Nonlinear dynamics of a harmonically-excited inelastic inverted pendulum

Journal of Engineering Mechanics

Volumn 127, Issue 1, 2001, Pages 52-57

  Williamson, Eric B ^a   Hjelmstad, Keith D ^b  

^a The University of Texas at Austin   (United States)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; ELASTICITY; EQUATIONS OF MOTION; LOADS (FORCES); MATHEMATICAL MODELS; MODEL STRUCTURES; RESONANCE; STABILITY; STIFFNESS;

CYCLIC RAMBERG-OSGOOD MODEL; DYNAMIC STABILITY; ELASTIC PERFECTLY PLASTIC MODEL; HARMONICALLY EXCITED INELASTIC INVERTED PENDULUM; MATHIEU EQUATION; SINGLE DEGREE OF FREEDOM SYSTEM; TIME VARYING AXIAL LOAD;

PENDULUMS;

EID: 0035156024     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(2001)127:1(52)     Document Type: Article

References (22)

1. Bolotin, V. V. (1964). The dynamic stability of elastic systems, Holden-Day, San Francisco.
2. Capecchi, D. (1993). "Asymptotic motions and stability of the elastoplastic oscillator studied via maps." Int. J. Solids and Struct., 30(23), 3303-3314.
3. Grimshaw, R. (1990). Nonlinear ordinary differential equations, Blackwell Scientific, Oxford, England.
4. Hjelmstad, K. D. (1997). Fundamentals of structural mechanics, Prentice-Hall, Upper Saddle River, N.J.
5. Hjelmstad, K. D., and Williamson, E. B. (1997). "Dynamic stability of structural systems subjected to base excitation." Engrg. Struct., 20(4-6), 425-432.
6. Jones, N., and Reis, M. (1980). "On the dynamic buckling of a simple elastic-plastic model." Int. J. Solids and Struct., 16, 969-989.
7. Kaplan, D., and Glass, L. (1995). Understanding nonlinear dynamics, Springer, New York.
8. Karagiozova, D., and Jones, N. (1992). "Dynamic pulse buckling of a simple elastic-plastic model including axial inertia." Int. J. Solids and Struct., 29(10), 1255-1272.
9. Lee, H. P. (1995). "Stability of a cantilever beam with tip mass subject to axial sinusoidal excitations." Sound and Vibration, 183(1), 91-98.
10. Lee, L. H. N. (1981). "Dynamic buckling of an inelastic column." Int. J. Solids and Struct., 17(3), 271-279.
11. MacRae, G. A. (1994). "P-Δ effects on single-degree-of-freedom structures in earthquakes." Earthquake Spectra, 10(3), 539-568.
12. Maier, G., and Perego, U. (1992). "Effects of softening in elastic-plastic structural dynamics." Int. J. Numer. Methods in Engrg., 34, 319-347.
13. Meirovitch, L. (1986). Elements of vibration analysis, McGraw-Hill, New York.
14. Merkin, D. R. (1997). Introduction to the theory of stability, Springer, New York.
15. Mitropolskii, Y. A., and Dao, N. V. (1997). Applied asymptotic methods in nonlinear oscillations, Kluwer, Dordrecht, The Netherlands.
16. Park, Y.-J., and Ang, A. H.-S. (1985). "Mechanistic seismic damage model for reinforced concrete." J. Struct. Engrg., ASCE, 111(4), 722-739.
17. Pratrap, R., Mukherjee, S., and Moon, F. C. (1994a). "Dynamic behavior of a bilinear hysteretic elasto-plastic oscillator, Part I: Free oscillations." Sound and Vibration, 172(3), 321-337.
18. Pratrap, R., Mukherjee, S., and Moon, F. C. (1994b). "Dynamic behavior of a bilinear hysteretic elasto-plastic oscillator, Part II: Oscillations under periodic impulse forcing." Sound and Vibration, 172(3), 339-358.
19. Saaty, T. L., and Bram, J. (1964). Nonlinear mathematics, Dover, New York.
20. Sun, C. K., Berg, G. V., and Hanson, R. D. (1973). "Gravity effect on single-degree inelastic systems." J. Engrg. Mech. Div., ASCE, 99(1), 183-200.
21. Williamson, E. B., and Hjelmstad, K. D. (1996). "Dynamic stability of damage-prone inelastic structural systems." Rep. No. SRS 609, UILU-ENG-96-2004. University of Illinois at Urbana-Champaign, Urbana, Ill.
22. Yue, Y., and Zheng, J. (1992). "Dynamic elastic-plastic buckling behavior illustrated by simple model." J. Engrg. Mech., ASCE, 118(10), 2005-2016.