Rovibrational coupling

Rotational–vibrational coupling occurs when the rotation frequency of an object is close to or identical to a natural internal vibration frequency. The animation on the right shows a simple example. The motion depicted in the animation is for the idealized situation that the force exerted by the spring increases linearly with the distance to the center of rotation. Also, the animation depicts what would occur if there would not be any friction.

In rotational-vibrational coupling there is an oscillation of the angular velocity. In pulling the circling masses closer to the center of rotation, the force exerted by the spring (a centripetal force) is doing work, converting stored strain energy in the spring into kinetic energy of the masses. As a consequence of that, the angular velocity increases. The force of the spring cannot pull the circling masses all the way to the center, for as the circling masses are moving closer to the center of rotation the force exerted by the spring gets weaker, and the velocity is steadily increasing. At some point the velocity has increased so much that the object starts to swing wide again, re-entering a phase of building up strain energy.

In helicopter design damping devices must be incorporated, because at specific angular velocities vibrations of the rotorblades can be reinforced by rotational-vibrational coupling, and build up catastrophically. Without the damping the vibrations will cause the rotorblades to break loose.

The animation on the right provides a clearer view on the oscillation of the angular velocity. There is a close analogy with harmonic oscillation.

When a harmonic oscillation is at its midpoint then all the energy of the system is kinetic energy. When the harmonic oscillation is at the points furthest away from the midpoint all the energy of the system is potential energy. The energy of the system is oscillating back and forth between kinetic energy and potential energy.

In the animation with the two circling masses there is a back and forth oscillation of kinetic energy and potential energy. When the spring is at its maximal extension then the potential energy is largest, when the angular velocity is at its maximum the kinetic energy is at largest.

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Wikipedia