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TECHNICAL PAPERS

Behavior of a Rubber Spring Pendulum

[+] Author and Article Information
R. Bhattacharyya

Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, India

J. Appl. Mech 67(2), 332-337 (Apr 07, 1998) (6 pages) doi:10.1115/1.1302304 History: Received June 26, 1997; Revised April 07, 1998
Copyright © 2000 by ASME
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References

Minorsky, N., 1962, Nonlinear Oscillations, Van Nostrand Reinhold, New York, p. 506.
Olsson,  M. G., 1976, “Why Does a Mass on a Spring Sometimes Misbehave?” Am. J. Phys., 44, No. 12, pp. 1211–1212.
Kane,  T. R., and Kahn,  M. E., 1968, “On a class of Two Degrees of Freedom Oscillations,” ASME J. Appl. Mech., Series E, 35, pp. 547–552.
Lai,  H. M., 1984, “On the Recurrence Phenomenon of a Resonant Spring Pendulum,” Am. J. Phys., 52, No. 3, pp. 219–223.
Anicin,  B. A., Davidovic,  D. M., and Babovic,  V. M., 1993, “On the Linear Theory of the Elastic Pendulum,” Eur. J. Phys., 14, pp. 132–135.
Ryland ,  H. G., and Meirovitch,  L., 1977, “Stability Boundaries of a Swinging Spring With Oscillating Support,” J. Sound Vib., 51, No. 4, pp. 547–560.
Nunez-Yepez,  N., Salas-Brito,  A. L., Vargas,  C. A., and Vincente,  L., 1990, “Onset of Chaos in an Extensible Pendulum,” Phys. Lett. A, 145, pp. 101–105.
Cuerno,  R., Ranada,  A. F., and Ruiz-Lorenzo,  J. J., 1992, “Deterministic Chaos in the Elastic Pendulum: A simple Laboratory for Nonlinear Dynamics,” Am. J. Phys., 60, No. 1, pp. 73–79.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillation, John Wiley and Sons, New York.
Beatty,  M. F., 1983, “Finite Amplitude Oscillations of a Simple Rubber Support System,” Arch. Ration. Mech. Anal., 83, No. 3, pp. 195–219.
Beatty,  M. F., and Bhattacharyya,  R., 1990, “Poynting Oscillations of a Rigid Disk Supported by a Neo-Hookean Rubber Shaft,” J. Elast., 24, pp. 135–186.
Bellman, R., 1969, Stability Theory of Differential Equations, Dover, New York.
Bhattacharyya,  R., 1995, “A Stability Theorem for Hill’s Equation for Engineering Applications,” ASME J. Vibr. Acoust., 117, pp. 380–381.
Zhou,  Z., 1993, “Coupled Shear-Torsional Motion of a Rubber Support System,” J. Elast., 30, pp. 123–189.
Cunningham, W. J., 1958, Introduction to Nonlinear Analysis, McGraw-Hill, New York.

Figures

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Static equilibrium stretch versus stiffness ratio for various values of B in the suspended pendulum case. Inset shows system schema.
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Linearized swing mode natural frequency versus static equilibrium stretch for various values of B
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Stability curves in κβc–plane for fixed support (B=0), obtained numerically from (4.16)
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Swing response curves obtained from Eqs. (4.1) and (4.2) for fixed support case (B=0)
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Stability curves for the special type of support motion with B=−0.2
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Stability curves for the special type of support motion with B=−0.6
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Stability curves for the special type of support motion with B=0.4
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Stability curves for the special type of support motion with B=0.6
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Stability curves for the special type of support motion with B=0.8
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Axial and swing response curves obtained from the solution of Eqs. (2.4) and (2.5) for fixed support case (B=0) with (κ,β)=(0.8,1.4). This point lies in the unstable region in Fig. 3.

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