A Hertz contact model with non-linear damping for pounding simulation

Abstract

SUMMARYThis paper investigates the cogency of various impact models in capturing the seismic pounding response of adjacent structures. The analytical models considered include the contact force-based linear spring, Kelvin and Hertz models, and the restitution-based stereomechanical approach. In addition, a contact model based on the Hertz law and using a non-linear hysteresis damper (Hertzdamp model) is also introduced for pounding simulation. Simple analytical approaches are presented to determine the impact sti ness parameters of the various contact models. Parameter studies are performed using two degreeof-freedom linear oscillators to determine the e ects of impact modelling strategy, system period ratio, peak ground acceleration (PGA) and energy loss during impact on the system responses. A suite of 27 ground motion records from 13 di erent earthquakes is used in the analysis. The results indicate that the system displacements from the stereomechanical, Kelvin and Hertzdamp models are similar for a given coe cient of restitution, despite using di erent impact methodologies. Pounding increases the responses of the sti er system, especially for highly out-of-phase systems. Energy loss during impact is more signiÿcant at higher levels of PGA. Based on the ÿndings, the Hertz model provides adequate results at low PGA levels, and the Hertzdamp model is recommended at moderate and high PGA levels.

Seismic Pounding of Multistoreyed Buildings

“…Pounding is critical on the responses of the stiff system, especially when the system is highly out-of-phase. Essentially, in-phase systems exhibit displacement amplifications that are much closer to one, independent of model type [2].…”

Nonsmooth Seismic Response Analysis of a Benchmark Straight Bridge With Deck-Abutment Impact-Induced Rotation

“…This study adopts the proposed stiffness and damping values of [17], [18], [19], and also examines other values of stiffness ranging from 10 -4 to 10 +2 k. Figure 7 plots the response history of the translational displacements and the in-plane rotation of the deck during Excitation No. 5.…”

Pounding force assessment in performance‐based design of bridges

“…In addition, with these models, a negative reaction force takes place just before the end of the contact. More recently, Hertz models have been used [1,12]. They provide a better fit with experimental results, although there are not many of them.…”

“…They provide a better fit with experimental results, although there are not many of them. For instance, Muthukamar and DesRoches [12] report a comprehensive inventory of experimental data available, including only five references. The authors conclude that, with this support, it is a difficult task to a priori choosing a restitution coefficient, the key parameter of all models.…”