Transverse Vibrations and Stability of Viscoelastic Axially Moving Rayleigh Beams Under Thermal Fields: an Analytical Approach

Abstract

In this work, the flexural vibrations and stability of viscoelastic beams under axial motion and thermal fields are investigated using Rayleigh beam theory. The viscoelastic behavior is modeled through the Kelvin-Voigt and Maxwell models, and the governing differential equation is derivative utilizing Hamilton's principle. To create a more realistic model, thermal stresses in the beam are simulated using both linear and non-linear models. An innovative analytical solution method for these equations is presented, employing a power series approach to solve equations. The research provides an explicit mathematical expression for the mixed vibration modes of the beam under axial motion. Various parameters, such as rotational inertia, linear and non-linear thermal stresses, structural damping, and axial movement speed, are analyzed for their effects on the dynamic characteristics and instability of viscoelastic Rayleigh beams under axial motion. The findings indicate that incorporating rotational inertia and Rayleigh beam theory reduces the natural frequencies at low axial speeds but consistently increases the system's critical speed. Furthermore, rotational inertia induces distortions in the vibration mode shapes. Notably, the impact of rotational inertia on the second mode shape is significant, resulting in the loss of the nodal point in the second vibration mode shape of the beam under axial motion.