MODAL ANALYSIS OF FRACTIONAL DERIVATIVE DAMPING MODEL OF FREQUENCY-DEPENDENT VISCOELASTIC SOFT MATTER

摘要

In this study, the fractional derivative is employed to describe the frequency-dependent damping behaviors of viscoelastic soft matter, and the modal analysis of such fractional derivative governing equation model is carried out in comparison with the corresponding integer-order derivative vibration models of classical viscous and hysteretic dampings. The Fourier transformation is used to derive frequency response functions and the Nyquist plots. And dynamic properties of viscoelastic soft matters, such as natural frequency, are displayed via the Nyquist plot and the frequency response function. For viscoelastic soft matter obeying frequency-dependent damping law, the Nyquist plot characterizes the features of both the viscous and the hysteretic systems, which varies with the order of the fractional derivative describing damping behaviors.