Improved Damping Constant of Hertz-Damp Model for Pounding between Structures

Dahai Zhao,Yong Liu

doi:10.1155/2016/9161789

Abstract

Earthquake-induced pounding between structures has been widely studied by using different impact models. In this paper, we first briefly introduced the existing impact analysis models and discussed their shortcomings. For the Hertz-damp impact analysis model, the damping constants do not accord with the physical facts; then, based on the Hertz theory, the expression of the damping constant in the Hertz-damp impact analysis model is improved. The approximate formula of the damping constant is theoretically derived, and the accuracy and effectiveness of the calculation formula of the damping constant are verified by the selected collision analysis problems.

Highlights

Structural pounding is a complicated nonlinear problem
Where δ is the relative displacement of two colliding objects, δexpresses the relative deformation velocity of the colliding objects during the impact process, kk is the impact spring stiffness of Kelvin model, and ck stands for the damping coefficient, which is determined by the following formula: ck
Where δ is the relative displacement of two colliding objects, δexpresses the relative deformation velocity of the colliding objects during the impact process, kh is the Hertz-damp model impact spring stiffness, and ch stands for the damping coefficient, and its expression is determined by the following formula: ch = ξδ3/2

Summary

Introduction

In order to effectively study the response of the adjacent structures under the impact, the reasonable impact analysis model is very significant. Since the Kelvin model is frequently used to simulate the collision of adjacent structures, the expression of the damping coefficient in Kelvin model has been derived by Ye et al [1]. In order to preferably simulate the force and displacement relationship in the process of simulation, many scholars have used the Hertz theory to study the impact response. In this paper, based on the review of the main impact models and the Hertz theory, a new approximate formula of the damping constant of Hertz-damp model is derived. The numerical simulation of the pounding analysis problems is conducted by MATLAB/Simulink software, the results of impact simulation show the correctness, accuracy, and effectiveness of the approximate formula of the damping constant of Hertz-damp model

Review of Existing Impact Models

Correction of Damping Constant

Numerical Verification

Findings

Conclusions