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Gaikwad, Kishor R.; Bhandwalkar, Vidhya G.

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

J. Korean Soc. Ind. Appl. Math. 25, No. 3, 117-131 (2021).
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.

Cited in 1 Document

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)
Full Text: DOI

References:

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