Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field

In the present research, vibration and instability of axially moving single-layered graphene sheet (SLGS) subjected to magnetic field is investigated. Orthotropic visco-Pasternak foundation is developed to consider the influences of orthotropy angle, damping coefficient, normal and shear modulus. Third order shear deformation theory (TSDT) is utilized due to its accuracy of polynomial functions than other plate theories. Motion equations are obtained by means of Hamilton’s principle and solved analytically. Influences of various parameters such as axially moving speed, magnetic field, orthotropic viscoelastic surrounding medium, thickness and aspect ratio of SLGS on the vibration characteristics of moving system are discussed in details. The results indicated that the critical speed of moving SLGS is strongly dependent on the moving speed. Therefore, the critical speed of moving SLGS can be improved by applying magnetic field. The results of this investigation can be used in design and manufacturing of marine vessels in nanoscale.