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Transient response in a piezoelastic medium due to the influence of magnetic field with memory-dependent derivative

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Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a piezoelastic half-space due to the influence of a magnetic field in the context of the dual-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The bounding plane of the medium is assumed to be stress free and subjected to a thermal shock. Employing the Laplace transform as a tool, the problem is transformed to the space domain, where the solution in the space–time domain is achieved by applying a suitable numerical technique based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are constructed. Excellent predictive capability is demonstrated due to the presence of electric field, memory-dependent derivative and magnetic field.

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Acknowledgements

We are grateful to the Editor and reviewers for their valuable suggestions for the improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Basirhat College, Kolkata, West Bengal, India

    Sudip Mondal

  2. Department of Mathematics, Techno India, EM 4/1, Salt Lake, Sector V, Kolkata, West Bengal, 700091, India

    Abhik Sur

  3. Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata, West Bengal, 700009, India

    M. Kanoria

  4. Department of Mathematics, Sister Nivedita University, Newtown, Kolkata, 700156, India

    M. Kanoria

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  1. Sudip Mondal
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Mondal, S., Sur, A. & Kanoria, M. Transient response in a piezoelastic medium due to the influence of magnetic field with memory-dependent derivative. Acta Mech 230, 2325–2338 (2019). https://doi.org/10.1007/s00707-019-02380-4

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