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The free and forced vibration behavior analysis of multi-stepped FGP-GPLRC curved beam with general boundary conditions

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Abstract

This paper plans to propose a general numerical model for investigating the free and forced vibration behaviors of the multi-stepped functionally graded porous graphene platelet-reinforced composite (FGP-GPLRC) curved beam with various boundary conditions based on the first-order shear deformation Timoshenko beam theory by employing Rayleigh–Ritz method in conjunction with Jacobi polynomials. Different porosity and GPL distribution types are considered. The general boundary conditions of the multi-stepped FGP-GPLRC curved beam and connecting conditions of the FGP-GPLRC curved beam elements are simulated by employing boundary springs and connecting springs, respectively. The convergence and validation of the proposed numerical model are demonstrated by comparing the proposed results with the corresponding results which come from open literature and finite element software ABAQUS. The free and forced vibration behavior analysis of multi-stepped FGP-GPLRC curved beam is carried out by investigating the influences of material property and geometric parameters on the natural frequency and displacement response in the frequency and time domains of multi-stepped FGP-GPLRC curved beam structure. The investigation results can offer the technique guidance for the design and manufacture of the multi-stepped FGP-GPLRC curved beam.

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Funding

This study was supported by the Project of Shandong Province Higher Educational Science and Technology Program (Grant No. J18KA035); Natural Science Foundation of Shandong Province (Grant Nos. ZR2022QE086 and ZR2023ME133).

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Zaozhuang University, Shandong, 277160, China

    C. Yu, J. Lu, Q. Yang, K. Yang, W. Xu & C. Chiu

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  1. C. Yu
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Correspondence to C. Chiu.

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Yu, C., Lu, J., Yang, Q. et al. The free and forced vibration behavior analysis of multi-stepped FGP-GPLRC curved beam with general boundary conditions. Acta Mech (2024). https://doi.org/10.1007/s00707-024-03886-2

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