Mobility analogy

The advantage of doing this is that there is a large body of theory and analysis techniques concerning complex electrical systems, especially in the field of filters.

The roles of voltage and current are reversed in these two methods, and the electrical representations produced are the dual circuits of each other.

These are filters that are intended for use in an electronic circuit, but work entirely by mechanical vibrational waves.

Transducers are provided at the input and output of the filter to convert between the electrical and mechanical domains.

The mechanical system is broken down into a number of ideal elements each of which can then be paired with an electrical analogue.

Analogies can also be developed for distributed elements such as transmission lines but the greatest benefits are with lumped-element circuits.

Mechanical analogies are required for the three passive electrical elements, namely, resistance, inductance and capacitance.

[8] The mechanical analogy of electrical resistance is the loss of energy of a moving system through such processes as friction.

It is connected with the fact that in mechanical systems the velocity of the mass (and more importantly, its acceleration) is always measured against some fixed reference frame, usually the earth.

Considered as a two-terminal system element, the mass has one terminal at velocity ''u'', analogous to electric potential.

[17] This led Malcolm C. Smith of the University of Cambridge in 2002 to define a new energy storing element for mechanical networks called inertance.

Smith did not just define a network theoretic element, he also suggested a construction for a real mechanical component and made a small prototype.

The plunger is connected to a rack and pinion gear which drives a flywheel inside the cylinder.

It is used as an alternative to the now banned tuned mass damper and forms part of the vehicle suspension.

The inerter is much smaller than the tuned mass damper and smoothes out contact patch load variations on the tyres.

A corresponding problem also occurs in the impedance analogy, but in that case it is ungrounded inductors, rather than capacitors, that cannot be represented with the standard elements.

Mechanical resonators are analogous to electrical LC circuits consisting of inductance and capacitance.

An example of a practical constant velocity generator is a lightly loaded powerful machine, such as a motor, driving a belt.

They are analogous to two-port networks and like those can be described by a pair of simultaneous equations and four arbitrary parameters.

There are numerous possible representations, but the form most applicable to the mobility analogy has the arbitrary parameters in units of admittance.

[29] The figure shows a mechanical arrangement of a platform of mass M that is suspended above the substrate by a spring of stiffness S and a damper of resistance Rm.

Mechanical admittance and the associated mobility analogy were introduced by F. A. Firestone in 1932 to overcome the issue of preserving topologies.

The mechanical symbol for a damper (left) and its electrical analogy (right). [ 9 ] The symbol is meant to be evocative of a dashpot . [ 10 ]
The mechanical symbol for a compliance element (left) and its electrical analogy (right). [ 6 ] The symbol is meant to be evocative of a spring. [ 12 ]
The mechanical symbol for a mass (left) and its electrical analogy (right). [ 6 ] The square angle below the mass is meant to indicate that movement of the mass is relative to a frame of reference. [ 15 ]
The mechanical symbol for a constant velocity generator (left) and its electrical analogy (right) [ 24 ]
The mechanical symbol for a constant force generator (left) and its electrical analogy (right) [ 25 ]
Simple mechanical resonator (left) and its mobility analogy equivalent circuit (right)