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Wave propagation analysis of functionally graded graphene origami-enabled auxetic metamaterial beams resting on an elastic foundation

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Abstract

Our study employs the Timoshenko beam theory to thoroughly investigate the propagation of waves in auxetic metamaterial beams enabled by functionally graded graphene origami. This exploration is conducted while the Winkler–Pasternak foundation supports the beams. In addition, many distinct graphene origami (GOri) distribution patterns have been explored, and the results have been shown to be uniform and functionally graded across the thickness direction. The kinetic equations of auxetic metamaterial beams may be captured with the help of Hamilton's principle, which is applied here. The analytical solution of the governing equations for the auxetic metamaterial beam is determined based on the received information. Comparisons have been made between the effects that a wide variety of parameters have on the wave frequency and phase velocity of the auxetic metamaterial beam. These parameters include graphene distribution pattern and content, GOri folding degree, temperature, wave number, and elastic foundation coefficients. The crucial aspects of each figure have been identified through in-depth analysis and comparison of the results.

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  1. Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran

    Farzad Ebrahimi & Mahdi Parsi

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  1. Farzad Ebrahimi
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Appendix

Appendix

$$ M = \left[ {\begin{array}{*{20}c} {m_{11} } & 0 & {m_{13} } \\ 0 & {m_{22} } & 0 \\ {m_{31} } & 0 & {m_{33} } \\ \end{array} } \right], \, K = \left[ {\begin{array}{*{20}c} {k_{11} } & 0 & {k_{13} } \\ 0 & {k_{22} } & {k_{23} } \\ {k_{31} } & {k_{32} } & {k_{33} } \\ \end{array} } \right] $$

where

$$ \begin{gathered} m_{11} = I_{1} {, }m_{13} = I_{2} \hfill \\ m_{22} = I_{1} \hfill \\ m_{31} = I_{2} , \, m_{33} = I_{3} \hfill \\ \end{gathered} $$
$$ \begin{gathered} k_{11} = - A_{11} \beta^{2} , \, k_{13} = - B_{11} \beta^{2} , \, \hfill \\ k_{22} = - A_{55} \beta^{2} - k_{w} - k_{p} \beta^{2} + N_{x}^{T} \beta^{2} , \, k_{23} = A_{55} \beta i \hfill \\ k_{31} = - B_{11} \beta^{2} , \, k_{32} { = } - A_{55} \beta i, \, k_{33} = - D_{11} \beta^{2} - A_{55} \hfill \\ \end{gathered} $$

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Ebrahimi, F., Parsi, M. Wave propagation analysis of functionally graded graphene origami-enabled auxetic metamaterial beams resting on an elastic foundation. Acta Mech 234, 6169–6190 (2023). https://doi.org/10.1007/s00707-023-03705-0

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