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Analytical Solutions of Viscoelastic Nonlocal Timoshenko Beams

Author

Listed:
  • Francesco Paolo Pinnola

    (Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21, Ed. 6, 80125 Naples, Italy)

  • Raffaele Barretta

    (Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21, Ed. 6, 80125 Naples, Italy)

  • Francesco Marotti de Sciarra

    (Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21, Ed. 6, 80125 Naples, Italy)

  • Antonina Pirrotta

    (Department of Engineering, University of Palermo, Via E. Basile, 90128 Palermo, Italy)

Abstract

A consistent nonlocal viscoelastic beam model is proposed in this paper. Specifically, a Timoshenko bending problem, where size- and time-dependent effects cannot be neglected, is investigated. In order to inspect scale phenomena, a stress-driven nonlocal formulation is used, whereas to simulate time-dependent effects, fractional linear viscoelasticity is considered. These two approaches are adopted to develop a new Timoshenko bending model. Analytical solutions and application samples of the proposed formulation are presented. Moreover, in order to show influences of viscoelastic and size effects on mechanical response, parametric analyses are provided. The contributed results can be useful for the design and optimization of small-scale devices exhibiting flexural behaviour.

Suggested Citation

  • Francesco Paolo Pinnola & Raffaele Barretta & Francesco Marotti de Sciarra & Antonina Pirrotta, 2022. "Analytical Solutions of Viscoelastic Nonlocal Timoshenko Beams," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:477-:d:740585
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    Citations

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    Cited by:

    1. Bekir Akgöz & Ömer Civalek, 2022. "Buckling Analysis of Functionally Graded Tapered Microbeams via Rayleigh–Ritz Method," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
    2. Krzysztof Kamil Żur & Jinseok Kim & Junuthula N. Reddy, 2022. "Special Issue of Mathematics : Analytical and Numerical Methods for Linear and Nonlinear Analysis of Structures at Macro, Micro and Nano Scale," Mathematics, MDPI, vol. 10(13), pages 1-2, June.
    3. Doaa Atta & Ahmed E. Abouelregal & Fahad Alsharari, 2022. "Thermoelastic Analysis of Functionally Graded Nanobeams via Fractional Heat Transfer Model with Nonlocal Kernels," Mathematics, MDPI, vol. 10(24), pages 1-24, December.

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