Abstract
In this paper, the dynamic Euler–Bernoulli PDE model based on the quadratic constitutive law are used for modeling of monolayer graphene sheets suspended in free vibration. The PDE model and corresponding lumped-parameter model are introduced. Analytical formulas for the lumped-parameter model and semi-analytic/numerical solutions of the model are presented by using several techniques of approximations. It is demonstrated analytically and numerically that the nonlinear quadratic term has a significant impact on the resonant frequency of the vibrating system. In additions to the numerical solution, the analytic solution obtained by the variational iteration method with Pade approximations indicates the existence of several natural frequencies of nonlinear models.
Original language | English |
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Article number | 117062 |
Journal | Journal of Sound and Vibration |
Volume | 534 |
DOIs | |
Publication status | Published - 15 Sept 2022 |
Externally published | Yes |
Keywords
- Graphene sheet
- Lumped-parameter model
- Natural frequency
- Stiffness coefficient
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Acoustics and Ultrasonics
- Mechanical Engineering