On the dynamics of rigid-block motion under harmonic forcing

Author:

Abstract

In this paper the simplest and most widely used model of a rigid block undergoing harmonic forcing is analysed in detail. The block is shown to possess extremely complicated dynamics, with many different types of response being revealed. Symmetric single-impact subharmonic orbits of all orders are found and regions of parameter space in which they occur are given. In particular, period-doubling cascades of asymmetric orbits are found, which ultimately produce an apparently non-periodic or chaotic response. Sensitivity to initial conditions is illustrated, which leads to uncertainty in the prediction of the asymptotic dynamics. Nevertheless, the transient response may be the most important in connection with real earthquakes. To this end, the concept of the domain of maximum transients is introduced. In this light the response is shown to be quite ordered and predictable, despite the chaotic nature of the asymptotic domain of attraction. It is shown that safety issues cannot be satisfactorily resolved until an agreed set of initial conditions is established. It appears that blocks may survive under very high accelerations and topple at very low accelerations provided the initial conditions are correct. Consideration is also given to the use of actual earthquake recordings in attempting to reproduce responses in given structures. If the present conclusions carry over to general excitations, then small errors in recordings may produce large differences in response. The present methods include orbital stability techniques together with detailed numerical computations. These results are backed up by encouraging qualitative agreement from an electronic analogue circuit.

Publisher

The Royal Society

Subject

Pharmacology (medical)

Reference35 articles.

1. Davis H. T. 1 9 6 2 Introduction to nonlinear differential and integral equations. New York: Dover.

2. Feigenbaum M. J. 1 9 7 8 Quantitative universality for a class of nonlinear transformations. J . statist. Phys. 19 25-52.

Cited by 152 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3