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On the rocking-uplifting motion of a rigid block in free and forced motion: influence of sliding and bouncing

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Summary

The problem of rocking response of a rigid block in free and forced motion has been studied for a number of technical reasons. Apart from the technical interests, the problem of rigid block rocking is intrinsically of interest from a theoretical point of view. In fact, the problem is highly nonlinear in nature.

Aim of this paper is to study the “contact-impact” problem of a rigid block colliding on a frictional base, by means of a numerical simulation, and to compare numerical results with analytical responses known from the literature.

The influence of sliding and bouncing on the orbit type and stability is analyzed by a 3-DOF model of the system and by a new refined model of the contact forces between block and base. Furthermore, attention has been paid to two-dimensional free motion of the block with three degrees of freedom. Refined analytical stress-strain relations in either normal and tangential directions with respect to the contact surfaces are formulated which allow to account for (i) up-lifting and hysteretic damping in normal direction, (ii) coupling between shear strength and compression force, friction dissipation and cumulating damage in tangential direction.

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Author notes

  1. U. Andreaus & P. Casini

    Present address: Dipartimento di Ingegneria Strutturale and Geotecnica Facoltà di Ingegneria, Università degli Studi di Roma “La Sapienza”, Via Eudossiana 18, 00184, Roma, Italy

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    1. U. Andreaus
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    2. P. Casini
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    Andreaus, U., Casini, P. On the rocking-uplifting motion of a rigid block in free and forced motion: influence of sliding and bouncing. Acta Mechanica 138, 219–241 (1999). https://doi.org/10.1007/BF01291846

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    • DOI: https://doi.org/10.1007/BF01291846

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