| Issue |
E3S Web of Conf.
Volume 389, 2023
Ural Environmental Science Forum “Sustainable Development of Industrial Region” (UESF-2023)
|
|
|---|---|---|
| Article Number | 01029 | |
| Number of page(s) | 9 | |
| Section | Materials Science Innovations, Green Chemistry and Emission Reduction | |
| DOI | https://doi.org/10.1051/e3sconf/202338901029 | |
| Published online | 31 May 2023 | |
Nonlinear Eigen frequencies of a functionally graded porous nano-beam with respect to the coulomb and Casimir forces
Yuri Gagarin State Technical University of Saratov, 77 Politechnicheskaya street, 410054, Saratov, Russia
* Corresponding author: ikravzova@mail.ru
A new mathematical model of a porous functionally graded micro/nano-beam under the action of the Casimir force and the Coulomb force is constructed in this paper. The construction of the mathematical model takes into account the Euler-Bernoulli kinematic model. The dimensional-dependent parameter is taken into account by modified moment theory of elasticity. The variational, differential equations, boundary and initial conditions are derived from Ostrogradsky-Hamiltonian variational principle. The problem of non-linear natural oscillations of a beam under the action of force Casimir and Coulomb force is solved. The influence of the Casimir and Coulomb forces on the nonlinear eigenfrequencies of the micro/nano-beam is shown.
© The Authors, published by EDP Sciences, 2023
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