Analysis of oscillations in 1D nanostructures influenced by different concrete potential functions

A family of nonlinear second-order partial differential equations based on concrete potential functions were formulated and analyzed. The occurrence of linear and nonlinear wave solutions were dependent on the interaction potential introduced into the nanostructure and on the initial conditions intr...

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Bibliographic Details
Published in:	International journal of non-linear mechanics Vol. 148; p. 104307
Main Authors:	Surulere, S.A., Shatalov, M.Y., Ehigie, J.O.
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01-01-2023
Subjects:	1D nanostructure Accreting nanostructures Interatomic potentials Nonlinear vibrations Variational principles Wave solutions 1D nanostructure Nonlinear vibrations Variational principles Interatomic potentials Accreting nanostructures Wave solutions
Online Access:	Get full text
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Summary:	A family of nonlinear second-order partial differential equations based on concrete potential functions were formulated and analyzed. The occurrence of linear and nonlinear wave solutions were dependent on the interaction potential introduced into the nanostructure and on the initial conditions introduced to the system. The family of nonlinear equations were numerically analyzed because at present, it is difficult (or not possible) to obtain their exact solutions. The law of linear growth was introduced into the nanostructure and space variables were transformed in terms of new variables. The accreting nanostructure was linearly growing for the interaction potentials introduced. Due to the nonlinear form of the formulated equations, the method of lines approach was used to obtain the numerical solutions of the governing equations. Copper atoms were used to in all simulations and calculations. •A family of nonlinear second-order partial differential equations based on concrete potential functions were formulated and numerically analysed. New equations based on the analytic forms of the potentials were constructed.•The law of linear growth was introduced into the nanostructure and space variables were transformed in terms of new variables. This resulted into the formulation of new governing equations also based on potentials.•Due to the stiffness of the governing equations, the method of lines approach was used to numerically analyse the nonlinear waves in the nanostructures.
ISSN:	0020-7462 1878-5638
DOI:	10.1016/j.ijnonlinmec.2022.104307