Free Vibration Analysis of FGM Plates under Initial Thermal Stresses

2013 ◽  
Vol 682 ◽  
pp. 49-56 ◽  
Author(s):  
A. Mahi ◽  
E.A. Adda-Bedia ◽  
A. Benkhedda
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Thermal Stresses ◽  
Plate Theory ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Energy Functional ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials

Functionally graded materials (FGMs) are a new kind of composite materials which have a smooth variation of material properties along one or more directions. At each interface, the material is chosen according to specific applications and environment loadings. This paper presents some solutions to study the free vibration of FGM plates made of ceramic and metal. The formulation used is based on Reddys higher order shear deformation plate theory. Material properties are taken to be temperature-dependent, and vary continuously through the thickness direction according to a power law distribution (P-FGM). The plate is assumed to be initially stressed by temperature rise through the thickness. The energy functional of the system is obtained by using energy principles. Free vibration frequencies are then obtained by using a set of characteristic orthogonal polynomials and by applying Ritz method.

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.

Free Vibration Analysis of Functionally Graded Cylindrical Shells Stiffened by Uniformly and Non-Uniformly Disturbuted Ring Stiffeners

2009 ◽  
Author(s):  
S. A. Moeini ◽  
M. Rahaeifard ◽  
M. T. Ahmadian ◽  
M. R. Movahhedy
Keyword(s):  
Free Vibration ◽  
Functionally Graded Materials ◽  
Vibration Analysis ◽  
Strain Energy ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Graded Materials ◽  
Energy Evaluation

Free vibration analysis of a transversely stiffened circular thin hollow cylinder made of functionally graded materials (FGMs) is analytically evaluated. Functionally graded materials are inhomogeneous composites which are usually made from a mixture of metal and ceramic. The gradient compositional variation of the constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses induced when two dissimilar materials with large differences in material properties are bonded. In this paper, application of an FGM made of two different materials is investigated by applying Ritz method. While cylinder is assumed to be thin, strain energy evaluation is performed by Sander’s theorem. Stiffeners which are not necessarily in the same uniform shape are treated as discrete elements and can be placed on both sides of the cylinder or concentrate in the middle wall. Bending, stretching and wrapping effects of stiffeners are considered in calculation of strain energy. Evaluation of kinetic energy of stiffeners is performed by taking into account rotary and translational inertia. To apply Ritz method, polynomial functions are used and natural frequencies and mode shapes of ring stiffened thin cylinder are investigated. Results are compared and verified with previous theoretical and experimental studies of stiffened thin cylinders. Comparison indicates a good agreement between results.

Static and Free Vibration Analysis of Structures Composed of Functionally Graded Material with Random Material Properties

2016 ◽  
Vol 857 ◽  
pp. 249-254
Author(s):  
Aswathy Komalan ◽  
Dhanya Krishnan
Keyword(s):  
Mechanical Properties ◽  
Free Vibration ◽  
Material Properties ◽  
Vibration Analysis ◽  
Structural Response ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Graded Materials ◽  
Graded Material ◽  
Random Material Properties

Functionally graded materials (FGMs) have mechanical properties that vary continuously from one phase to another within a confined volume. In general, these materials exhibit certain amount of scatter in their properties due to different factors. The dispersion in the response values of a structure is due to the scatter in the values of material properties and applied external load. For design purposes, it is essential to know the potential variations in the structural response due to the system material or external randomness. In the present work, free vibration and static analysis on FGM structures with material randomness are considered.

Free Vibration Analysis of Rotating Axially Functionally Graded Tapered Timoshenko Beams

2016 ◽  
Vol 16 (05) ◽  
pp. 1550007 ◽  
Author(s):  
Jian-Shi Fang ◽  
Ding Zhou
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Chebyshev Polynomials ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Speed Ratio ◽  
Timoshenko Beams ◽  
Graded Materials ◽  
Minimization Procedure

The free vibration of rotating tapered Timoshenko beams (TBs) made of the axially functionally graded materials (FGMs) is studied. The Chebyshev polynomials multiplied by the boundary functions are selected as the admissible functions in the Ritz minimization procedure, which is called the Chebyshev–Ritz method. As such, the geometric boundary conditions are satisfied, while the numerical robustness is guaranteed through use of the Chebyshev polynomials. The Ritz approach provides an upper bound of the exact frequencies. The effectiveness of the method is confirmed in the convergence and comparison studies. The effects of hub radius ratio, rotational speed ratio, taper ratios, rotary inertia and material gradient on the natural frequencies of the TBs for six different sets of boundary conditions are studied in detail.

scholarly journals Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Ning Zhang ◽  
Tahir Khan ◽  
Haomin Guo ◽  
Shaoshuai Shi ◽  
Wei Zhong ◽  
...  
Keyword(s):  
Free Vibration ◽  
Functionally Graded Materials ◽  
Vibration Analysis ◽  
Single Point ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Graded Materials ◽  
The Past ◽  
Future Work ◽  
Advanced Development

Functionally graded materials (FGMs) are novel materials whose properties change gradually with respect to their dimensions. It is the advanced development of formerly used composite materials and consists of two or more materials in order to achieve the desired properties according to the application where an FGM is used. FGMs have obtained a great attention of researchers in the past decade due to their graded properties at every single point in various dimensions. The properties of an FGM are not identical to the materials that constitute it. This paper aims to present an overview of the existing literature on stability, buckling, and free vibration analysis of FGM carried out by numerous authors in the past decade. Moreover, the analyses of mathematical models adopted for the aforementioned analyses are not the core purpose of this paper. At the end, future work is also suggested in this review paper.

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.

Analytical Solution of Thermal Stresses in a Functionally Graded Solid Cylinder within Parabolic Continuous Grading

2013 ◽  
Vol 307 ◽  
pp. 364-367 ◽  
Author(s):  
Ali Ozturk ◽  
Müfit Gülgeç
Keyword(s):  
Thermal Expansion ◽  
Analytical Solution ◽  
Material Properties ◽  
Thermal Conduction ◽  
Thermal Stresses ◽  
Elasticity Modulus ◽  
Functionally Graded ◽  
Solid Cylinder ◽  
Graded Materials ◽  
Parabolic Form

This paper presents analytical solutions of the thermal stresses in a functionally graded solid cylinder with fixed ends in elastic region. These thermal stresses are due to the uniform heat generation inside the cylinder. Material properties of the functionally graded (FG) cylinder vary radially according to a parabolic form. The material properties are assumed to be independent of the temperature which are yield strength, elasticity modulus, thermal conduction coefficient, thermal expansion coefficient and Poisson’s ratio. The solutions for the thermal stresses are valid for both homogeneous and functionally graded materials.

Hypersonic Flutter Analysis of Functionally Graded Panels under Thermal and Aerodynamic Loads

2009 ◽  
Vol 631-632 ◽  
pp. 41-46
Author(s):  
Sun Bae Kim ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Virtual Work ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Aerodynamic Loads ◽  
Linear Rule ◽  
Structural Nonlinearity ◽  
Post Buckling

In this work, hypersonic aero-thermo post-buckling and thermal flutter behaviors of Functionally Graded (FG) panels under thermal and aerodynamic loads are investigated. The volume fractions of constitutive materials of the panels are gradually varied from ceramic to metal in the thickness direction based on a simple power law distribution. Thus, the material properties of the panel are also changed by a linear rule of mixture. Furthermore, the material properties are assumed to be temperature dependent because the panels are mainly used in the high temperature environments. Using the principle of virtual work, the equations of motion of the first-order shear deformation plate theory (FSDPT) are derived and the finite element method is applied to get the solution. In the formulation, the von Karman strain-displacement relationship is used for structural nonlinearity, and the partial second-order piston theory is adopted to consider the aerodynamic nonlinearity. Newton-Raphson iterative technique is used to solve the governing equations, and linear eigenvalue analysis is performed to obtain the hypersonic flutter boundaries.

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