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Two-phase nonlocal integral models with a bi-Helmholtz averaging kernel for nanorods

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Abstract

In this work, the static tensile and free vibration of nanorods are studied via both the strain-driven (StrainD) and stress-driven (StressD) two-phase nonlocal models with a bi-Helmholtz averaging kernel. Merely adjusting the limits of integration, the integral constitutive equation of the Fredholm type is converted to that of the Volterra type and then solved directly via the Laplace transform technique. The unknown constants can be uniquely determined through the standard boundary conditions and two constrained conditions accompanying the Laplace transform process. In the numerical examples, the bi-Helmholtz kernel-based StrainD (or StressD) two-phase model shows consistently softening (or stiffening) effects on both the tension and the free vibration of nanorods with different boundary edges. The effects of the two nonlocal parameters of the bi-Helmholtz kernel-based two-phase nonlocal models are studied and compared with those of the Helmholtz kernel-based models.

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Acknowledgements

The authors appreciate the support of the Priority Academic Program Development of Jiangsu Higher Education Institutions of China.

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Pei Zhang & Hai Qing

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  1. Pei Zhang
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  2. Hai Qing
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Correspondence to Hai Qing.

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Project supported by the National Natural Science Foundation of China (No. 12172169) and the China Scholarship Council (CSC) (No. 202006830038)

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Zhang, P., Qing, H. Two-phase nonlocal integral models with a bi-Helmholtz averaging kernel for nanorods. Appl. Math. Mech.-Engl. Ed. 42, 1379–1396 (2021). https://doi.org/10.1007/s10483-021-2774-9

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  • DOI: https://doi.org/10.1007/s10483-021-2774-9

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