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

doi:10.1007/s10483-021-2774-9

摘要/Abstract

摘要： 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.

关键词: two-phase nonlocal integral model, bi-Helmholtz kernel, tensile analysis, free vibration, exact solution, Laplace transform

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.

Key words: two-phase nonlocal integral model, bi-Helmholtz kernel, tensile analysis, free vibration, exact solution, Laplace transform

中图分类号:

74K10

Pei ZHANG, Hai QING. Two-phase nonlocal integral models with a bi-Helmholtz averaging kernel for nanorods[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(10): 1379-1396.

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