pasternak foundations) are investigated using a first-order shear-deformation theory. To enhance the accuracy of the results, the transverse stress components are derived based on the three dimensional theory of elasticity. The solution is obtained by employing the differential transform method (DTM). The material properties are assumed to vary in both transverse and radial directions according to power and exponential laws, respectively. Intensity of the transverse load is considered to vary according to a second-order polynomial. The performed convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the approach. A sensitivity analysis consisting of evaluating effects of different parameters (e.g., exponents of the material properties, thickness to radius ratio, trend of variations of the foundation stiffness, and edge conditions) is carried out. Results reveal that in contrast to the available constitutive-law-based solutions, present solution guarantees continuity of the transverse stresses at the interfaces between layers and may also be used for stress analysis of the sandwich panels. The results are reported for the first time and are discussed in detail. تفاصيل المقالة
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  12 - Asymmetric buckling analysis of the circular FGM plates with temperature-dependent properties under elastic medium
  علیرضا نداف اسکویی هادی محمدی هویه وحید علایی خداداد واحدی
  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 أکثر

  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. تفاصيل المقالة
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  13 - Applying Differential Transform Method on the Effect of the Elastic Foundation on the out - Plane Displacement of the Functionally Graded Circular Plates
  سمیه عباسی فاطمه فرهت نیا سعید رسولی جزی
  In this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to s أکثر

  In this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to solve various types of differential equations. Using this method, governing differential equations are transformed into recursive relations and boundary conditions are changed into algebraic equations. Since the problem of plates on elastic foundation have a great practical importance in modern engineering structures and Winkler foundation model is widely used, plate is assumed on Winkler elastic foundation. In this article functionally graded plate is considered in which material properties vary through the thickness direction by power-law distribution. Analysis results of out of plane displacement of plate on elastic foundation under uniform transverse loads are obtained in different terms of foundation stiffness, material properties and boundary conditions. In order to validate the solution technique, results obtained are compared with the results of the finite element method (FEM). تفاصيل المقالة
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  14 - Thermal Buckling Analysis of Circular FGM Plate with Actuator/Actuator Piezoelectric Layer Based on Neutral Plane
  محمد مهدی نجفی زاده محسن مالمراد آرش شریفی
  In this paper, the thermal buckling analysis of a circular plate made of FGM materials with actuator/actuator piezoelectric layers based on neutral plane, classical plate theory and first order shear deformation plate theory is investigated. Reddy's model is assumed for أکثر

  In this paper, the thermal buckling analysis of a circular plate made of FGM materials with actuator/actuator piezoelectric layers based on neutral plane, classical plate theory and first order shear deformation plate theory is investigated. Reddy's model is assumed for material properties of FGM plate. Plate under the thermal loading, nonlinear temperature rise through the thickness and clamped edges is considered. Equilibrium and stability equations are drived using the calculus of variations and applying Euler equations. The obtained results are compared with the numerical values of the critical buckling temperature based on the theories mentioned above, and good agreement is observed between them. تفاصيل المقالة