Dynamics of spinning axially graded porous nanoscale beams with rectangular cross-section incorporating rotary inertia effects

Abstract

The impacts of axially functionally graded (AFG) materials, porosity distribution patterns, rotary inertia factor, hygro-thermo-magnetic environments, non-uniform elastic substrates, axisymmetric cross-sections, axial and distributed tangential loads on the stability, and dynamics of spinning are analyzed. The governing equations of lateral displacements of the nanobeam are extracted based on the modified nonlocal theory (MNT) and the Rayleigh beam theory assumptions. The vibration frequencies are identified by solving the eigenvalue problem and exploiting the Galerkin discretization scheme. Stability maps and Campbell diagrams are presented to survey divergence and flutter behaviors with the help of numerical and analytical treatments. Comparative studies in various system circumstances are conducted to confirm the accuracy of the model and methodology. Results revealed that contrary to the square cross-section case, a divergence instability region is detected in the stability evolution of the nanobeam with a rectangular cross-section. Also, ascending the porosity factor leads to a more stable structure for low AFG indices. Moreover, the nanobeam can experience flutter instability by considering rotary inertia effects. The present research results could be advantageou for the design of high-tech inhomogeneous spinning systems.