Dynamics of Functionally Graded Porous Rotating Rayleigh Microbeams with Longitudinal Movement in Complex Fields

As a first attempt, the vibration of rotating functionally graded porous Rayleigh beams under longitudinal motion in hygro-thermo-magnetic fields is scrutinized numerically and analytically based on the scale-dependent strain gradient theory. Also, parametric studies are performed to diagnose the impacts of critical factors such as the functionally graded index, rotary inertia parameter, porosity distribution, foundation characteristics, environmental loads, boundary conditions, axial and tangential follower forces on the microbeam stability. It is assumed that the material properties of the microbeam are graded across the thickness according to a power-law function with six different porosity models. The dynamical equations of the functionally graded microbeam are derived based on the extended Hamilton's principle. Then, backward and forward vibrational frequencies are computed with the aid of the Galerkin discretization scheme and eigenvalue analysis. For validation purposes, the results are compared with published reports. Furthermore, the instability border of the microbeam is determined via an analytical approach. Critical rotational and longitudinal speeds as well as Campbell and stability diagrams are obtained to identify the stability evolution. The results declared that as the functionally graded index and rotary inertia parameter ascend, divergence and flutter speeds of the microbeam descend. The presented outcomes could be helpful in the optimum design of inhomogeneous gyroscopic microsystems.