277 research outputs found

    Analytical approaches to vibration analysis of circular, annular and sectorial plates subjected to classical and arbitrary boundary conditions – a literature survey

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    Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibration characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of circular, annular and sector plates. The aim of this paper is to compile prominent studies related to circular, annular and sector plates subjected to classical and arbitrary boundary conditions under different supports and loadings. This review also identifies the analytical methods and approaches used to study the vibration characteristics of circular, annular and sector plates based on classical plate theories, Mindlin plate theory and higher order shear deformation theories. Few important citations related to functionally graded circular, annular and sector plates have also been included. Apart from helping researchers and engineers to identify relevant literature quickly and easily, this review will also help them to apply some of these analytical methods to study the vibration characteristics of other 2D and 3D built up and coupled structures

    Isogeometric analysis for functionally graded microplates based on modified couple stress theory

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    Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table

    A closed-form solution for asymmetric free vibration analysis of composite cylindrical shells with metamaterial honeycomb core layer based on shear deformation theory

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    Asymmetric free vibration analysis of composite cylindrical shells with a honeycomb core layer and adjustable Poisson’s ratio is performed analytically in this study. The equations of motion which are a system of coupled partial differential equations are extracted using Hamilton’s principle by employing the first-order shear deformation theory and they are solved analytically. To study the sensitivity of the results to the different parameters of the honeycomb structure, geometrical parameters, and boundary conditions, a parametric study is presented. It is concluded that for the auxetic composite shell with a negative Poisson’s ratio, by decreasing the Poisson ratio, the frequency decreases. Also, it is shown that by employing the composite shells the weight decreases significantly, while the asymmetric frequency will not change remarkably. By adjusting the Poisson ratio, the frequency variations are studied for a composite shell with a honeycomb core layer. The results are compared with the finite element method and some other references

    Free Vibrational Behavior of Bi-Directional Functionally Graded Composite Panel with and Without Porosities Using 3D Finite Element Approximations

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    Abstract: In the present study, the frequency characteristics of bi-directional functionally graded panels in rectangular planform with and without porosities are examined using 3D finite element approximations. In this work, the graded panel is consisted of metal and ceramic material, in which material properties vary smoothly in two directions. The material properties of this highly heterogeneous material are obtained using the Voigt model via extended power-law distribution of volume fractions. The present model is developed using a customized computer code and discretized using three dimensional solid 20-noded quadrilateral elements. The mesh refinement is carried out to conduct the convergence test and the validation test by comparing the obtained results with the previous reported results. At a later stage, a comprehensive parametric study is conducted through numerical illustrations which reveal that the geometrical and material parameters of bi-directional functionally graded panel affect its frequency characteristics, significantly

    Free Vibrational Behavior of Bi-Directional Functionally Graded Composite Panel with and Without Porosities Using 3D Finite Element Approximations

    Get PDF
    Abstract: In the present study, the frequency characteristics of bi-directional functionally graded panels in rectangular planform with and without porosities are examined using 3D finite element approximations. In this work, the graded panel is consisted of metal and ceramic material, in which material properties vary smoothly in two directions. The material properties of this highly heterogeneous material are obtained using the Voigt model via extended power-law distribution of volume fractions. The present model is developed using a customized computer code and discretized using three dimensional solid 20-noded quadrilateral elements. The mesh refinement is carried out to conduct the convergence test and the validation test by comparing the obtained results with the previous reported results. At a later stage, a comprehensive parametric study is conducted through numerical illustrations which reveal that the geometrical and material parameters of bi-directional functionally graded panel affect its frequency characteristics, significantly

    Analytical approaches to vibration analysis of circular, annular and sectorial plates subjected to classical and arbitrary boundary conditions – a literature survey

    Get PDF
    Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibration characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of circular, annular and sector plates. The aim of this paper is to compile prominent studies related to circular, annular and sector plates subjected to classical and arbitrary boundary conditions under different supports and loadings. This review also identifies the analytical methods and approaches used to study the vibration characteristics of circular, annular and sector plates based on classical plate theories, Mindlin plate theory and higher order shear deformation theories. Few important citations related to functionally graded circular, annular and sector plates have also been included. Apart from helping researchers and engineers to identify relevant literature quickly and easily, this review will also help them to apply some of these analytical methods to study the vibration characteristics of other 2D and 3D built up and coupled structures

    Analytical approaches to vibration analysis of circular, annular and sectorial plates subjected to classical and arbitrary boundary conditions – a literature survey

    Get PDF
    Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibration characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of circular, annular and sector plates. The aim of this paper is to compile prominent studies related to circular, annular and sector plates subjected to classical and arbitrary boundary conditions under different supports and loadings. This review also identifies the analytical methods and approaches used to study the vibration characteristics of circular, annular and sector plates based on classical plate theories, Mindlin plate theory and higher order shear deformation theories. Few important citations related to functionally graded circular, annular and sector plates have also been included. Apart from helping researchers and engineers to identify relevant literature quickly and easily, this review will also help them to apply some of these analytical methods to study the vibration characteristics of other 2D and 3D built up and coupled structures

    Axisymmetric Thermoelastic Response in a Semi-elliptic Plate With Kassir’s Nonhomogeneity in the Thickness Direction

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    The main objective is to investigate the transient thermoelastic reaction in a nonhomogeneous semi-elliptical elastic plate heated sectionally on the upper side of the semi-elliptic region. It has been assumed that the thermal conductivity, calorific capacity, elastic modulus and thermal coefficient of expansion were varying through thickness of the nonhomogeneous material according to Kassir’s nonhomogeneity relationship. The transient heat conduction differential equation is solved using an integral transformation technique in terms of Mathieu functions. In these formulations, modified total strain energy is obtained by incorporating the resulting moment and force within the energy term, thus reducing the step of the calculation. The thermal deflection equation derived from the Berger approach is compared with Von Karman approaches, and its maximum normal stresses are determined. The numerical calculation is performed over the metal-metal based composite and graphically portrayed. Furthermore, by applying limiting conditions, the semi-elliptic region can be degenerate into a semi-circular plate. Results reveal that the highest tensile stress exists on the semi-circular core relative to the semi-elliptical core, suggesting the propagation of low heating due to insufficient heat penetration into the elliptic surface

    Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk

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    AbstractThis paper considers the bending of transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate, subject to a transverse load in the form of qrk (k is zero or a finite even number). The differential equations satisfied by stress functions for the particular problem are derived. An elaborate analysis procedure is then presented to derive these stress functions, from which the analytical expressions for the axial force, bending moment and displacements are obtained through integration. The method is then applied to the problem of transversely isotropic functionally graded circular plate subject to a uniform load, illustrating the procedure to determine the integral constants from the boundary conditions. Analytical elasticity solutions are presented for simply-supported and clamped plates, and, when degenerated, they coincide with the available solutions for an isotropic homogenous plate. Two numerical examples are finally presented to show the effect of material inhomogeneity on the elastic field in FGM plates
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