The force-current and force-voltage analogies between mechanical and
electrical networks are basic and very well-known. What is also
well-known, but not always emphasised, is that the mass element fails to
be a true network dual of the spring. This is due simply to the fact that
Newton's Second Law relates the acceleration of the mass to a fixed point
in an inertial frame, which in network terms means that one "terminal"
of the mass is grounded. Such a restriction does not apply to the spring
or damper, or to any of the three basic electrical elements.
This fact has important consequences for network synthesis. Realisation
procedures of Brune, Bott-Duffin, Darlington etc show that any passive
electrical impedance is positive real, and that any positive real rational
function may be realised as the driving-point impedance of a network
comprising the three basic electrical elements. There is a clear problem
in translating this result over to mechanical networks if a given
realisation contains a capacitor (in the force-current analogy) which has
neither terminal connected to ground. A further drawback arises with the
use of the mass element as the dual of the spring for the purpose of
synthesis. Namely, it may be important to assume that the mechanical
device associated with the "black-box impedance" to be designed has
negligible mass compared to other masses in the system. Clearly this is
unreasonable if (possibly) large masses may be required for its
realisation.
The purpose of this talk is to introduce a way to overcome the above
problems. Possible applications in linear vibrations and vehicle
suspensions will be discussed.
