The many steady state responses of a rigid block under harmonic forcing

S. J. Hogan*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

101 Citations (Scopus)


Recent mathematical advances in the study of the response of a rigid block to horizontal simple harmonic forcing conclude that (i) all types of subharmonic response are possible, (ii) several types can occur at one point in parameter space, (iii) exact expressions are available for stability boundaries in parameter space, (iv) asymmetric solutions exist just outside the upper boundaries of symmetric solutions, (v) period‐ and impact‐doubling cascades occur as parameter values are varied even further outside the boundaries, (vi) aperiodic (or chaotic) responses are possible, (vii) periodic responses can occur which appear to violate West's formula and (viii) steady state responses of the forced system can be so large as to produce toppling of the block if the system were unforced. These results are used to explain and extend recent computational work. Also we find quantitative agreement between our theoretical work and some recent experimental work of Tso and Wong.

Original languageEnglish
Pages (from-to)1057-1071
Number of pages15
JournalEarthquake Engineering and Structural Dynamics
Issue number7
Publication statusPublished - 1 Jan 1990

Structured keywords

  • Engineering Mathematics Research Group


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