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**Fractional order thermoelastic problem for finite piezoelectric rod subjected to different types of thermal loading – direct approach.**
*(English)*
Zbl 1496.35379

Summary: The problem of generalized thermoelasticity of two-temperature for finite piezoelectric rod will be modified by applying three different types of heating applications namely, thermal shock, ramp-type heating and harmonically vary heating. The solutions will be derived with direct approach by the application of Laplace transform and the Caputo-Fabrizio fractional order derivative. The inverse Laplace transforms are numerically evaluated with the help of a method formulated on Fourier series expansion. The results obtained for the conductive temperature, the dynamical temperature, the displacement, the stress and the strain distributions have represented graphically using MATLAB.

### MSC:

35Q74 | PDEs in connection with mechanics of deformable solids |

35B07 | Axially symmetric solutions to PDEs |

35G30 | Boundary value problems for nonlinear higher-order PDEs |

35K05 | Heat equation |

44A10 | Laplace transform |

74F05 | Thermal effects in solid mechanics |

74F15 | Electromagnetic effects in solid mechanics |

78A55 | Technical applications of optics and electromagnetic theory |

26A33 | Fractional derivatives and integrals |

35R11 | Fractional partial differential equations |

### Keywords:

Caputo-Fabrizio fractional order derivative; piezothermoelasticity; ramp-type heating; harmonically varying temperature; thermal loading### Software:

Matlab
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\textit{K. R. Gaikwad} and \textit{V. G. Bhandwalkar}, J. Korean Soc. Ind. Appl. Math. 25, No. 3, 117--131 (2021; Zbl 1496.35379)

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### References:

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