Effects of combined material and geometric nonlinearities on dynamic response of embedded nanobeams

Exact prediction of the mechanical behavior of nano-sensors and nano-actuators directly depends on the models applied to analyze their nano-components. From their dynamic behavior point of view, despite many studies related to the geometrical nonlinearities in modeling the nanostructures, one of the main issues that has not been addressed appropriately is the effects of material nonlinearity. Hence, this paper intends to fill this gap and deals with an investigation of combined geometrical and material nonlinearities on the nonlinear dynamic response of the embedded nanobeams in their free vibration as well as the primary and superharmonic resonances. The material nonlinearity considered in this research is formulated based on the sum of linear and cubic relations between the stress and strain. The results reveal that, for the material and boundary conditions of the embedded nanobeam studied in this research, the material nonlinearity tries to cause softening effects while the geometrical nonlinearity attempts to make hardening influences. The competition between these two effects leads to interesting nonlinear behaviors of the nanobeam for different dimensions and dynamic regimes that are scrutinized in this paper. In addition, the effects of applying external magnetic fields on the nonlinear responses of the nanobeams are investigated. (paper)