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Axial wave propagation and vibration of nonlocal nanorods with radial deformation and inertia
Author(s) -
Li XianFang,
Shen ZhiBin,
Lee Kang Yong
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201500186
Subject(s) - inertia , wavenumber , elasticity (physics) , vibration , classical mechanics , physics , nanorod , stiffness , equations of motion , normal mode , mathematical analysis , mechanics , mathematics , materials science , optics , quantum mechanics , thermodynamics , nanotechnology
Longitudinal dynamic problems of nanorods or nanobars are analyzed based on the nonlocal elasticity theory and Bishop's assumptions. Radial deformation and inertia are considered. A governing equation for axial motion of circular nanorods is derived via Hamilton's principle. The phase speed of longitudinal waves is determined in explicit form and the dispersion curve is displayed. Exact frequency equations for clamped‐free, clamped‐clamped, and free‐free nanorods are obtained and mode shapes are derived. A unified approximation for low frequencies is given and compared with exact results. The Love theory of nonlocal rods is a special case of the present with shear stiffness vanishing. Classical Bishop and Love rod theories can be recovered only letting the size effect disappear. The simple nonlocal rod model is reduced if setting Poisson's ratio to zero. Illustrative examples of nanofibers and nanotubes are given to show the influence of the nonlocal scale parameter on the phase speed and the natural frequencies.