Analysis of sandwich Timoshenko porous beam with temperature-dependent material properties: Magneto-electro-elastic vibration and buckling solution

2019 ◽  
Vol 25 (23-24) ◽  
pp. 2875-2893 ◽  
Author(s):  
M. Bamdad ◽  
M. Mohammadimehr ◽  
K. Alambeigi
Keyword(s):  
Timoshenko Beam ◽  
Material Properties ◽  
Vinylidene Fluoride ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Distribution Patterns ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Temperature Dependent

Vibration and buckling analysis of a magneto-electro-elastic sandwich Timoshenko beam with a porous core and poly-vinylidene fluoride (PVDF) matrix reinforced by carbon nanotubes (CNTs) is considered as face layers and material properties of CNTs and PVDF are assumed to be temperature-dependent. Different CNT distribution patterns including uniform distribution, AV (which top and bottom face sheets have functionally graded-A (FG-A) and functionally graded-V (FG-V) CNT distribution patterns, respectively) and VA patterns are employed. The governing equations of motion are derived based on Timoshenko beam theory, and Navier's solution is used to solve these equations. The sandwich beam resting on a Pasternak foundation and face layers are subjected to electric and magnetic potentials. The effect of different parameters such as porosity coefficient, electric and magnetic potential, parameters of foundation, and geometrical parameters are investigated on vibration and buckling behavior of the sandwich beam. Numerical results of this paper show that porosity distribution has a significant effect on the stiffness of the sandwich beam. The results can be used for future analysis of magneto-electro-mechanical sandwich systems as actuators and sensors.

Temperature-Dependent Vibration of Various Types of Sandwich Beams with Porous FGM Layers

2020 ◽  
pp. 2150016
Author(s):  
Mohsen Rahmani ◽  
Sajjad Dehghanpour
Keyword(s):  
Thermal Stresses ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Type I ◽  
Sandwich Beams ◽  
Temperature Dependent ◽  
The Core ◽  
Graded Layers ◽  
Lagrange Strain

By using a high order sandwich beams theory which is modified by considering the transverse flexibility of the core, free vibration characteristics of two models of sandwich beams are studied in this paper. In type-I, functionally graded layers coat a homogeneous core, and in type-II, an FG core is covered by homogeneous face sheets. To increase the accuracy of the model of the FGM properties, even and uneven porosity distributions are applied, and all materials are considered temperature-dependent. Nonlinear Lagrange strain and thermal stresses of the face sheets and in-plane strain of the core are considered. To obtain the governing equations of motion, Hamilton’s principle is used and a Galerkin method is used to solve them for simply supported and clamped boundary conditions. To verify the results of this study, they are compared with the results of literatures. Also, the effect of variation of temperature, some geometrical parameters and porosities on the frequency are studied.

scholarly journals A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Ali Jafari
Keyword(s):  
Differential Equations ◽  
Porous Material ◽  
Power Law ◽  
Material Properties ◽  
Solution Method ◽  
Equations Of Motion ◽  
Higher Order ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Temperature Dependent

In the present paper, thermomechanical vibration characteristics of functionally graded (FG) Reddy beams made of porous material subjected to various thermal loadings are investigated by utilizing a Navier solution method for the first time. Four types of thermal loadings, namely, uniform, linear, nonlinear, and sinusoidal temperature rises, through the thickness direction are considered. Thermomechanical material properties of FG beam are assumed to be temperature-dependent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of motion are derived based on higher order shear deformation beam theory. Hamilton’s principle is applied to obtain the governing differential equations of motion which are solved by employing an analytical technique called the Navier type solution method. Influences of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, thermal effects, and slenderness ratios on natural frequencies of the temperature-dependent FG beams with porosities are investigated and discussed in detail. It is concluded that these effects play significant role in the thermodynamic behavior of porous FG beams.

scholarly journals A study on dynamic response of functionally graded sandwich beams under different dynamic loadings

2018 ◽  
Vol 192 ◽  
pp. 02011
Author(s):  
Wachirawit Songsuwan ◽  
Monsak Pimsarn ◽  
Nuttawit Wattanasakulpong
Keyword(s):  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Functionally Graded ◽  
Transverse Shear Deformation ◽  
Sandwich Beams ◽  
Governing Equations ◽  
Dynamic Loadings ◽  
Parametric Studies

In this research, free and forced vibration of functionally graded sandwich beams is considered using Timoshenko beam theory which takes into account the significant effects of transverse shear deformation and rotary inertia. The governing equations of motion are formulated from Lagrange's equations and they are solved by using The Ritz and Newmark methods. The results are presented in both tabular and graphical forms to show the effects of layer thickness ratios, boundary conditions, length to height ratios, etc. on natural frequencies and dynamic deflections of the beams. According to the numerical results, all parametric studies considered in this research have significant impact on free and forced behaviour of the beams; for example, the frequency is low and the dynamic deflection is large for the beams which are hinged at both ends.

Finite element based vibration analysis of functionally graded spinning shaft system

2014 ◽  
Vol 228 (18) ◽  
pp. 3306-3321 ◽  
Author(s):  
Debabrata Gayen ◽  
Tarapada Roy
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Material Properties ◽  
Beam Theory ◽  
Beam Element ◽  
Functionally Graded ◽  
Conventional Steel ◽  
Shaft System ◽  
Hysteretic Damping ◽  
Spinning Shaft

The present work deals with the study of vibration and stability analysis of a functionally graded spinning shaft system using three-noded beam element based on the Timoshenko beam theory. Material properties are assumed to be graded in radial direction according to power law gradation. In the present analysis, the mixture of aluminum oxide (Al2O3) and stainless steel (SUS304) has been considered as functionally graded material where metal (SUS304) content decreases towards the outer diameter of the shaft. The functionally graded shafts has been modeled as a Timoshenko beam, which contains discrete isotropic rigid disks supported by flexible bearing. The functionally graded shaft has been modeled based on first-order shear deformation beam theory with transverse shear deformation, rotary inertia, gyroscopic effect, strain and kinetic energy of shafts by adopting three-dimensional constitutive relations. The derivation of governing equations of motion has been obtained using Hamilton’s principle. Three-noded beam element with four degrees of freedom per node has been used to solve the govering equations. In this work, the effects of both internal viscous and hysteretic damping have also been incorporated in the finite element model. Various results have been obtained such as Campbell diagram, stability speed limit, damping ratio, and time responses for functionally graded shaft and also compared with conventional steel shaft. It has been found that the responses of the functionally graded spinning shaft are significantly influenced by material properties, radial thickness, power law gradient index, and internal (viscous and hysteretic) damping. The obtained results also show the advantages of functionally graded shaft over conventional steel shaft.

scholarly journals FREE VIBRATION OF TWO-DIRECTIONAL FGM BEAMS USING A HIGHER-ORDER TIMOSHENKO BEAM ELEMENT

2018 ◽  
Vol 56 (3) ◽  
pp. 380 ◽  
Author(s):  
Tran Thi Thom ◽  
Nguyen Dinh Kien
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Beam Element ◽  
Higher Order ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Power Law Distribution ◽  
Graded Material

Free vibration of two-directional functionally graded material (2-D FGM) beams is studied by the finite element method (FEM). The material properties are assumed to be graded in both the thickness and longitudinal directions by a power-law distribution. Equations of motion based on Timoshenko beam theory are derived from Hamilton's principle. A higher-order beam element using hierarchical functions to interpolate the displacements and rotation is formulated and employed in the analysis. In order to improve the efficiency of the element, the shear strain is constrained to constant. Validation of the derived element is confirmed by comparing the natural frequencies obtained in the present paper with the data available in the literature. Numerical investigations show that the proposed beam element is efficient, and it is capable to give accurate frequencies by a small number of elements. The effects of the material composition and aspect ratio on the vibration characteristics of the beams are examined in detail and highlighted.

Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

2021 ◽  
Vol 2 (110) ◽  
pp. 72-85
Author(s):  
S.H. Bakhy ◽  
M. Al-Waily ◽  
M.A. Al-Shammari
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Functionally Graded Materials ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Gradient Index ◽  
Sandwich Beams ◽  
Graded Materials ◽  
The Impact

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

Geometrically nonlinear dynamic response and vibration of shear deformable eccentrically stiffened functionally graded material cylindrical panels subjected to thermal, mechanical, and blast loads

2018 ◽  
Vol 22 (3) ◽  
pp. 658-688 ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Ngo Duc Tuan ◽  
Pham Hong Cong ◽  
Ngo Dinh Dat ◽  
Nguyen Dinh Khoa
Keyword(s):  
Dynamic Response ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Nonlinear Dynamic ◽  
Functionally Graded ◽  
Blast Loads ◽  
Temperature Dependent ◽  
Nonlinear Dynamic Response ◽  
Cylindrical Panels ◽  
Graded Material

Based on the first order shear deformation shell theory, this paper presents an analysis of the nonlinear dynamic response and vibration of imperfect eccentrically stiffened functionally graded material (ES-FGM) cylindrical panels subjected to mechanical, thermal, and blast loads resting on elastic foundations. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to simple power-law distribution in terms of the volume fractions of the constituents. Both functionally graded material cylindrical panels and stiffeners having temperature-dependent properties are deformed under temperature, simultaneously. Numerical results for the dynamic response of the imperfect ES-FGM cylindrical panels with two cases of boundary conditions are obtained by the Galerkin method and fourth-order Runge–Kutta method. The results show the effects of geometrical parameters, material properties, imperfections, mechanical and blast loads, temperature, elastic foundations and boundary conditions on the nonlinear dynamic response of the imperfect ES-FGM cylindrical panels. The obtained numerical results are validated by comparing with other results reported in the open literature.

scholarly journals A state-based peridynamic formulation for functionally graded Kirchhoff plates

2020 ◽  
pp. 108128652096338
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Material Properties ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Benchmark Problems ◽  
Transverse Loading ◽  
Stress Concentrations ◽  
Element Analysis ◽  
Kirchhoff Plates ◽  
Peridynamic Model

Functionally graded materials are a potential alternative to traditional fibre-reinforced composite materials as they have continuously varying material properties which do not cause stress concentrations. In this study, a state-based peridynamic model is presented for functionally graded Kirchhoff plates. Equations of motion of the new formulation are obtained using the Euler–Lagrange equation and Taylor’s expansion. The formulation is verified by considering several benchmark problems including a clamped plate subjected to transverse loading and a simply supported plate subjected to transverse loading and inclined loading. The material properties are chosen such that Young’s modulus is assumed to be varied linearly through the thickness direction and Poisson’s ratio is constant. Peridynamic results are compared against finite element analysis results, and a very good agreement is obtained between the two approaches.

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