The Indian rope trick effect is when a vibrating soft rope, with its one end fixed, takes a stable vertical position and maintains it at any deviation. The name of the effect is associated with the legend of Indian fakirs who managed to maintain vertical stability of a long rope with a monkey climbing to its top.

The works [1–8] study this phenomenon. The vibrational mechanics approach provides the following simple physical explanation for the effect [6–8]: as a result of vibration, the rope acquires additional bending rigidity EJ_v, which increases at higher products of amplitude A to vibration frequency ω. The same effect occurs for a string under rapid periodical tension changes. As a result, the string acquires additional vibrational rigidity, acting as an elastic rod (similarly to the Indian rope). Changes in vibration parameters may therefore be used to control the effective elastic properties of bodies, transforming them, in a way, into new (dynamic) materials.

In experiments [8] performed using a vibration stand, the length of the rope was 100 mm, the vibration amplitude was A = 7.5 mm, and the frequency was smoothly increased to reach ω = 200 s^-1 (32 Hz). The bending vibrations observed are associated with the resonant phenomena that occur at higher frequencies. A sufficiently long rope may be straightened out on a vibrating flat support [8].

References

1. Otterbein S. Stabilisierung des n-Pendels und der Indische Seiltrick // Arch. for Rational Mech. and Analysis. 1982. Vol. 78. pp. 381–393.
2. Champneys A. R., Fraser W. B. The “Indian rope trick” for a parametrically excited flexible rod: linearized analysis // Proc. Roy. Soc. London. 2000. Vol. A456. pp. 553–570.
3. Fraser W. B., Champneys A. R. The “Indian rope trick” for a parametrically excited flexible rod: nonlinear and subharmonic analysis // Proc. Roy. Soc. London. 2002. Vol. A458. p. 1353–1373.
4. Weibel S., Kaper T. J., Baillieul J. Global dynamics of a rapidly forced cart and pendulum // Nonlinear Dynamics.1997. Vol. 13. pp. 131–170.
5. Blekhman I. I., Dresig H., Shishkina E. V. On the Theory of the Indian Magic Rope. Chapter 8. pp. 139–149. In: Selected Topics in Vibrational Mechanics (Ed. by I.I. Blekhman). Singapore, World Scientific, 2004.
6. Blekhman I. I. Vibrational Mechanics and Vibrational Rheology (Theory and Applications). Moscow. Fizmatlit. 2018. pp. 38–39; 147–172; 183–189.
7. Shishkina E. V., Blekhman I. I., Cartmell M. P., Gavrilov S. N. Application of the method of direct separation of motions to the parametric stabilization of an elastic wire // Nonlinear Dynamics. 2008. Vol. 54. pp. 313–331.
8. Vasilkov V. B. Influence of vibration on nonlinear effects in mechanical systems. Doctor of Engineering Dissertation, St. Petersburg / Institute of Problems of Mechanical Engineering of RAS, 2009