Revisiting the rocking block: Closed-form solutions and similarity laws

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 468, Issue 2144, 2012, Pages 2294-2318

  Dimitrakopoulos, Elias G ^a   DeJong, Matthew J ^b  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Closed form solutions; Earthquake engineering; Orientational analysis; Rocking; Self similarity

Indexed keywords

CIVIL ENGINEERING;

CLOSED FORM SOLUTIONS; EARTHQUAKE ENGINEERING; ORIENTATIONAL ANALYSIS; ROCKING; SELF-SIMILARITIES;

DYNAMIC RESPONSE;

EID: 84864578728     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2012.0026     Document Type: Conference Paper

References (27)

1. Anooshehpoor, A., Heaton, T. H., Shi, B. & Brune, J. N. 1999 Estimates of the ground accelerations at point Reyes station during the 1906 San Francisco earthquake. Bull. Seismol. Soc. Am. 89, 845-853. (Pubitemid 30024807)
2. Araneda, J. 1996 Dimensional-directional analysis by a quaternionic representation of physical quantities. J. Franklin Inst. 333, 113-126. (doi:10.1016/0016-0032 (96) 85843-1) (Pubitemid 126347199)
3. Augusti, G. & Sinopoli, A. 1992 Modelling the dynamics of large block structures. Meccanica 27, 195-211. (doi:10.1007/BF00430045)
4. Barenblatt, G. 1996 Scaling, self-similarity, and intermediate asymptotics. Cambridge, UK: Cambridge University Press.
5. Brogliato, B. 1999 Nonsmooth mechanics: models, dynamics, and control, 2nd edn. London, UK: Springer.
6. Buckingham, E. 1914 On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev. 4, 345-376. (doi:10.1103/PhysRev. 4.345)
7. Contento, A. & Di Egidio, A. 2009 Investigations into the benefits of base isolation for non-symmetric rigid blocks. Earthq. Eng. Struct. Dyn. 38, 849-866. (doi:10.1002/eqe.870)
8. De Jong, M. J. In press. Amplification of rocking due to horizontal ground motion. Earthq. Spectra.
9. De Jong, M. J., De Lorenzis, L., Adams, S. & Ochsendorf, J. A. 2008 Rocking stability of masonry arches in seismic regions. Earthq. Spectra 24, 847-865. (doi:10.1193/1.2985763)
10. Dimitrakopoulos, E. G. & De Jong, M. J. In press. Overturning of retrofitted rocking structures under pulse-type excitation. J. Eng. Mech. (ASCE) (doi:10.1061/(ASCE) EM.1943-7889. 0000410).
11. Dimitrakopoulos, E. G., Kappos, A. J. & Makris, N. 2009a Dimensional analysis of yielding and pounding structures for records without distinct pulses. Soil Dyn. Earthq. Eng. 29, 1170-1180. (doi:10.1016/j.soildyn. 2009.02.006)
12. Dimitrakopoulos, E. G., Makris, N. & Kappos, A. J. 2009b Dimensional analysis of the earthquake-induced pounding between adjacent structures. Earthq. Eng. Struct. Dyn. 38, 867-886. (doi:10. 1002/eqe.872)
13. Dimitrakopoulos, E. G., Makris, N. & Kappos, A. J. 2010 Dimensional analysis of the earthquake-induced pounding between inelastic structures. Bull. Earthq. Eng. 9, 561-579. (doi:10.1007/s10518-010-9220-8)
14. El Gawady, M. A., Ma, Q., Butterworth, J. W. & Ingham, J. 2010 Effects of interface material on the performance of free rocking blocks. Earthq. Eng. Struct. Dyn. 40, 375-392. (doi:10.1002/eqe.1025)
15. Glocker, C. 2001 On frictionless impact models in rigid-body systems. Phil. Trans. R. Soc Lond. A 359, 2385-2404. (doi:10.1098/rsta.2001.0857) (Pubitemid 33374603)
16. Hogan, S. J. 1989 On the dynamics of rigid-block motion under harmonic forcing. Proc. R. Soc. Lond. A 425, 441-476. (doi:10.1098/rspa.1989.0114)
17. Hogan, S. J. 1990 The many steady state responses of a rigid block under harmonic forcing. Earthq. Eng. Struct. Dyn. 19, 1057-1071. (doi:10.1002/eqe. 4290190709)
18. Housner, G. W. 1963 The behavior of inverted pendulum structures during earthquakes (in an engineering report on the Chilean earthquakes on May 1960, Housner). Bull. Seismol. Soc. Am. 53, 403-417.
19. Makris, N. & Black, C. J. 2004 Dimensional analysis of rigid-plastic and elastoplastic structures under pulse-type excitations. J. Eng. Mech. 130, 1006-1018. (doi:10.1061/(ASCE) 0733-9399 (2004) 130:9 (1006)) (Pubitemid 39174732)
20. Makris, N. & Psychogios, T. 2006 Dimensional response analysis of yielding structures with first-mode dominated response. Earthq. Eng. Struct. Dyn. 35, 1203-1224. (doi:10.1002/eqe.578) (Pubitemid 44177968)
21. Mylonakis, G. & Voyagaki, E. 2006 Yielding oscillator subjected to simple pulse waveforms: numerical analysis & closed-form solutions. Earthq. Eng. Struct. Dyn. 35, 1949-1974. (doi:10. 1002/eqe.615) (Pubitemid 44830946)
22. Priestley, M. J. N., Evison, R. J. & Carr, A. J. 1978 Seismic response of structures free to rock on their foundations. Bull. N. Z. Natl. Soc. Earthq. Eng. 11, 1978-1909.
23. Prieto, F., Lourenço, P. B. & Oliveira, C. S. 2004 Impulsive Dirac-delta forces in the rocking motion. Earthq. Eng. Struct. Dyn. 33, 839-857. (doi:10.1002/eqe.381) (Pubitemid 38688673)
24. Sedov, L. 1992 Similarity and dimensional methods in mechanics, 10th edn. Boca Raton, FL: CRC Press.
25. Siano, D. 1985 Orientational analysis: a supplement to dimensional analysis: I. J. Franklin Inst. 320, 267-283. (doi:10.1016/0016-0032 (85) 90031-6)
26. Yilmaz, C., Gharib, M. & Hurmuzlu, Y. 2009 Solving frictionless rocking block problem with multiple impacts. Proc. R. Soc. A 465, 3323-3339. (doi:10.1098/rspa.2009.0273)
27. Zhang, J. & Makris, N. 2001 Rocking response of free-standing blocks under cycloidal pulses. J. Eng. Mech. 127, 473. (doi:10.1061/(ASCE) 0733-9399 (2001) 127:5 (473))