Nonlinear Dynamics of NEMS/MEMS Elements in the Form of Beams Taking into Account the Temperature Field, Radiation Exposure, Elastoplastic Deformations

Abstract

AbstractIn this work, a nonlinear vibrations theory of NEMS/MEMS beam elements is constructed. Nanobeams are considered as a Cosserat continuum with constrained rotation of particles (pseudo-continuum). Size-dependent effects are taken into account according to the modified moment theory, as well as the gradient theory of elasticity. Elastoplastic deformations are taken into account according to the deformation theory of plasticity; material properties depend on temperature and radiation exposure. The dependence of the stress intensity on the strain intensity taking into account the temperature field was obtained experimentally. The body is isotropic, but inhomogeneous. The Euler-Bernoulli kinematic model is adopted. The variational equations and the beam equations of motion, as well as the initial and boundary conditions, are obtained from the Hamilton-Ostrogradsky principle. The system of nonlinear partial differential equations is reduced to the Cauchy problem by the finite differences method of the second accuracy order in the spatial coordinate. The Cauchy problem is solved by several methods: the Runge-Kutta-type methods from the second to eighth accuracy orders and the Newmark method for obtaining reliable results. The stress-strain state static problem for the beams under the action of force, temperature, and radiation fields was solved by the steady solution method, which is a generalization by the continuation method in terms of parameters. Dynamic and static problems for beams were investigated taking into account physical nonlinearity and dimension-dependent parameters, boundary, and initial conditions. The theory, algorithms, and numerical experiment are obtained for the first time for beams according to the modified moment theory.KeywordsModified couple stress theoryPhysically nonlinear nanobeam