Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load

Abstract

For the first time, the structural dynamics and vibrational stability of a viscoelastic axially functionally graded (AFG) beam with both spinning and axial motions subjected to an axial load are analyzed, with the aim to enhance the performance of bi-gyroscopic systems. A detailed parametric study is also performed to emphasize the influence of various key factors such as material distribution type, viscosity coefficient, and coupled rotation and axial translation on the dynamical characteristics of the system. The material properties of the system are assumed to vary linearly or exponentially in the longitudinal direction with viscoelastic effects. Adopting the Laplace transform and a Galerkin discretization scheme, the critical axial and spin velocities of the system are obtained. An analytical approach is applied to identify the instability thresholds. Stability maps are examined, and for the first time in this paper, it is demonstrated that the stability evolution of the system can be altered by fine-tuning of axial grading or viscosity of the material. The variation of density and elastic modulus gradient parameters are found to have opposite effects on the divergence and flutter boundaries of the system. Furthermore, the results indicate that the destabilizing effect of the axial compressive load can be significantly alleviated by the simultaneous determination of density and elastic modulus gradation in the axial direction of the system.