Vibrational behavior of viscoelastic AFG rotating micro-beam with longitudinal motion under axial load in magnetic field based on the modified couple stress theory

The vibrational behavior of an axially graded micro-beam with both axial and rotational motion under axial load have been studied in the magnetic field. A detailed parametric study was performed to explain the effect of various factors such as range of axial graded of materials, type of material distribution, viscosity coefficient, and magnetic field strength, length scale parameter of material, rotation and coupling crossing motion on the dynamical characteristics of the system. It is assumed that the material properties of the system change linearly or exponentially in the longitudinal direction. The critical axial and rotational speeds of the system are obtained by using Galerkin discretization technique and eigenvalue analysis. An analytical method has also been used to identify system instability thresholds. System stability maps were tested, and it has been shown that by increasing the magnetic field strength and the length scale parameter, the system stability can be improved. The results also show that the simultaneous determination of density gradient and elastic modulus in the longitudinal direction can reduce the destructive effects of compressive axial load.