Hysteretic damping of a material or structure loaded within its elastic region is the dissipation of mechanical energy at a rate independent of the frequency of vibration while at the same time directly proportional to the square of the displacement. Generally, reproducing this frequency-independent damping can be computationally complex and requires prior knowledge of the system’s natural frequencies or the full time history of the system’s response. In this paper, a new model and numerical procedure are proposed whereby hysteretic material damping is achieved in the time domain. The proposed procedure is developed based on modifying the viscous model through a correction factor calculated exclusively using the local response. The superiority of the proposed approach lies in its ability to capture material hysteresis without any knowledge of the eigen- or modal frequencies of the system and without knowledge of the past time history of the system’s response or the characteristics of any excitation forces. A numerical procedure is also presented for implementing the proposed model in vibration analysis. The simplicity of the approach enables its generalisation to continuous systems and to systems of multi-degrees of freedom as demonstrated herein. The proposed model is presented as a correction to the viscous damping model which makes it attractive to implement into commercial finite element package using user-defined element subroutines as demonstrated in this study.

负载在其弹性区内的材料或结构的滞后阻尼是指机械能的耗散，其速率与振动频率无关，而同时又与位移的平方成正比。通常，再现这种与频率无关的阻尼可能会导致计算复杂，并且需要事先了解系统的固有频率或系统响应的全时历史。本文提出了一种新的模型和数值程序，可以在时域内实现滞回材料的阻尼。拟议的程序是基于通过使用局部响应专门计算出的校正因子修改粘性模型而开发的。所提出的方法的优越性在于它能够捕获材料的磁滞，而无需了解系统的本征或模态频率，也无需了解系统过去的响应时间历史或任何激励力的特性。还提出了一个数值程序，用于在振动分析中实施所提出的模型。该方法的简单性使其能够推广到连续系统和本文所证明的多自由度系统。提出的模型是对粘性阻尼模型的修正，这使它很有吸引力，可以使用用户定义的元素子例程实现到商业有限元软件包中，如本研究所示。