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

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The objectives of this work were: to design and build material specimens which behave, under mechanical loading, such as functionally graded materials; to perform dynamic vibration tests on the produced specimens, and; to numerically simulate the vibration tests in order to validate a proposed numerical model for functionally graded materials characterization. The work was divided in the following phases: confection of the specimens; adoption of the composite beam model for the produced specimens; preparation and execution of the vibration laboratory tests; mathematical modeling for the analytical resolution of the composite beam vibration problem; definition of the numerical model to be applied to the problem; execution of the numerical simulation of the dynamic tests, and; comparative analysis between the analytical, experimental, and numerical results. The experimental, analytical, and numerical tests present similar results for all specimens. Natural vibration frequencies, whether obtained by any means (experimental, analytical, or numerical) differ not more than 15.4%. The proposed numerical method presents itself, thus, adequate for layered material modeling.
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Elastic Properties; Finite Element Analysis (FEA); Functional Composite; Modelling; Vibration

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L. Banks-Sills, R. Eliasi, and Y. Berlin. Modeling of functionally graded materials dynamic analyses. Composites: Part B: Engineering, 33:7–15, 2002.

R. J. Butcher, C. E. Rousseau, and H. V. Tippur. A functionally graded particulate composite: Preparation, measurements and failure analysis. Acta Materialia, 47(1):259–268, 1998.

M. M. Gasik. Micromechanical modeling of functionally graded materials. Composite Materials and Science, 13:42–55, 1998.

Y. Gu, T. Nakamura, L. Prchlik, S. Sampath, and J. Wallace. Micro-indentation and inverse analysis to characterize elastic-plastic graded materials. Materials Science and Engineering, A345:223–233, 2003.

T. Nakamura, T. Wang, and S. Sampath. Determination of properties of graded materials by inverse analysis and instrumented indentation. Acta Materialia, 48:4293–4306, 2000.

G. R. Liu, X. Han, Y.G. Xu, and K.Y. Lam. Material characterization of functionally graded material by means of elastic waves and a progressive-learning neural network. Composites Science and Technology, 61(10):1401–1411, 2001.

Benmansour, T., Bensmail, K., Homogenisation approach for linear free dynamic analysis of energy dissipative multilayered beams:Application to mirror symmetry bernoulli beams, (2010) International Review of Mechanical Engineering (IREME), 4 (3), pp. 322-329.

Shahrjerdi, A., Bayat, M., Mustapha, F., Sapuan, S.M., Zahari, R., Stress analysis a functionally graded quadrangle plate using second order shear deformation theory, (2010) International Review of Mechanical Engineering (IREME), 4 (1), pp. 92-105.

Isvandzibaei, M.R., Analysis free vibration of FGM cylindrical shells under clamped-simply support boundary conditions, (2011) International Review of Mechanical Engineering (IREME), 5 (1), pp. 71-78.

Setareh, M., Isvandzibaei, M.R., Behaviors clamped-free boundary conditions for a functionally graded material hollow cylindrical shell under vibration with third order shear deformation theory, (2011) International Review of Mechanical Engineering (IREME), 5 (4), pp. 680-687.

Goudarzi, A.M., Saadati, S., Paknahad, A., Stress analysis of FG thick pressure vessels considering the effects of material gradations and poisson's ratio using DQ method, (2012) International Review of Mechanical Engineering (IREME), 6 (1), pp. 55-60.

C. A. D. Fraga, Filho. Análise dinâmica com recuperação de tensões para materiais com gradação funcional: simulação numérica e validação experimental. Master’s thesis, Programa de Pós-Graduação em Engenharia Mecânica - PPGEM, Universidade Federal do Espírito Santo, Brazil, 2007.

R. H. Paulino, J. S. Romero, and F. C. M. Menandro. A higher order stress post-processing for the elasticity equation applied to a functionally graded material (FGM). In CILAMCE 2004, Recife, PE, Brazil, november 2004.

R. H. Paulino, J. S. Romero, and F. C. M. Menandro. Recuperação de tensões e análise dinâmica de materiais com gradação funcional. In CILAMCE 2005, Guarapari, ES, Brazil, october 2005.

K. G. McConnell. Vibration Testing- Theory and Practice. John Wiley and Sons, Inc., 1995.

R. Kuerten, M. Zaro, L.C. Gomes, M. Marranghello, and V.T. Batista. Análise teórica e prática da resposta em freqüência de diapasão mecânico (em forma de y) e comparação com método numérico (via elementos finitos). Tecnologia, Revista de Engenharia, Energia e Desenvolvimento Sustentável, 6(2), Brazil, 2005.

O. X. B. Carrillo. Detecção de dano a partir da resposta dinâmica da estrutura: Estudo analítico com aplicação a estruturas do tipo viga. Master’s thesis, Universidade de São Carlos, Brazil, 2004.


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