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

Abstract

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.