TY - JOUR

T1 - The many steady state responses of a rigid block under harmonic forcing

AU - Hogan, S. J.

PY - 1990/1/1

Y1 - 1990/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025507204&partnerID=8YFLogxK

U2 - 10.1002/eqe.4290190709

DO - 10.1002/eqe.4290190709

M3 - Article (Academic Journal)

AN - SCOPUS:0025507204

VL - 19

SP - 1057

EP - 1071

JO - Earthquake Engineering and Structural Dynamics

JF - Earthquake Engineering and Structural Dynamics

SN - 0098-8847

IS - 7

ER -