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1 - Determination of the amplitude-frequency for strongly nonlinear oscillator by two approximate analytical techniques
Amir Ayazi Hadi Ebrahimi KhahAbstractIn this paper, we investigate two of the analytical approximate techniques, energy balance method and amplitude-frequency formulation, and these approximate techniques are applied to solve the strongly nonlinear differential equation of a mass attached to the ce أکثرAbstractIn this paper, we investigate two of the analytical approximate techniques, energy balance method and amplitude-frequency formulation, and these approximate techniques are applied to solve the strongly nonlinear differential equation of a mass attached to the center of a stretched elastic wire. We present a comparative study between the energy balance method and amplitude-frequency formulation with exact solution. The approximate results reveal that these methods are very effective and convenient for determining the frequencies of nonlinear dynamical systems. تفاصيل المقالة -
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2 - The comparison of homotopy perturbation method with finite difference method for determination of maximum beam deflection
Masoud Saravi Martin Hermann Hadi Ebrahimi KhahAbstractThis paper deals with the determination of maximum beam deflection using homotopy perturbation method (HPM) and finite difference method (FDM). By providing some examples, we compare the results with exact solutions and conclude that HPM is more accurate, more s أکثرAbstractThis paper deals with the determination of maximum beam deflection using homotopy perturbation method (HPM) and finite difference method (FDM). By providing some examples, we compare the results with exact solutions and conclude that HPM is more accurate, more stable and effective and can therefore be found widely applicable in structrue engineering. تفاصيل المقالة -
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3 - جواب‌های دقیق و تقریبی برای یک فرم تعمیم یافته از معادله غیرخطی شرودینگر
بهزاد قنبریدر این مقاله، یک فرم تعمیم یافته از معادله غیرخطی شرودینگر همراه با ضریب پراکندگی مکانی از مرتبه دوم بررسی خواهد شد. در تعیین جواب‌های دقیق جدید این معادله از روش توابع نمایی کسری تعمیم یافته و در تعیین جواب‌های تقریبی از یک تکنیک عددی استفاده شده است. شبیه سازی‌های عدد أکثردر این مقاله، یک فرم تعمیم یافته از معادله غیرخطی شرودینگر همراه با ضریب پراکندگی مکانی از مرتبه دوم بررسی خواهد شد. در تعیین جواب‌های دقیق جدید این معادله از روش توابع نمایی کسری تعمیم یافته و در تعیین جواب‌های تقریبی از یک تکنیک عددی استفاده شده است. شبیه سازی‌های عددی مختلف نیز به منظور نمایش رفتار جواب‌های دقیق و نیز تایید دقت روش عددی ارائه شده است. به وضوح می‌توان دید که این روش‌ها، روش‌هایی ساده در عین حال کارآمد در تعیین جواب‌های این معادله هستند. به علاوه آن‌ها را می‌توان در حل بسیاری مسائل غیرخطی در ریاضی، فیزیک و سایر شاخه‌های مهندسی به کارگرفت. در انجام کلیه محاسبات و شبیه‌سازی‌های عددی از نرم افزار متمتیکا استفاده شده است. تفاصيل المقالة -
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4 - Elasticity Exact Solution for an FGM Cylindrical Shaft with Piezoelectric Layers Under the Saint-Venant Torsion by Using Prandtl’s Formulation
M. R Eslami M Jabbari A Eskandarzadeh SabetFunctionally graded materials (FGMs) belong to a noble family of composite material possess material properties varying gradually in a desired direction or orientation. In a past decade, functionally graded materials were remained in an interest of material investigator أکثرFunctionally graded materials (FGMs) belong to a noble family of composite material possess material properties varying gradually in a desired direction or orientation. In a past decade, functionally graded materials were remained in an interest of material investigators due to its prominent features, and have extensively used in almost every discipline of engineering which in turn significantly increases the number of research publication of FGM. In this paper the exact elasticity solution for an FGM circular shaft with piezo layers is analysed. piezoelectric layers are homogeneous and the modulus of elasticity for FGM varies continuously with the form of an exponential function. The shear modulus of the non-homogeneous FGM shaft is a given function of the Prandtl’s stress function of considered circular shaft when its material is homogeneous. state equations are derived. The Prandtl’s stress function and electric displacement potential function satisfy all conditions. The shearing stresses, torsional rigidity, torsional function for FGM layer and shearing stresses, electric displacements, torsional rigidity, electrical torsional rigidity ,torsional and electrical potential functions for piezoelectric layers are obtained. Exact analytical solution for hollow circular cross-section presented. At the end some graphs and conclusions are given. تفاصيل المقالة -
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5 - Closed-Form Formulation for Bending Analysis of Functionally Graded Thick Plates
M Shaban M. J KhoshgoftarDue to their continuous material variation and eliminating the mismatch stress field in the thickness direction, Functionally Graded Materials (FGMs) have found wide applications in aerospace and mechanical engineering. This article presents closed-form solution for thi أکثرDue to their continuous material variation and eliminating the mismatch stress field in the thickness direction, Functionally Graded Materials (FGMs) have found wide applications in aerospace and mechanical engineering. This article presents closed-form solution for thick functionally graded plate based on three-dimensional elasticity theory. To this end, first, the characteristic equation of FG plate is derived and general closed-form is obtained analytically. Both positive and negative discriminant of characteristic equation is considered and solved. The presented method is validated with finite element results by considering isotropic thick plate. Several parametric studies are carried out to investigate the effect of geometric and material parameters. The aim of this research is to present analytical solution form for thick FG plate and work out the problem of inconsistency for corresponding displacements field. The presented solution can be used to examine accuracy of various plate theories such as first-order, third order shear deformation theories and other equivalent plate theories. تفاصيل المقالة -
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6 - An Exact Solution for Classic Coupled Magneto-Thermo-Elasticity in Cylindrical Coordinates
M Jabbari H DehbaniIn this paper, the classic coupled Magneto-thermo-elasticity model of hollow and solid cylinders under radial-symmetric loading condition (r, t) is considered. A full analytical and the direct method based on Fourier Hankel series and Laplace transform is used, and an e أکثرIn this paper, the classic coupled Magneto-thermo-elasticity model of hollow and solid cylinders under radial-symmetric loading condition (r, t) is considered. A full analytical and the direct method based on Fourier Hankel series and Laplace transform is used, and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body force, the heat source and magnetic field vector are considered in the most general forms, where no limiting assumption is used. This generality allows to simulate a variety of applicable problems. The results are presented for thermal and mechanical shock, separately, and compare the effect of magnetic field on temperature and displacement. تفاصيل المقالة -
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7 - Vibration Response of an Elastically Connected Double-Smart Nanobeam-System Based Nano-Electro-Mechanical Sensor
A Ghorbanpour Arani S.A Mortazavi R Kolahchi A.H Ghorbanpour AraniNonlocal vibration of double-smart nanobeam-systems (DSNBSs) under a moving nanoparticle is investigated in the present study based on Timoshenko beam model. The two smart nanobeams (SNB) are coupled by an enclosing elastic medium which is simulated by Pasternak foundat أکثرNonlocal vibration of double-smart nanobeam-systems (DSNBSs) under a moving nanoparticle is investigated in the present study based on Timoshenko beam model. The two smart nanobeams (SNB) are coupled by an enclosing elastic medium which is simulated by Pasternak foundation. The energy method and Hamilton’s principle are used to establish the equations of motion. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, elastic medium coefficients, external voltage, length of SNB and the mass of attached nanoparticle on the frequency of piezoelectric nanobeam. The results depict that the imposed external voltage is an effective controlling parameter for vibration of the piezoelectric nanobeam. Also increase in the mass of attached nanoparticle gives rise to a decrease in the natural frequency. This study might be useful for the design and smart control of nano-devices. تفاصيل المقالة -
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8 - An Exact Solution for Classic Coupled Thermoporoelasticity in Axisymmetric Cylinder
M Jabbari H DehbaniIn this paper, the classic coupled poro-thermoelasticity model of hollow and solid cylinders under radial symmetric loading condition is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The thermal أکثرIn this paper, the classic coupled poro-thermoelasticity model of hollow and solid cylinders under radial symmetric loading condition is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The thermal and pressure boundary conditions, the body force, the heat source and the injected volume rate per unit volume of a distribute water source are considered in the most general forms and no limiting assumption is used. This generality allows simulation of several of the applicable problems. تفاصيل المقالة -
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9 - An Exact Solution for Kelvin-Voigt Model Classic Coupled Thermo Viscoelasticity in Spherical Coordinates
S Bagheri M JabbariIn this paper, the classic Kelvin-Voigt model coupled thermo-viscoelasticity model of hollow and solid spheres under radial symmetric loading condition is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is prese أکثرIn this paper, the classic Kelvin-Voigt model coupled thermo-viscoelasticity model of hollow and solid spheres under radial symmetric loading condition is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body force, and the heat source are considered in the most general forms and where no limiting assumption is used. This generality allows simulate varieties of applicable problems. At the end, numerical results are presented and compared with classic theory of thermoelasticity. تفاصيل المقالة -
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10 - An Exact Solution for Vibration Analysis of Soft Ferromagnetic Rectangular Plates Under the Influence of Magnetic Field with Levy Type Boundary Conditions
S.A Mohajerani A Mohammadzadeh M Nikkhah BahramiIn this paper vibration of ferromagnetic rectangular plates which are subjected to an inclined magnetic field is investigated based on classical plate theory and Maxwell equations. Levy type solution and Finite element method using Comsol software are used to obtain the أکثرIn this paper vibration of ferromagnetic rectangular plates which are subjected to an inclined magnetic field is investigated based on classical plate theory and Maxwell equations. Levy type solution and Finite element method using Comsol software are used to obtain the frequency of the plate subjected to different boundary conditions, good agreements is obtained when computed results are compared with those obtained by Comsol software, the results have shown that the frequency of the plates increases with the magnetic field and the effect of magnetic field is similar to the Winkler’s foundation. تفاصيل المقالة -
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11 - An Exact Solution for Lord-Shulman Generalized Coupled Thermoporoelasticity in Spherical Coordinates
M Jabbari H DehbaniIn this paper, the generalized coupled thermoporoelasticity model of hollow and solid spheres under radial symmetric loading condition (r, t) is considered. A full analytical method is used and an exact unique solution of the generalized coupled equations is presented. أکثرIn this paper, the generalized coupled thermoporoelasticity model of hollow and solid spheres under radial symmetric loading condition (r, t) is considered. A full analytical method is used and an exact unique solution of the generalized coupled equations is presented. The thermal, mechanical and pressure boundary conditions, the body force, the heat source and the injected volume rate per unit volume of a distribute water source are considered in the most general forms and where no limiting assumption is used. This generality allows simulate varieties of applicable problems. At the end, numerical results are presented and compared with classic theory of thermoporoelasticity. تفاصيل المقالة -
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12 - An Exact Solution for Classic Coupled Thermoporoelasticity in Cylindrical Coordinates
M Jabbari H DehbaniIn this paper the classic coupled thermoporoelasticity model of hollow and solid cylinders under radial symmetric loading condition (r, t) is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The the أکثرIn this paper the classic coupled thermoporoelasticity model of hollow and solid cylinders under radial symmetric loading condition (r, t) is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The thermal and pressure boundary conditions, the body force, the heat source, and the injected volume rate per unit volume of a distribute water source are considered in the most general forms, and no limiting assumption is used. This generality allows simulation of various applicable problems. تفاصيل المقالة -
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13 - Exact Closed-Form Solution for Vibration Analysis of Truncated Conical and Tapered Beams Carrying Multiple Concentrated Masses
K Torabi H Afshari M Sadeghi H ToghianIn this paper, an exact closed-form solution is presented for free vibration analysis of Euler-Bernoulli conical and tapered beams carrying any desired number of attached masses. The concentrated masses are modeled by Dirac’s delta functions which creates no need أکثرIn this paper, an exact closed-form solution is presented for free vibration analysis of Euler-Bernoulli conical and tapered beams carrying any desired number of attached masses. The concentrated masses are modeled by Dirac’s delta functions which creates no need for implementation of compatibility conditions. The proposed technique explicitly provides frequency equation and corresponding mode as functions with only two integration constants which leads to solution of a two by two eigenvalue problem for any number of attached masses. Using Basic functions which are made of the appropriate linear composition of Bessel functions leads to make implementation of boundary conditions much easier. The proposed technique is employed to study effect of quantity, position and translational inertia of the concentrated masses on the natural frequencies and corresponding modes of conical and tapered beams for all standard boundary conditions. Unlike many of previous exact approaches, presented solution has no limitation in number of concentrated masses. In other words, by increase in number of attached masses, there is no considerable increase in computational effort. تفاصيل المقالة -
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14 - Free and Forced Transverse Vibration Analysis of Moderately Thick Orthotropic Plates Using Spectral Finite Element Method
M.R Bahrami S HatamiIn the present study, a spectral finite element method is developed for free and forced transverse vibration of Levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. Levy solution assumption was used to convert the two- أکثرIn the present study, a spectral finite element method is developed for free and forced transverse vibration of Levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. Levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. In the first step, the governing out-of-plane differential equations are transformed from time domain into frequency domain by discrete Fourier transform theory. Then, the spectral stiffness matrix is formulated, using frequency-dependent dynamic shape functions which are obtained from the exact solution of the governing differential equations. An efficient numerical algorithm, using drawing method is used to extract the natural frequencies. The frequency domain dynamic responses are obtained from solution of the spectral element equation. Also, the time domain dynamic responses are derived by using inverse discrete Fourier transform algorithm. The accuracy and excellent performance of the spectral finite element method is then compared with the results obtained from closed form solution methods in previous studies. Finally, comprehensive results for out-of-plane natural frequencies and transverse displacement of the moderately thick rectangular plates with six different combinations of boundary conditions are presented. These results can serve as a benchmark to compare the accuracy and precision of the numerical methods used. تفاصيل المقالة -
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15 - The cosine method to Gardner equation and (2+1)- dimensional breaking soliton system
Parvin Nabipour KisomiIn this letter, we established a traveling wave solution by using cosine function algorithm for Gardnerequation and (2+1)-dimensional breaking soliton system. The cosine method is used to obtain theexact solution.In this letter, we established a traveling wave solution by using cosine function algorithm for Gardnerequation and (2+1)-dimensional breaking soliton system. The cosine method is used to obtain theexact solution. تفاصيل المقالة -
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16 - A New Classes of Solutions of the Einstein-Maxwell Field Equations with Pressure Anisotropy
Kalikkuddy KomathirajIn this paper, we present a class of exact solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere. The field equations are integrated by specifying the forms of the electric field, anisotropic factor, and one أکثرIn this paper, we present a class of exact solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere. The field equations are integrated by specifying the forms of the electric field, anisotropic factor, and one of the gravitational potentials which are physically reasonable. By reducing the condition of pressure isotropy to a linear, second order differential equation which can be solved in general, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. The solution is regular, well behaved and complies with all the requirements of a realistic stellar model. An interesting feature of the new class of solutions is that one can easily switch off the electric and/or anisotropic effects in this formulation. Consequently, we regain some of the earlier solutions. تفاصيل المقالة -
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17 - Anisotropic Charged Stellar Models
Kalikkuddy KomathirajA new class of exact solutions of the Einstein-Maxwell system is found in closed form for a static spherically symmetric anisotropic star in the presence of an electric field by generalizing earlier approaches. The field equations are integrated by specifying one of the أکثرA new class of exact solutions of the Einstein-Maxwell system is found in closed form for a static spherically symmetric anisotropic star in the presence of an electric field by generalizing earlier approaches. The field equations are integrated by specifying one of the gravitational potentials, the anisotropic factor and electric field which are physically reasonable. We demonstrate that it is possible to obtain a more general class of solutions to the Einstein-Maxwell system in the form of series with anisotropic matter. For specific parameter values it is possible to find new exact models for the Einstein-Maxwell system in terms of elementary functions from the general series solution. Our results contain particular solutions found previously including models of Thirukkanesh and Maharaj (2009) and Komathiraj and Maharaj (2007) charged relativistic models. تفاصيل المقالة
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