scholarly journals On the Effect of Functionally Graded Materials on Resonances of Rotating Beams

2012 ◽  
Vol 19 (6) ◽  
pp. 1315-1326 ◽  
Author(s):  
Arnaldo J. Mazzei Jr.
Keyword(s):  
Young’S Modulus ◽  
Functionally Graded Materials ◽  
Young's Modulus ◽  
Ritz Method ◽  
Turbine Blades ◽  
Functionally Graded ◽  
Graded Materials ◽  
Rotating Beams ◽  
Helicopter Blades ◽  
Aerospace Applications

Radially rotating beams attached to a rigid stem occur in several important engineering applications. Some examples include helicopter blades, turbine blades and certain aerospace applications. In most studies the beams have been treated as homogeneous. Here, with a goal of system improvement, non-homogeneous beams made of functionally graded materials are explored. The effects on the natural frequencies of the system are investigated. Euler-Bernoulli theory, including an axial stiffening effect and variations of both Young's modulus and density, is employed. An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. It was found, for example, that allowing Young's modulus and density to vary by approximately 2.15 and 1.15 times, respectively, leads to an increase of 23% in the lowest bending rotating natural frequency of the beam.

scholarly journals On the Effect of Functionally Graded Materials on Resonances of Rotating Beams

2012 ◽  
Vol 19 (4) ◽  
pp. 707-718 ◽  
Author(s):  
Arnaldo J. Mazzei Jr.
Keyword(s):  
Young’S Modulus ◽  
Functionally Graded Materials ◽  
Young's Modulus ◽  
Ritz Method ◽  
Turbine Blades ◽  
Functionally Graded ◽  
Graded Materials ◽  
Rotating Beams ◽  
Helicopter Blades ◽  
Aerospace Applications

Radially rotating beams attached to a rigid stem occur in several important engineering applications. Some examples include helicopter blades, turbine blades and certain aerospace applications. In most studies the beams have been treated as homogeneous. Here, with a goal of system improvement, non-homogeneous beams made of functionally graded materials are explored. The effects on the natural frequencies of the system are investigated. Euler-Bernoulli theory, including an axial stiffening effect and variations of both Young's modulus and density, is employed. An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. It was found, for example, that allowing Young's modulus and density to vary by approximately 2.15 and 1.15 times, respectively, leads to an increase of 23% in the lowest bending rotating natural frequency of the beam.

Inversion of Functionally Graded Materials to Improve the Elastic Ultimate Bearing Capacity of Thick-Walled Hollow Cylinder

2011 ◽  
Vol 378-379 ◽  
pp. 116-120 ◽  
Author(s):  
Ai Zhong Lu ◽  
Ning Zhang
Keyword(s):  
Bearing Capacity ◽  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Functionally Graded Materials ◽  
Young's Modulus ◽  
Ultimate Bearing Capacity ◽  
Functionally Graded ◽  
The Body ◽  
Graded Materials ◽  
Homogeneous Materials

Thick-walled hollow cylinder is an important class of engineering structure, the stress state of which depends on the loads and properties of the body materials. Under the assumptions of σθ-σr=c (σθ and σr denote the hoop stress and radial stress, respectively, c is a constant), inverse analysis of thick-walled hollow cylinder composed of functionally graded materials with uniform pressure acting on the outer surface is carried out. Analytical solutions for the Young’s modulus variation in the radial direction are obtained. It is found that only when the Young’s modulus E(r) is a specific monotone increasing function of the radius r, the pre-specified stress distribution can be satisfied. Comparing with classical homogeneous materials, stress concentration at the inner surface of hollow cylinder composed of functionally graded materials can be alleviated. Hence the elastic ultimate bearing capacity of hollow cylinder can be improved strikingly. For functionally graded materials, the elastic ultimate bearing capacity can be improved strikingly by increasing the thickness of cylinder, which is not so obvious for classical homogeneous materials.

scholarly journals Design of Kinematic Connectors for Microstructured Materials Produced by Additive Manufacturing

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1500
Author(s):  
Miguel R. Silva ◽  
João A. Dias-de-Oliveira ◽  
António M. Pereira ◽  
Nuno M. Alves ◽  
Álvaro M. Sampaio ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Functionally Graded Materials ◽  
Cellular Structure ◽  
Young's Modulus ◽  
Functionally Graded ◽  
Graded Materials ◽  
Mean Values ◽  
Shear Moduli ◽  
Young’S Moduli ◽  
Unit Cells

The main characteristic of materials with a functional gradient is the progressive composition or the structure variation across its geometry. This results in the properties variation in one or more specific directions, according to the functional application requirements. Cellular structure flexibility in tailoring properties is employed frequently to design functionally-graded materials. Topology optimisation methods are powerful tools to functionally graded materials design with cellular structure geometry, although continuity between adjacent unit-cells in gradient directions remains a restriction. It is mandatory to attain a manufacturable part to guarantee the connectedness between adjoining microstructures, namely by ensuring that the solid regions on the microstructure’s borders i.e., kinematic connectors) match the neighboring cells that share the same boundary. This study assesses the kinematic connectors generated by imposing local density restrictions in the initial design domain (i.e., nucleation) between topologically optimised representative unit-cells. Several kinematic connector examples are presented for two representatives unit-cells topology optimised for maximum bulk and shear moduli with different volume fractions restrictions and graduated Young’s modulus. Experimental mechanical tests (compression) were performed, and comparison studies were carried out between experimental and numerical Young’s modulus. The results for the single maximum bulk for the mean values for experimental compressive Young’s modulus (Ex¯) with 60%Vf show a deviation of 9.15%. The single maximum shear for the experimental compressive Young’s modulus mean values (Ex¯) with 60%Vf, exhibit a deviation of 11.73%. For graded structures, the experimental mean values of compressive Young’s moduli (Ex¯), compared with predicted total Young’s moduli (ESe), show a deviation of 6.96 for the bulk graded structure. The main results show that the single type representative unit-cell experimental Young’s modulus with higher volume fraction presents a minor deviation compared with homogenized data. Both (i.e., bulk and shear moduli) graded microstructures show continuity between adjacent cells. The proposed method proved to be suitable for generating kinematic connections for the design of shear and bulk graduated microstructured materials.

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.

Modelling and Analysis of Functionally-Graded Cracked Beams Subjected to Static and Dynamic Loadings

2020 ◽  
pp. 306-326
Author(s):  
B. Panigrahi ◽  
Goutam Pohit
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Ritz Method ◽  
Beam Theory ◽  
Functionally Graded ◽  
Structural Elements ◽  
Cracked Beam ◽  
Graded Materials ◽  
Detailed Method ◽  
Dynamic Loadings

In last few decades, continuous efforts have been put by the researchers on developing the field of structural systems considering the applicability and enhancing material properties of the structural elements. In this regard functionally graded materials (FGMs) have gained tremendous popularity and have been the active area of research interest for researchers in recent decades. In this chapter, a detailed method of analysis for FGM cracked beam subjected to static and dynamic loadings is presented. Method based on Timoshenko beam theory and Ritz method is successfully implemented to get the displacement and natural frequency of cracked beam subjected to static as well as dynamic loadings.

Measurement Model for Young's Modulus of Axially Functionally Graded Materials

2017 ◽  
Vol 748 ◽  
pp. 391-395
Author(s):  
Xiao Liang Chen ◽  
Long Zhang ◽  
Ding Yu Li
Keyword(s):  
Elastic Modulus ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Beam Theory ◽  
Measurement Model ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Graded Materials ◽  
Experiment Method ◽  
Euler Bernoulli Beam

For axially functionally graded beams with elastic modulus varying through the longitudinal directions, a measurement model for Young's modulus is presented based on the classic Euler-Bernoulli beam theory. When the force and deflection of cantilever beams are measured by the experiment method, the Young's modulus of axially functionally graded beams can be obtained by the measurement model. By the derivation rule of compound functions, the validity of the measurement model is proved. For the axially functionally graded beams with elastic modulus varying according to the power law and the exponential law respectively, the deflection is simulated by the finite element method. The simulated elastic modulus by the model is in accord with the theoretical value well.

Dynamic Analysis with Stress Recovery for Functionally Graded Materials: Numerical Simulation and Experimental Benchmarking

2014 ◽  
Vol 2 (1) ◽  
pp. 21
Author(s):  
Carlos Alberto Dutra Fraga Filho ◽  
Fernando César Meira Menandro ◽  
Rivânia Hermógenes Paulino de Romero ◽  
Juan Sérgio Romero Saenz
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Stress Recovery ◽  
Graded Materials
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