Large Amplitude Free Vibration Analysis of Functionally Graded Annular Plates

2014 ◽  
Vol 971-973 ◽  
pp. 548-564 ◽  
Author(s):  
Boutahar Lhoucine ◽  
Khalid El Bikri ◽  
Benamar Rhali
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Effective Properties ◽  
Plate Thickness ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Graphical Form ◽  
Wide Range ◽  
Non Linear

The geometrically non-linear axisymmetric free vibration of functionally graded annular plate (FGAP) having both edges clamped is analyzed in this paper. The material properties of the constituents are assumed to be temperature-independent and the effective properties of FGAP are graded in thickness direction according to a simple power law function in terms of the volume fractions. Based on the classical Plate theory and von Karman type non-linear strain-displacement relationships, the nonlinear governing equations of motion are derived using Hamilton’s principle. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to twice the plate thickness. The numerical results are given for the first two axisymmetric non-linear mode shapes, for a wide range of vibration amplitudes and they are presented either in a tabular or in a graphical form, to show the significant effects that the large vibration amplitudes and the variation in material properties have on the non-linear frequencies and the associated bending stresses of the FGAP.

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

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.

Free vibration analysis of functionally graded double-tapered beam rotating in thermal environment considering geometric nonlinearity, shear deformability, and Coriolis effect

2017 ◽  
Vol 232 (12) ◽  
pp. 2244-2262 ◽  
Author(s):  
Suman Pal ◽  
Debabrata Das
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Material Properties ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Coriolis Effect ◽  
Governing Equations

The present work investigates the free vibration behavior of double-tapered functionally graded beams rotating in thermal environment, using an improved mathematical model. The functional gradation for ceramic–metal compositions, following power-law, is considered to be symmetric with respect to the mid-plane, leading to metal-rich core and ceramic-rich outer surfaces of the beam. The temperature dependence of the material properties are considered using Touloukian model. The nonlinearity in strain–displacement relationships for both the axial and transverse shear strains are considered. Firstly, the governing equations for deformed beam configuration under time-independent centrifugal loading are obtained using minimum total potential energy principle, and the solution is obtained following Ritz method. Then the free vibration problem of the centrifugally deformed beam is formulated employing Lagrange’s principle and considering tangent stiffness of the deformed beam configuration. Coriolis effect is considered in the mathematical model, and the governing equations are transformed to the state-space for obtaining an eigenvalue problem. The results for the first two modes of both chord-wise and flap-wise vibrations are presented in nondimensional plane to show the effects of taperness parameter, root-offset parameter, volume fraction exponent, operating temperature, and functionally graded material composition. The results in comparative form are presented for both temperature-dependent and temperature-independent material properties.

scholarly journals Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Composite Doubly Curved Shallow Shell Panels Using a New Four-Variable Refined Theory

2019 ◽  
Vol 3 (4) ◽  
pp. 104 ◽  
Author(s):  
Vu Van Tham ◽  
Tran Huu Quoc ◽  
Tran Minh Tu
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Shallow Shell ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Refined Theory ◽  
Reinforced Composite ◽  
Doubly Curved

In this paper, a new four-variable refined shell theory is developed for free vibration analysis of multi-layered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shell panels. The theory has only four unknowns and satisfies zero stress conditions at the free surfaces without correction factor. Five different types of carbon nanotube (CNTs) distribution through the thickness of each FG-CNT layer are considered. Governing equations of simply supported doubly curved FG-CNTRC panels are derived from Hamilton’s principle. The resultant eigenvalue system is solved to obtain the frequencies and mode shapes of the anti-symmetric cross-ply laminated panels by using the Navier solution. The numerical results in the comparison examples have proved the accuracy and efficiency of the developed model. Detailed parametric studies have been carried out to reveal the influences of CNTs volume fraction, CNTs distribution, CNTs orientation, dimension ratios and curvature on the free vibration responses of the doubly curved laminated FG-CNTRC panels.

FREE VIBRATION OF FUNCTIONALLY GRADED PLATES WITH A HIGHER-ORDER SHEAR AND NORMAL DEFORMATION THEORY

2013 ◽  
Vol 13 (01) ◽  
pp. 1350004 ◽  
Author(s):  
D. K. JHA ◽  
TARUN KANT ◽  
R. K. SINGH
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Normal Deformation ◽  
Fg Plates

Free vibration analysis of functionally graded elastic, rectangular, and simply supported (diaphragm) plates is presented based on a higher-order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson ratios of the FG plates are assumed to be constant, but their Young's modulii and densities vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modeled as a power law function. The equations of motion are derived using Hamilton's principle for the FG plates on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of Navier solution method. The accuracy of the numerical solutions is first established through comparison with the exact three-dimensional (3D) elasticity solutions and the present solutions are then compared with available solutions of other models.

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

2020 ◽  
Vol 23 (16) ◽  
pp. 3415-3428
Author(s):  
Yusuf Cunedioglu ◽  
Shkelzen Shabani
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Single Edge ◽  
Functionally Graded Beam ◽  
Cross Sectional

Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

Free vibration analysis of functionally graded beams using an exact plane elasticity approach

2014 ◽  
Vol 228 (14) ◽  
pp. 2488-2494 ◽  
Author(s):  
K Celebi ◽  
N Tutuncu
Keyword(s):  
Free Vibration ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Future Research ◽  
Graded Material ◽  
Beam Thickness ◽  
Plane Elasticity Theory

Exact natural frequencies of functionally graded beams are determined using plane elasticity theory. The analysis yields infinitely many frequencies. For verification purposes, a comparison with the existing beam theory results is performed and a close agreement is observed for slender members. The elasticity solutions are general in the sense that they are valid for slender members as well as short and thick structural elements. Both flexural and axial free vibration mode shapes are presented for top and bottom surfaces and the effect of the beam thickness is discussed. The exact results presented herein can be used as benchmarks for future research of free vibration behavior of short and thick functionally graded material beams.

A two-dimensional free vibration analysis of functionally graded sandwich beams under thermal environment

2012 ◽  
Vol 226 (12) ◽  
pp. 2860-2873 ◽  
Author(s):  
AR Setoodeh ◽  
M Ghorbanzadeh ◽  
P Malekzadeh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Thermal Environment ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Sandwich Beams ◽  
Two Dimensional

In this article, free vibration analysis of elastically supported sandwich beams with functionally graded face sheets subjected to thermal environment is presented. In order to accurately include the transverse shear deformation and the inertia effects, two-dimensional elasticity theory is used to formulate the problem. The layerwise theory in conjunction with the differential quadrature method is employed to discretize the governing equations in the thickness and axial directions, respectively. The material properties of functionally graded face sheets are assumed to be temperature-dependent and graded in the thickness direction according to a power-law distribution. For the purpose of comparison, the problem under consideration is also solved using two-dimensional finite element method and the first-order shear deformation theory. The accuracy, convergence, and versatility of the method are demonstrated by comparing the results with those of the two aforementioned approaches and also with the existing solutions in literature. Eventually, some new numerical results are presented which depict the effects of different material and geometrical parameters on natural frequencies and mode shapes of the beam.

scholarly journals A Finite Element Formulation and Nonlocal Theory for the Static and Free Vibration Analysis of the Sandwich Functionally Graded Nanoplates Resting on Elastic Foundation

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Van-Ke Tran ◽  
Thanh-Trung Tran ◽  
Minh-Van Phung ◽  
Quoc-Hoa Pham ◽  
Trung Nguyen-Thoi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Material Properties ◽  
Free Vibration Analysis ◽  
Nonlocal Theory ◽  
Functionally Graded ◽  
Element Formulation ◽  
Proposed Model ◽  
Homogeneous Core

This article presents a finite element method (FEM) integrated with the nonlocal theory for analysis of the static bending and free vibration of the sandwich functionally graded (FG) nanoplates resting on the elastic foundation (EF). Material properties of nanoplates are assumed to vary through thickness following two types (Type A with homogeneous core and FG material for upper and lower layers and Type B with FG material core and homogeneous materials for upper and lower layers). In this study, the formulation of the four-node quadrilateral element based on the mixed interpolation of tensorial components (MITC4) is used to avoid “the shear-locking” problem. On the basis of Hamilton’s principle and the nonlocal theory, the governing equations for the sandwich FG nanoplates are derived. The results of the proposed model are compared with published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and material properties on the static and free vibration behaviors of nanoplates are investigated in detail.

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