# مقالههای M.M. Alipour

**توجه:**محتویات این صفحه به صورت خودکار پردازش شده و مقالههای نویسندگانی با تشابه اسمی، همگی در بخش یکسان نمایش داده میشوند.

##### ۱Analytic Approach to Investigation of Fluctuation and Frequency of the Oscillators with Odd and Even Nonlinearities

اطلاعات انتشار:
International Journal of Engineering،
بيست و سوم،شماره۱، Jan۲۰۱۰،
سال ۰

تعداد صفحات:
۱۶

In this paper we examine fluctuation and frequency of the governing equation ofoscillator with odd and even nonlinearities without damping and we present a new efficientmodification of the He’s homotopy perturbation method for this equation. We applied standard andmodified homotopy perturbation method and compare them with the numerical solution (NS), also weapplied He’s Energy balance method (EBM) for study frequency of this equation. By comparemodified homotopy perturbation method with numerical solution we find that this modified homotopyperturbation method works very well for the wide range of time and boundary conditions fornonlinear oscillator, and comparison of the result obtained using this method for frequency with thoseobtained by Energy balance method reveals that the former is very effective and convenient. The newmodified method accelerates the rapid convergence of the solution, reduces the error solution andincreases the validity range for fluctuation and frequency.

##### ۲A Semi–Analytical Solution for Free Vibration and Modal Stress Analyses of Circular Plates Resting on Two–Parameter Elastic Foundations

اطلاعات انتشار:
Journal of Solid Mechanics،
دوم،شماره۱، Winter ۲۰۱۰،
سال ۰

تعداد صفحات:
۱۶

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.

##### ۳Stress Analysis of Two Directional FGM Moderately Thick Constrained Circular Plates with Non–uniform Load and Substrate Stiffness Distributions

اطلاعات انتشار:
Journal of Solid Mechanics،
دوم،شماره۴، Autumn ۲۰۱۰،
سال ۰

تعداد صفحات:
۱۶

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.

##### ۴A Power Series Solution for Free Vibration of Variable Thickness Mindlin Circular Plates with Two– Directional Material Heterogeneity and Elastic Foundations

اطلاعات انتشار:
Journal of Solid Mechanics،
سوم،شماره۲، Spring ۲۰۱۱،
سال ۰

تعداد صفحات:
۱۵

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.

##### ۵A Zigzag Theory with Local Shear Correction Factors for Semi–Analytical Bending Modal Analysis of Functionally Graded Viscoelastic Circular Sandwich Plates

اطلاعات انتشار:
Journal of Solid Mechanics،
چهارم،شماره۱، Winter ۲۰۱۲،
سال ۰

تعداد صفحات:
۲۲

Free bending vibration analysis of the functionally graded viscoelastic circular sandwich plates is accomplished in the present paper, for the first time. Furthermore, local shear corrections factors are presented that may consider simultaneous effects of the gradual variations of the material properties and the viscoelastic behaviors of the materials, for the first time. Moreover, in contrast to the available works, a global–local zigzag theory rather than an equivalent single–layer theory is employed in the analysis. Another novelty is solving the resulted governing equations by a power series that may cover several boundary conditions. To extract more general conclusions, sandwich plates with both symmetric and asymmetric (with a bending–extension coupling) layups are considered. Results are validated by comparing some of them with results of the three–dimensional theory of elasticity, even for the thick plates. Influences of various geometric and material properties parameters on free vibration of the circular sandwich plates are evaluated in detail in the results section.

##### ۶An Analytical Shear Factor for FGM Circular Plates with Non–uniform Elastic Foundations and Normal and Shear Tractions

اطلاعات انتشار:
Ianian Journal of Mechanical Engineering Transactions،
چهاردهم،شماره۲(پياپي ۲۱)، Sep ۲۰۱۳،
سال ۰

تعداد صفحات:
۲۳

The available shear correction factors have mainly been developed for homogeneous isotropic plates and\or assuming that no shear tractions are imposed on the top and bottom surfaces of the plate. In the present research, a more general case of a circular functionally graded plate subjected to nonuniform normal and shear tractions at the top and bottom surfaces is considered. These non–uniform tractions may stem from the imposed non–uniform inclined tractions at the top surface and resting on the non–uniform Winkler–Pasternak elastic foundations. Instead of using the approximate numerical methods, the solutions are derived using a pure analytical method. In this regard, influences of the proposed analytical correction factor are evaluated on results of both the modal and the stress analyses.

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