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New findings in the rocking instability of one and two rigid block systems under ground motion

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Abstract

The rocking (overturning) instability of one and two rigid—block assemblies underground motion of sinus and cosinus pulses is reconsidered. The Housner effect according to which between two geometrically similar (rectangular) rigid blocks, the taller is more stable (than the lower one) is extended to the case where between two rigid blocks having the same width, the taller is generally more stable. It was also found that overturning for one rigid block (1-DOF) system without or after one impact occurs through an unstable equilibrium (saddle) point via an escaped motion (inflection point in the curve relating the unknown rotation to the time). Such a critical state happens always during a free motion regime regardless of whether impact occurs before or after the external excitation expires. The condition of overturning after one impact (occurring after the external excitation expires) was established through one elegant equation which relates directly the minimum amplitude ground excitation to the external frequency. For a two-rigid block (2-DOF) system overturning without or after impact (associated with a minimum amplitude ground excitation) occurs in the upper rigid block according to the aforementioned inflection point criterion. All linearized results were also verified via non-linear numerical analysis, properly adjusted to include the rotational friction of the block pivot axis at the rocking initiation.

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  1. Office of Theoretical and Applied Mechanics, The Academy of Athens, Soranou Efessiou 4, 115-27, Athens, Greece

    Anthony N. Kounadis

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  1. Anthony N. Kounadis
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Correspondence to Anthony N. Kounadis.

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Kounadis, A.N. New findings in the rocking instability of one and two rigid block systems under ground motion. Meccanica 50, 2219–2238 (2015). https://doi.org/10.1007/s11012-015-0167-3

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  • DOI: https://doi.org/10.1007/s11012-015-0167-3

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