Size-dependent nonlinear analysis of piezo-electrostatically actuated porous functionally graded nanobeams incorporating flexoelectricity

Xie, Zili; Zheng, Shijie; Chen, Dejin

doi:10.1007/s40430-022-03983-0

Cited by 4 publications

(1 citation statement)

References 44 publications

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“…In the above papers, the authors consider homogeneous materials. Functionally graded porous beams under the action of Casimir and Coulomb forces were considered in [18]. The authors considered the effects of geometric nonlinearity, flexoelectricity, material distribution on the free vibrations of the beams and the retraction effect.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Eigen frequencies of a functionally graded porous nano-beam with respect to the coulomb and Casimir forces

Папкова

Yakovleva

2023

E3S Web of Conf.

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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.

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Section: Introductionmentioning

confidence: 99%