Resonance. The effect of resonance in a mechanical system is very important to engineers. Nearly every mechanical system will exhibit some resonance (vibration) and can with the application of even a very small external pulsed force, be stimulated to do just that.
If an externally timed and pulsed (or periodic) force is applied in-phase with the naturally occurring resonance of a system, the frequency amplitude is further excited and increases and the system can become very unstable and be threatened by so called resonance-catastrophe (or self-amplifying destruction). Engineers usually work very hard to eliminate resonance from a mechanical system, as they perceive it to be counter-productive.
It is however impossible to prevent all resonance in a system. But we can limit or control its effect, either through the use of timed and pulsed (180 degrees out-of-phase) counter-frequencies, or by building a system in a such a way that it dampens down the self-exciting frequency so that it does not become unstable and self-destructive.
Systems that are able to resonate usually have more than one frequency at which they can resonate or oscillate. This can be called the system harmonics and is a characteristic exploited in the building of musical instruments, for example, to give tonal variations etc.
Forced Oscillation and Differential Equations
The principle of Forced Oscillation, and the equations used to explain it, explores the relationship between the amount of Inertia Force ( IF ), with Friction Force ( FF ) and Conservation Force ( CF ) and simply says the sum of these forces is not equal to zero, and by deduction the resultant force to balance both sides of the equation is Disturbed Force ( DF ). It could also be called a Stimulating Force.
In other words an external Disturbed Force ( DF ), which has a regular Sine shape and is pulsed (dependent on time) acts on the system such that : DF = MF sin wt (where MF is Maximum Force and the Impulse Frequency is w).
Forced Oscillation therefore can be explained by the Differential Equation : DF = IF + FF + CF
Furthermore : s + (b/m)s + (D/m)s = (MF/m)sin wt
The calculation of the Disturbed or Stimulating Force, the system frequencies, the system amplitude and the system null phase angle is shown in the book : Physic for Ingenieure ISBN 3-519-26508-7 on pages 289 / 290.
Besslerwheel : Swash-Plate Clutch
Bessler’s Wheel and the modern day Swash-Plate Clutch (used in some pumps, helicopter rotor hubs, vehicle clutches etc) are believed to both be devices that can harness and use the principle of Forced Oscillation and Disturbed Force. In the Besslerwheel, such as when under load or rotational acceleration, the periodic use of Disturbed Force is used to increase the system’s amplitude and again when the wheels rotational speed increases close to optimal the Disturbed Force reduces its input into the system.
Because the system is self-regulating (or self-governing) it is not threatened by so-called resonance catastrophe.
By way of example : imagine a child tapping a hoop as he runs beside it. Once up to speed the child taps only lightly on the hoop to maintain the required speed. But as he reaches a gentely climbing slope (ie the hoop comes under load) much more periodic force is required to maintain the original speed. As a mechanical flyweight engine rpm regulating system is self-governing so the Forced Oscillation Principle is self-governing also.
In the Swash-Plate Clutch analogy it is possible to adjust the Disturbed Force as required. Any difference in speed between the eccentric outer housing and the inner axle results in a more or less large disturbance of the movement of the swash plate.This system is, if not carefully managed, threatened from resonance-catastrophe or self-destruction. Both systems use increasing resonance at particular times to gain energy.