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.
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.
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.