Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions
An analytical modelling is carried out to determine the Lamb wave’s propagation behavior in a thermal stress relaxation type functionally graded material (FGM) plate, which is a composite of two kinds of materials. The mechanical parameters depend on the volume fractions, which are nonintegral power...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Materials Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2015/137913 |
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| author | Xiaoshan Cao Zhen Qu Junping Shi Yan Ru |
| author_facet | Xiaoshan Cao Zhen Qu Junping Shi Yan Ru |
| author_sort | Xiaoshan Cao |
| collection | DOAJ |
| description | An analytical modelling is carried out to determine the Lamb wave’s propagation behavior in a thermal stress relaxation type functionally graded material (FGM) plate, which is a composite of two kinds of materials. The mechanical parameters depend on the volume fractions, which are nonintegral power functions, and the gradient coefficient is the power value. Based on the theory of elastodynamics, differential equations with variable coefficients are established. We employ variable substitution for theoretical derivations to solve the ordinary differential equations with variable coefficients using the Taylor series. The numerical results reveal that the dispersion properties in some regions are changed by the graded property, the phase velocity varies in a nonlinear manner with the gradient coefficient, nondispersion frequency exists in the first mode, and the set of cutoff frequencies is a union of two series of approximate arithmetic progressions. These results provide theoretical guidance not only for the experimental measurement of material properties but also for their nondestructive testing. |
| format | Article |
| id | doaj-art-fc3d2dfe7bf14fbb9d894e0fdcc11d15 |
| institution | Kabale University |
| issn | 1687-8434 1687-8442 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Materials Science and Engineering |
| spelling | doaj-art-fc3d2dfe7bf14fbb9d894e0fdcc11d152025-02-03T06:11:46ZengWileyAdvances in Materials Science and Engineering1687-84341687-84422015-01-01201510.1155/2015/137913137913Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume FractionsXiaoshan Cao0Zhen Qu1Junping Shi2Yan Ru3Department of Engineering Mechanics, School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an 710048, ChinaDepartment of Engineering Mechanics, School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an 710048, ChinaDepartment of Engineering Mechanics, School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an 710048, ChinaDepartment of Engineering Mechanics, School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an 710048, ChinaAn analytical modelling is carried out to determine the Lamb wave’s propagation behavior in a thermal stress relaxation type functionally graded material (FGM) plate, which is a composite of two kinds of materials. The mechanical parameters depend on the volume fractions, which are nonintegral power functions, and the gradient coefficient is the power value. Based on the theory of elastodynamics, differential equations with variable coefficients are established. We employ variable substitution for theoretical derivations to solve the ordinary differential equations with variable coefficients using the Taylor series. The numerical results reveal that the dispersion properties in some regions are changed by the graded property, the phase velocity varies in a nonlinear manner with the gradient coefficient, nondispersion frequency exists in the first mode, and the set of cutoff frequencies is a union of two series of approximate arithmetic progressions. These results provide theoretical guidance not only for the experimental measurement of material properties but also for their nondestructive testing.http://dx.doi.org/10.1155/2015/137913 |
| spellingShingle | Xiaoshan Cao Zhen Qu Junping Shi Yan Ru Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions Advances in Materials Science and Engineering |
| title | Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions |
| title_full | Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions |
| title_fullStr | Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions |
| title_full_unstemmed | Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions |
| title_short | Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions |
| title_sort | lamb waves in a functionally graded composite plate with nonintegral power function volume fractions |
| url | http://dx.doi.org/10.1155/2015/137913 |
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