Effect of magnetic field and fluid on primary and secondary frequency response of carbon nanotube conveying nanoflow using SDM

In this paper, the nonlinear forced vibrations of carbon nanotubes conveying magnetic nanofluids under a longitudinal magnetic field are investigated. Using Von Karmen nonlinear strain field and Euler-Bernoulli beam theory, the equations governing the nonlinear vibrations of simply supported carbon nanotubes are extracted. Using the multiple scale method, the frequency response is obtained in primary resonance, supperharmonic resonance and subharmonic resonance. The stress driven nonlocal integral model has been used to consider the effects of nano size. Finally, the effect of magnetic fluid and magnetic field strength on frequency response and force response is investigated. From the results it can be found that the presence of a magnetic field causes the vibrational amplitude of the system to be unstable and to have a limit cycle. Under these conditions the vibrational response is quasi-alternative. However, the presence of a magnetic fluid causes the vibration amplitude to be stable and the temporal response to be alternative; So that the Poincaré diagram shows a point on the phase plane. In primary resonance, despite the longitudinal magnetic field, with increasing excitation amplitude, the frequency response curves include two sub-amplitudes. One is an asymptotic curve with a horizontal axis and the other consists of a closed curve.