A causal fractional-order lter to approximate the performance of rate-independent linear damping Part 1: The proposed model

摘要

In structural dynamics, damping is usually an unignorableand even critical factor, and thus should be carefullyconsidered and properly simulated. In many cases,a linear viscous damping model is used, partly becauseit provides convenience to the mathematical analyses ofstructure in both the frequency and time domains; however, such a damping model exhibits the energy dissipated in one cycle of sinusoidal deformation proportional to the vibration frequency, which violates the experimental results of many engineering solid materials . The concept of rate-independent linear damping (RILD) is introduced to represent the rate-independent energy dissipation behavior,which is also referred to as structural damping,complex-value stiffness, linear hysteretic damping, or ideal hysteretic damping. It is well known that the ideal RILD model is non-causal, and several causal RILD models were proposed in the past decades. Recently, Keivan et al. proposed semi-active methods to mimic the behavior of RILD by using a first-order all-pass filter, whichis further passively realized by using a mechanical systemconsisting of a negative stiffness element and a Maxwellelement connected with each other in parallel. In thisstudy, a fractional-order RILD model is proposed to representthe rate-independent dissipation behavior, whichincludes the model used in the past studies as a specialcase, and can also provide a good approximation ofthe Makris' model over the frequency range of interest.