Buckling and vibration analysis of layered and multiphase magneto‐electro‐elastic cylinders subjected to uniform thermal loading
12 Nov 2010-Multidiscipline Modeling in Materials and Structures (Emerald Group Publishing Limited)-Vol. 6, Iss: 4, pp 475-492
TL;DR: In this article, the authors investigated the linear thermal buckling and vibration analysis of layered and multiphase magneto-electro-elastic cylinders made of piezoelectric/piezomagnetic materials using finite element method.
Abstract: Purpose – The purpose of the paper is to investigate the linear thermal buckling and vibration analysis of layered and multiphase magneto‐electro‐elastic (MEE) cylinders made of piezoelectric/piezomagnetic materials using finite element methodDesign/methodology/approach – The constitutive equations of MEE materials are used to derive the finite element equations involving the coupling between mechanical, electrical, magnetic and thermal fields The present study is limited to clamped‐clamped boundary conditions The linear thermal buckling is carried out for an axisymmetric cylinder operating in a steady state axisymmetric uniform temperature rise The influence of stacking sequences and volume fraction of multiphase MEE materials on critical buckling temperature and vibration behaviour is investigated The influence of coupling effects on critical buckling temperature and vibration behaviour is also studiedFindings – The critical buckling temperature is higher for MEE axisymmetric cylinder as compared
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TL;DR: In this paper, a finite element formulation accounting for multiphysics response of multilayered magneto-electro-elastic (MEE) plates in the thermal environment has been presented.
Abstract: In this article, a finite element (FE) formulation accounting for multiphysics response of multilayered magneto-electro-elastic (MEE) plates in the thermal environment has been presented. The equilibrium equations of motion are attained using the principle of total potential energy and coupled constitutive relations of MEE material. Maxwell’s equation of electrostatics and magnetostatics are used to model the electric and magnetic behavior. The influence of various through thickness temperature distributions on the static parameters of stepped functionally graded magneto-electro-elastic ( SFG- MEE) plates is investigated. Further, an extra attention has been devoted to evaluate the effect of product properties (pyroelectric and pyromagnetic coupling), boundary conditions and aspect ratio on the direct (displacements, electric potential and magnetic potential) and derived quantities (stresses, electric displacement, and magnetic flux density) of the SFG- MEE plate. A comparative study is also carried out to analyse the effect of stacking sequence, boundary conditions, pyroeffects, length-to-width ratio and aspect ratios of the SFG- MEE plate. The credibility of the proposed FE model is verified with the results available in the literature. It is expected that the findings in this article may be useful for accurate design and analysis of MEE structures under the thermal environment.
87 citations
TL;DR: In this article, the static response of magneto-electro-elastic (MEE) plate subjected to hygrothermal loads is investigated using the finite element (FE) method.
Abstract: In this article, the static response of magneto-electro-elastic (MEE) plate subjected to hygrothermal loads is investigated using the finite element (FE) method. A FE formulation is derived using the principle of total potential energy and linear coupled constitutive equations of MEE materials by taking into account the thermal and hygroscopic field effects. A uniform temperature rise and moisture concentration rise has been considered. The variations of static parameters are estimated along the MEE plate length by considering the temperature and moisture dependant elastic stiffness coefficients. The coupled FE equilibrium equations in terms of displacements, electric and magnetic potentials are solved directly using condensation procedure. Numerical examples of the FE results are presented and discussed in detail to understand the significant effects of hygrothermal loading, temperature and moisture dependent material properties, boundary conditions and aspect ratio on the direct (displacements, electric potential and magnetic potential) and derived quantities (stresses, electric displacement and magnetic flux density) of MEE plate.
74 citations
TL;DR: The present study is in no ways exhaustive to the methods and results observed, but it may be considered as a guide to researchers and scholars about the behavior of MEE materials, wherein critical observations and analyses’ techniques are discussed.
Abstract: Magneto-electro-elastic (MEE) materials have been receiving a special attention from the research community owing to their specialized performance and coupled behavior under thermal, electric, magnetic and mechanical loads. The possibility of prospective energy conversion means, have additionally been added to the cause of researching about these materials. Therefore, the review presented here may be considered as a topical discussion on MEE materials and structures. Through this paper, all critical concepts revolving around MEE materials are discussed in separate sections ranging from the very definition of MEE materials, their material phenomenon, types and properties, to certain fundamental theories and micromechanical models, structural analyses of MEE structures and their nano-sized counterparts, effects of various external and internal parameters and prospective applications of these materials. The present study is in no ways exhaustive to the methods and results observed, but it may be considered as a guide to researchers and scholars about the behavior of MEE materials, wherein critical observations and analyses’ techniques are discussed.
56 citations
TL;DR: In this paper, the influence of full coupling between thermal, elastic, magnetic, and electric fields on the natural frequency of functionally graded magneto-electro-thermo-elastic plates has been investigated.
Abstract: In this article, the influence of full coupling between thermal, elastic, magnetic, and electric fields on the natural frequency of functionally graded magneto-electro-thermo-elastic plates has bee...
51 citations
Cites methods from "Buckling and vibration analysis of ..."
...Kumaravel et al. (2007, 2010) used the FE model for linear buckling and vibration behavior of multiphase MEE cantilever beam and studied the influence of material constants on critical buckling load....
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TL;DR: In this paper, two comprehensive micromechanical models for the analysis of piezo-magneto-thermo-elastic smart composite structures with orthotropic constituents are developed and applied to examples of practical importance.
Abstract: Two comprehensive micromechanical models for the analysis of piezo-magneto-thermo-elastic smart composite structures with orthotropic constituents are developed and applied to examples of practical importance. Details on the derivations of the aforementioned models are given in Part I of this work. The present paper solves the derived unit cell problems and obtains expressions for such effective coefficients as piezomagnetic, piezoelectric, elastic and many others. Of particular importance are the effective product properties, such as magnetoelectric, pyroelectric and pyromagnetic coefficients which, in general, manifest themselves in the macroscopic composite as a consequence of the interactions of the different constituents but are not exhibited by the constituents themselves as individual entities. The effective coefficients are universal in nature and once determined, can be used to examine a number of boundary value problems associated with a given composite geometry. The present work illustrates the use of the developed models and compares the results obtained with corresponding results stemming from other analytical and/or numerical models. Furthermore, results from the two micromechanical models presented here are also compared with each other. The mathematical model developed in this work can be used in analysis and design to tailor the effective elastic, piezoelectric, piezomagnetic, magnetoelectric etc. coefficients of smart composite structures to meet the design criteria of different engineering applications by a judicious selection of different geometric and/or material parameters of interest.
38 citations
References
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TL;DR: In this article, a study on the vibration of cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented, the objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies.
Abstract: Functionally gradient materials (FGMs) have attracted much attention as advanced structural materials because of their heat-resistance properties In this paper, a study on the vibration of cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies The properties are graded in the thickness direction according to a volume fraction power-law distribution The results show that the frequency characteristics are similar to that observed for homogeneous isotropic cylindrical shells and the frequencies are affected by the constituent volume fractions and the configurations of the constituent materials The analysis is carried out with strains–displacement relations from Love’s shell theory and the eigenvalue governing equation is obtained using Rayleigh–Ritz method The present analysis is validated by comparing results with those in the literature
726 citations
"Buckling and vibration analysis of ..." refers methods in this paper
...The vibration behaviour of functionally graded cylindrical shells based on Love's theory and the Rayleigh Ritz method presented by Loy et al. (1999)...
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TL;DR: In this article, the vibration of a functionally graded cylindrical shell made up of stainless steel and zirconia is studied and its properties are graded in the thickness direction of the shell according to volume fraction power law distribution.
Abstract: In the recent years, functionally gradient materials (FGMs) have gained considerable attention in the high temperature environment applications. In the present work, study of the vibration of a functionally graded cylindrical shell made up of stainless steel and zirconia is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. Effects of boundary conditions and volume fractions (power law exponent) on the natural frequencies of the FG cylindrical shell are studied. Frequency characteristics of the FG shell are found to be similar to those of isotropic cylindrical shells. Further, natural frequencies of these shells are observed to be dependent on the constituent volume fractions and boundary conditions. Strain displacement relations from Love's shell theory are employed. Rayleigh method is used to derive the governing equations. Further, analytical results are validated with those reported in the literature.
406 citations
TL;DR: In this paper, a homogenization micromechanical method is employed for the prediction of the effective moduli of electro-magneto-thermo-elastic composites.
Abstract: A homogenization micromechanical method is employed for the prediction of the effective moduli of electro-magneto-thermo-elastic composites. These include the effective elastic, piezoelectric, piezomagnetic, dielectric, magnetic permeability and electromagnetic coupling moduli, as well as the effective thermal expansion coefficients and the associated pyroelectric and pyromagnetic constants. Comparisons between the present homogenization theory, the generalized method of cells and the Mori-Tanaka predictions are given. Results are presented for fibrous and periodically bilaminated composites.
326 citations
TL;DR: In this article, an approximate solution for the free vibration problem of two-dimensional magneto-electro-elastic laminates is presented to determine their fundamental behavior, which is composed of linear homogeneous elastic, piezoelectric, or magnetostrictive layers with perfect bonding between each interface.
Abstract: An approximate solution for the free vibration problem of two-dimensional magneto-electro-elastic laminates is presented to determine their fundamental behavior. The laminates are composed of linear homogeneous elastic, piezoelectric, or magnetostrictive layers with perfect bonding between each interface. The solution for the elastic displacements, electric potential, and magnetic potential is obtained by combining a discrete layer approach with the Ritz method. The model developed here is not dependent on specific boundary conditions, and it is presented as an alternative to the exact or analytical approaches which are limited to a very specific set of edge conditions. The natural frequencies and through-thickness modal behavior are computed for simply supported and cantilever laminates. Solutions for the simply supported case are compared with the known exact solution for piezoelectric laminates, and excellent agreement is obtained. The present approach is also validated by comparing the natural frequencies of a two-layer cantilever plate with known analytical solution and with results obtained using commercial finite element software.
244 citations
TL;DR: In this paper, the authors presented linear thermal buckling and free vibration analysis for functionally graded cylindrical shells with clamped-clamped boundary condition based on temperature-dependent material properties.
Abstract: Linear thermal buckling and free vibration analysis are presented for functionally graded cylindrical shells with clamped–clamped boundary condition based on temperature-dependent material properties. The material properties of functionally graded materials (FGM) shell are assumed to vary smoothly and continuously across the thickness. With high-temperature specified on the inner surface of the FGM shell and outer surface at ambient temperature, 1D heat conduction equation along the thickness of the shell is applied to determine the temperature distribution; thereby, the material properties based on temperature distribution are made available for thermal buckling and free vibration analysis. First-order shear deformation theory along with Fourier series expansion of the displacement variables in the circumferential direction are used to model the FGM shell. Numerical studies involved the understanding of the influence of the power-law index, r/h and l/r ratios on the critical buckling temperature. Free vibration studies of FGM shells under elevated temperature show that the fall in natural frequency is very drastic for the mode corresponding to the lowest natural frequency when compared to the lowest buckling temperature mode.
196 citations
"Buckling and vibration analysis of ..." refers background in this paper
...The static thermal buckling and vibration behaviour of piezoelectric composite cylindrical shells were examined by Ravikiran and Ganesan (2006)...
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