Engineering Transactions, 46, 2, pp. 143–164, 1998
10.24423/engtrans.649.1998

Rocking-Sliding of a Rigid Block: Friction Influence on Free Motion

U. Andreaus
Universita Degli Studi di Roma "La Sapienza"
Italy

P. Casini
Universita Degli Studi di Roma "La Sapienza"
Italy

Many technical problems involve contact and impact between bodies. The contact problem is locally characterized by normal and shear forces; this contact may represent different types of phenomena such as rolling, sliding, impact and shock, unilateral contact, etc. The 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. FVictional contact is taken into account by means of shear forces concentrated at a discrete number of points. Attention has been paid to two-dimensional free motion of the block with three degrees of freedom. Wide ranges of block slenderness and friction angle have been investigated and numerical results have been synthesized by means of the energy reduction ratio, which accounts for contact phenomena occurring during impact.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

K. MUTO, H. TAKASE, K. HORIKOSHI and H. UENO, 3-D nonlinear dynamic analysis of stacked blocks, Proc. 2nd Special Conf. on "Dynamic response of structures: experimentation, observation, prediction and control", Mech. Div., ASCE, Atalanta, Georgia, 917–930, 1981.

G.W. HOUSNER, The behaviour of inverted pendulum structures during earthquakes, Bull. Seism. Soc. of Amer., 53, 2, 403–417, 1963.

Y. ISHIYAMA, Motions of rigid bodies and criteria for overturning by earthquake excitations, Earthquake Engrg. Struct. Dyn., 10, 635–650, 1982.

A. SINOPOLI, Dynamics and impact in a system with unilateral constraints. The relevance of dry friction, Meccanica, 22, 4, 210–215, 1987.

G. AUGUSTI and A. SINOPOLI, Modelling the dynamics of large block structures, Meccanica, 27, 3, 195–211, 1992.

A. SINOPOLI and V. SEPE, Coupled motion in the dynamic analysis of a three block structure, Appl. Mech. Rev., 46, 11, Part 2, 186–197, 1993.

J.J. MOREAU, Unilateral contact and dry friction in finite friction dynamics, [in:] Non Smooth Mechanics and Applications, J.J. MOREAU and P.D. PANAGIOTOPOULOS [Eds.], CISM Courses and Lectures, 302, Springer-Verlag, 1–82, 1988.

Y. ISHIYAMA, Review and discussion on overturning of bodies by earthquake motion, Rep. Build. Res. Inst., Min. of Constr., Japan, June 1980.

J. MILNE, Experiments in observational seismology, Trans, of the Seism. Soc. of Japan, 3, 12–24, 1881.

J. PERRY, Note on the rocking of a column, Trans. of the Seism. Soc. of Japan, 3, 103–106, 1881.

H. KIMURA and K. IIDA, On rocking of rectangular columns (I) [in Japanese], Zishin (J. of the Seism. Soc. of Japan), 6, 3, 125–149, 1934; H. KIMURA and K. IIDA, On rocking of rectangular columns (II) [in Japanese], Zishin (J. of the Seism. Soc. of Japan), 6, 4, 165–212, 1934.

R. GIANNINI, Considerazioni sulla modellazione numerica di sistemi di blocchi rigidi sovrapposti [in Italian], Proc. Conf. on "Stato dell'arte in Italia sulla meccanica delle murature", Rome, 677–685, 1985.

P.R. LIPSCOMBE, Dynamics of rigid block structures, Dissertation submitted to the University of Cambridge for the degree of Doctor of Philosophy, 1990.

R.N. IYBNGAR and D. ROY, Nonlinear dynamics of a rigid block on a rigid base, J. Appl. Mech., 63, 55, 55–61, 1996.

P. CUNDALL, A computer model for simulating progressive large-scale movements of blacky rock system, Proc. of the Symposium of the Int. Soc. of Rock Mechanics, Nancy, France, Vol. I, 132–150, 1971.

I.N. PSYCHARIS and P.C. JENNINGS, Rocking of slender rigid bodies allowed to uplift, Earthquake Engrg. Struct. Dyn., 11, 1, 57–76, 1983.

F. ANGOTTI and P. TONI, Oscillazioni non lineari di corpi rigidi su semispazi elastici monolaterali [in Italian], Proc. 6th Conf. AIMeTA, 134–143, Genoa 1982.

F. ANGOTTI, S. CHIOSTRINI and P. TONI, Analisi dinamica e sismica di strutture a deformabilità limitata su suolo monolaterale [in Italian], Proc. 7th Conf. AIMeTA, 5, 409–420, Trieste 1984.

U. ANDREAUS, A frictional model for sliding of jointed blocks, Proc. ICCLEM (Asia), 1, 249–254, Chongqing, China 1989.

U. ANDREAUS, Dynamic analysis of deformable block-work structures, Proc. 9th Conf. on Earthquake Engineering, 7–C, 61–70, Moscow 1990.

U. ANDREAUS, Sliding-uplifting response of rigid blocks to base excitation, Earthquake Engrg. Struct. Dyn., 19, 1181–1196, 1990.

U. ANDREAUS and N. NISTICO, An analytical-numerical model for contact-impact problems: theory and implementation in a 2-D distinct element algorithm, Computer Modelling and Simulation in Engineering, 3, 2, 98–110, 1998.

N.C. BARTON and V. CHOUBEY, The shear strength of rock joints in theory and practice, Rock Mech., 10, 1–54, 1977.

S.C. BANDIS, A.C. LUMSDEN and N.C. BARTON, Fundamentals of rock joint deformation, Int. J. Min. Sci. and Geomech. Abstr., 20, 6, 249–268, 1983.

N.C. BARTON, S.C. BANDIS and K. BAKHTAR, Strength, deformation and conductivity coupling of rock joints, Int. J. Min. Sci. and Geomech. Abstr., 22, 3, 121–140, 1985.

S.C. BANDIS, A.C. LUMSDEN and N.C. BARTON, Experimental studies of scale effects on the shear behaviour of rock joints, Int. J. Min. Sci. and Geomech. Abstr., 18, 1, 1–21, 1981.

T. LEVI CIVITA and U. AMALDI, Lezioni di Meccanica Razionale [in Italian], Zanichelli 1927.

M. RAOUS, Experimental analysis of the rocking of a rigid block, 3rd Pan-American Congress of Applied Mechanics (PACAM III), 61–64, Sao Paolo 1993.




DOI: 10.24423/engtrans.649.1998