The dynamic problem of thermoelectroelasticity for functionally graded layer
DOI:
https://doi.org/10.7242/1999-6691/2017.10.2.10Keywords:
thermoelectroelasticity, thermal impact, functionally gradient layerAbstract
A general formulation for the problem of motion of inhomogeneous thermoelectroelastic body is considered. The problem of heat flow impact on the functionally graded layer made of piezoceramics is considered as an example. One plane of the layer is grounded, while the other has an electric potential induced by a pyroelectric effect. Nondimensionalization of the boundary value problem of thermoelectroelasticity allows us to identify the coupling parameters. After excluding the electric potential from the formulation, the problem of thermoelectroelasticity is reduced to the problem of themoelasticity with modified coefficients. Upon the application of the Laplace transformation, the problem of themoelasticity is reduced to the system of the Fredholm integral equations of the second kind and is solved numerically by the collocation method using the trapezoid quadrature formula. The original solutions are found using the residue theory. A comparison between the results of the numerical and analytical solutions is made, using as an example, a homogeneous layer of barium titanate. The influence of different forms of the thermal impact on the behavior of the induced electric potential is investigated. The dependence of the induced electrical potential on the distribution of inhomogeneities in the class of power and exponential functions is explored. It has been found that the form of the laws governing the distribution of inhomogeniety of heat conduction and heat capacity coefficients has an essential effect on the shape of the induced potential. And vice versa, the form of the laws governing the distribution of inhomogeneity of the elastic modulus, material density and coefficient of thermal stresses do not affect the shape of the induced potential. These findings are attributed to smallness of the thermomechanical coupling parameter for real materials and should be taken into account in designing various technical devices, which make use of functionally-graded materials with specified properties.
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Hussain T.M., Baig A.M., Saadawi T.N., Ahmed S.A. Infrared pyroelectric sensor for diction of vehicular traffic using digital signal processing techniques // IEEE T. Veh. Technol. - 1995. - Vol. 44, no. 3. - P. 683-689. DOI
2. Danilovskaa V.I. Temperaturnye naprazenia v uprugom poluprostranstve, voznikausie vsledstvie vnezapnogo nagreva granicy // PMM. - 1952. - T. 16, No 3. - S. 341-344.
3. Mindlin R.D. On the equations of motion of piezoelectric crystals // Problems of continuum mechanics / Ed. by N.I. Muskilishivili. - Philadelphia: SIAM, 1961. - P. 282-290.
4. Mindlin R.D. Equations of high frequency vibrations of thermopiezoelectric crystal plates // Int. J. Solids Struct. - 1974. - Vol. 10, no. 6. - P. 625-637. DOI
5. Nowacki W. Some general theorems of thermopiezoelectricity // J. Therm. Stresses. - 1978. - Vol. 1, no. 2. - P. 171-182. DOI
6. Novackij V. Elektromagnitnye effekty v tverdyh telah. - M.: Mir, 1986. - 160 s.
7. Vatul’an A.O, Kirutenko A.U., Nasedkin A.V. Ploskie volny i fundamental’nye resenia v linejnoj termoelektrouprugosti // PMTF. - 1996. - T. 37, No 5. - S. 135-142.
8. Vatul’an A.O, Kirutenko A.U., Fedorova V.V. Zadaca Danilovskoj v termoelektrouprugosti // Mezvuzovskij sbornik naucnyh trudov <>. - Rostov-na-Donu: DGTU, 1997. - No 2. - S. 25-30.
9. Vatul’an A.O. Teplovoj udar po termoelektrouprugomu slou // Vestnik DGTU. - 2001. - T. 1(7), No 1. - S. 82-89.
10. Bassiouny E., Youssef H.M. Two-temperature generalized thermopiezoelasticity of finite rod subjected to different types of thermal loading // J. Therm. Stresses. - 2008. - Vol. 31, no. 3. - P. 233-245. DOI
11. Bassiouny E., Youssef H.M. Thermo-elastic properties of thin ceramic layers subjected to thermal loadings // J. Thermoelasticity. - 2013. - Vol. 1, no. 1. - P. 4-12. (URL: http://researchpub.org/journal/jot/number/vol1-no1/vol1-no1-1.pdf).
12. Zhu X., Meng Z. Operational principle, fabrication and displacement characteristics of a functionally gradient piezoelectric ceramic actuator // Sensors Actuat. A-Phys. - 1995. - Vol. 48, no. 3. - P. 169-176. DOI
13. Wu C.C.M., Kahn M., Moy W. Piezoelectric ceramics with functional gradients: A new application in material design // J. Am. Ceram. Soc. - 1996. -Vol. 79, no. 3. - P. 809-812. DOI
14. Shen S., Kuang Z.-B. An active control model of laminated piezothermoelastic plate // Int. J. Solids Struct. - 1999. - Vol. 36, no. 13. - P. 1925-1947. DOI
15. Lee W.Y., Stinton D.P., Berndt C.C., Erdogan F., Lee Y.-D., Mutasim Z. Concept of functionally graded materials for advanced thermal barrier coatings applications // J. Am. Ceram. Soc. - 1996. - Vol. 79, no. 12. - P. 3003-3012. DOI
16. Wang B.L., Noda N. Design of a smart functionally graded thermopiezoelectric composite structure // Smart. Mater. Struct. - 2001. - Vol. 10, no. 2. - P. 189-193. DOI
17. Wu X.-H., Shen Y.-P., Chen C. An exact solution for functionally graded piezothermoelastic cylindrical shell as sensor or actuators // Mater Lett. - 2003. - Vol. 57, no. 22-23. - P. 3532-3542. DOI
18. Ying C., Zhefei S. Exact solutions of functionally gradient piezothermoelasic cantilevers and parameter identification // J. Intel. Mat. Syst. Str. - 2005. - Vol. 16, no. 6. - P. 531-539. DOI
19. Zhong Z., Shang E.T. Exact analysis of simply supported functionally graded piezothermoelectric plates // J. Intel. Mat. Syst. Str. - 2005. - Vol. 16, no. 7-8. - P. 643-651. DOI
20. Ootao Y., Tanigawa Y. The transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply // Arch. Appl. Mech. - 2005. - Vol. 74, no. 7. - P. 449-465. DOI
21. Ootao Y., Tanigawa Y. Transient piezothermoelastic analisys for a functionally graded thermopiezoelectrical hollow sphere // Compos. Struct. - 2007. - Vol. 81, no. 7. - P. 540-549. DOI
22. Nedin R., Nesterov S., Vatulyan A. On an inverse problem for inhomogeneous thermoelastic rod // Int. J. Solids Struct. - 2014. - Vol. 51, no. 3-4. - P. 767-773. DOI
23. Vatul’an A.O., Nesterov S.A. Ob odnom sposobe identifikacii termouprugih harakteristik dla neodnorodnyh tel // Inzenerno-fiziceskij zurnal. - 2014. - T. 87, No 1. - S. 217-224. DOI
24. Durbin F. Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method // Comput. J. - 1974. - Vol. 17, no. 4. - P. 371-376. DOI
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