Time-Domain Analysis of Linear Hysteretic Damping

Abstract

SUMMARYTwo linear-hysteretic-damping models that provide energy dissipation independent of the deformation frequency, are studied in this paper: a hysteretic Kelvin element and a hysteretic Maxwell element. Both models use the Hilbert transform and yield integro-differential equations for the equations of motion of structures when real-valued signals are utilized in the formulation. It is shown that the use of analytic (complex-valued) signals allows the transformation of these integro-differential equations into differential equations with analytic input signals and complex-valued coefficients. These differential equations show both stable and unstable poles. A technique for the solution of these differential equations is presented; it consists of a conventional modal decomposition of the state-space equations and the integration of the differential equations forward in time for the modal co-ordinates associated with stable poles, and backwards in time for the modal co-ordinates associated with unstable poles. Some numerical examples are presented to illustrate the characteristics of the models and the proposed analysis technique.

Experimental and numerical studies on new multi-dimensional earthquake isolation and mitigation device: Horizontal properties

“…A large number of studies [3-5, 18, 19] and the aforementioned test results showed that the storage modulus G 1 decreases with increasing temperature and increases with increasing frequency, and the loss factor η has an optimal value with varying temperature and frequency. In order to describe the characteristics of viscoelastic devices or materials, some mathematical models, such as the Kelvin model, the Maxwell model and the standard linear solid model have been proposed [3][4][5], while these models can not explicitly reflect temperature and frequency effects at the same time. But in fact, temperature and frequency are very important factors affecting the characteristics of viscoelastic materials.…”

“…Among these devices, viscoelastic damper is the most popular because of its cost-effectiveness and high energy dissipation capability. Many studies and tests on viscoelastic dampers have shown that the properties of energy absorption depend on various parameters such as ambient temperature, excitation frequency and its amplitude [1][2][3][4][5][6][7]. In addition, a number of earthquake mitigation devices using viscoelastic materials have been also proposed.…”

Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness Matrices

“…A constant damping factor (loss factor) is taken for the modeling of the dissipation in materials, and joints are modeled with thin layer elements representing equivalent dissipation and stiffness of the joints [1]. This method shows a better correlation with real life structures, however it can be used only in frequency domain, since in time domain it leads to non-causal material behavior [8,9]. Some investigations to this model have been made already and show a good correlation with experimentally determined joint parameters [10,11].…”

A new type of damper with friction-variable characteristics

“…From this book, I learned about the Energy Dissipating Restraint (EDR) system, as improved by Nims et al (1993) and based on a normal friction damper with rectangular hysteretic loop fi rst introduced by the Sumitomo Company in Japan. Via certain refi nements, it was found that EDR can be remolded as a passive friction energy dissipating device, which can provide several hysteretic behaviors (Nims et al, 1993;Kelly, 1993, 1995;Inaudi and Nicos, 1996;Inaudi et al, , 1994, such as triangular, double fl ag and rectangular hysteretic modes (see . The triangular and double fl ag hysteretic modes have some characteristics that were not observed in normal energy dissipation devices (such as metallic dampers, Pall friction damper, etc.).…”