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Homotopy solution for nonlinear vibration analysis of multilayer graphene platelets-reinforced thin-walled pipes conveying fluid with rectangular cross-section

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Abstract

Nonlinear vibration of fluid-conveying pipes with thin-walled rectangular cross-sections is analytically explored for the first time. The pipe is considered to be multilayer which is reinforced by graphene platelets by considering four distribution patterns. The nonlinear vibration of fluid-conveying pipes with three cross-sections of square, horizontal, and vertical rectangle is studied. For modeling the pipe, the thin-walled Euler–Bernoulli beam theory is applied. By considering von Kármán’s nonlinearities, the nonlinear equations of motion are derived using Hamilton’s principle. The nonlinear partial differential equation of motion is discretized by the Galerkin method. The analytical solutions for the time response and nonlinear frequency of the pipe are presented by applying the homotopy analysis method. The main novelty of this research is about the investigation of the nonlinear vibration of pipes conveying fluid with thin-walled rectangular cross-sections which has not been investigated in the former works. Numerical investigations in this study are carried out by studying the effects of cross-section, fluid velocity, length of the pipe, distribution patterns, and weight fraction of graphene platelets on the nonlinear frequency, backbone curves, and time history of graphene platelets-reinforced fluid-conveying thin-walled pipe. The different numerical results indicate that reinforcing the pipe with graphene platelets and the type of the pipe’s cross-section have significant effects on the performance of the fluid-conveying pipe systems.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Rasoul Khodabakhsh, Ali Reza Saidi & Reza Bahaadini

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  1. Rasoul Khodabakhsh
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  2. Ali Reza Saidi
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Khodabakhsh, R., Saidi, A.R. & Bahaadini, R. Homotopy solution for nonlinear vibration analysis of multilayer graphene platelets-reinforced thin-walled pipes conveying fluid with rectangular cross-section. Acta Mech 234, 577–598 (2023). https://doi.org/10.1007/s00707-022-03389-y

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