Inverse Method for Determining Profiles of Elastic Parameters in the Functionally Graded Materials using Love Waves

2016 ◽  
Vol 102 (3) ◽  
pp. 428-435
Author(s):  
P. Kiełczyński ◽  
M. Szalewski ◽  
A. Balcerzak ◽  
K. Wieja
Keyword(s):  
Functionally Graded Materials ◽  
Inverse Method ◽  
Functionally Graded ◽  
Love Waves ◽  
Elastic Parameters ◽  
Graded Materials

scholarly journals Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

2015 ◽  
Vol 40 (2) ◽  
pp. 273-281 ◽  
Author(s):  
Piotr Kiełczyński ◽  
Marek Szalewski ◽  
Andrzej Balcerzak ◽  
Krzysztof Wieja
Keyword(s):  
Group Velocity ◽  
Half Space ◽  
Functionally Graded Materials ◽  
Integral Formula ◽  
Liouville Problem ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Love Waves ◽  
Graded Materials ◽  
Sturm Liouville

AbstractThis paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method.The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

A non-iterative inverse method for the identification of time and space-dependent heat sources of multi-dimensional FGMs by boundary temperature data

2021 ◽  
Vol 01 ◽  
Author(s):  
Chuang Xu ◽  
Chunying Dong
Keyword(s):  
Functionally Graded Materials ◽  
Inverse Method ◽  
Temperature Data ◽  
Functionally Graded ◽  
Least Square ◽  
Heat Sources ◽  
Graded Materials ◽  
Precise Integration ◽  
Boundary Temperature ◽  
Error Method

Background: Detection of heat sources is frequently encountered in many fields of science and engineering and plays a significant role in monitoring and control of many engineering thermal systems. Objective: The objective of this paper is to estimate the space and time-dependent heat sources in multi-dimensional functionally graded materials using boundary temperature data. Methods: First, the dimensionless temperature at the measurement points on the boundary is obtained by a direct process. Then, the objective function is obtained by a series of matrix operations, and the relationship between the temperature at the measurement points and the unknown parameters is established. After that, the strength of the heat sources can be inversed directly by the least-square error method, then the location and number of the heat sources can be obtained directly from the strength distribution of heat sources. The coefficient expansion method and truncated singular value decomposition method are applied to reduce the ill-posed degree of the inverse process. Results: Through the analysis of typical 2-dimensional and 3-dimensional examples, the influence of various factors such as the type of basis functions, the circular supported radius and the measurement noise on the inversion results is discussed, which shows that this method can identify the strength, location and number of heat sources of FGMs well. Conclusion: A non-iterative inverse method based on precise integration finite element method and least-square error method is established to estimate the strength, location and number of the unknown heat sources of functionally graded materials using boundary temperature data.

Propagation of ultrasonic Love waves in nonhomogeneous elastic functionally graded materials

Ultrasonics ◽  
2016 ◽  
Vol 65 ◽  
pp. 220-227 ◽  
Author(s):  
P. Kiełczyński ◽  
M. Szalewski ◽  
A. Balcerzak ◽  
K. Wieja
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Love Waves ◽  
Graded Materials

A two-stage inverse method for the evaluation of volume fraction distributions in 2D and 3D functionally graded materials

2011 ◽  
Vol 225 (7) ◽  
pp. 1550-1564 ◽  
Author(s):  
M A Nematollahi ◽  
M R Hematiyan ◽  
M Farid
Keyword(s):  
Functionally Graded Materials ◽  
Inverse Analysis ◽  
Inverse Method ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Unknown Parameters ◽  
Graded Materials ◽  
Fraction Distribution ◽  
Two Stages

In this article, an inverse method is proposed to determine the volume fraction distributions in functionally graded materials (FGMs). By determining the space-dependent volume fractions of the FGM phases, the properties of the FGMs are characterized. The proposed method, which is based on a steady-state thermal test, is applied in two stages. In the first stage, the two- or three-dimensional material is considered piecewise homogenous and its properties are found by a simple inverse analysis. In the second stage, the unknown volume fraction distribution is considered as a continuous function with several unknown parameters. Estimated values of these unknown parameters are found using the results obtained in the first stage and by another inverse analysis. The obtained results show that the presented method is efficient in estimating the volume fraction distributions in FGMs.

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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