New insights on nonlocal spherical shell model and its application to free vibration of spherical fullerene molecules

• Published in: International journal of mechanical sciences Vol. 161-162; p. 105046
• Main Authors: Ghavanloo, Esmaeal, Rafii-Tabar, Hashem, Fazelzadeh, S. Ahmad
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2019
• Subjects: Axisymmetric free vibration; Fullerene molecule; Nonlocal model; Spherical shell; Spherical shell; Nonlocal model; Axisymmetric free vibration; Fullerene molecule
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2019.105046

•A new nonlocal spherical shell model is developed for free vibration of spherical nanoshells.•An explicit closed-form solution for the axisymmetric free vibration is presented.•The method is compared against existing numerical and experimental results.•Results show that the nonlocal parameter does not play any role in the mode shapes of the axisymmetric vibration. Nonlocal elasticity theory was developed in order to describe some phenomena that cannot properly be described by the classical local elasticity theory. The formalism incorporates the long range interactions between points in continuum media. In this paper, a novel form of the nonlocal spherical shell model is formulated for application to the problem of the free vibration of nanoshells of spherical geometry. In contrast to previous studies which employ the Laplacian of the components of the stress tensor, in this proposed model the expressions for the Laplacian of the stress tensor components are used to drive the governing equations. Using the Legendre and the associated Legendre functions, a general solution for the differential equations of a momentless spherical shell subject to axisymmetric free vibration is presented. In addition, the validity of the present model is tested via some of the existing numerical and experimental results. [Display omitted]