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National Advisory Committee for Aeronautics, Technical Notes - Introduction to Electrical Circuit Analogies for Beam Analysis

An application is described of the well-known analogy between elec-
trical and mechanical systems to the calculation of stresses and deflec-
tions of beams. The object of the present paper is to give an explanation
of the analogies in an elementary manner which will enable a structural
engineer to understand the process of designing'the electrical circuits.
The analogies which are discussed are those that are now being used in
the Cal—Tech analog computer. Analogies are given for beams in bending
and torsion with static loads and in.vibrational motion.

In recent years a considerable amount of progress has been made in
the development of applications of electrical-circuit analogies to prob-
, lems in structural analysis. Many solutions of such problems have been
obtained on the Cal-Tech analog computer. A number of papers have also
been written in which the electrical analdgies for various problems have
been presented. These papers have been written mainly by electrical
engineers and have assumed the reader to be reasonably familiar with
circuit theory. Consequently structural engineers have found some dif-
ficulty in appreciating and evaluating this new method of analysis. In
the present paper the design of the electrical circuits will be explained
in complete detail without assuming any knowledge of circuit theory on
the part of the reader. It is hOped that this paper will assist structural
engineers in reaching a better understanding of the practical utility of
electrical analogies in structural analysis.

In order to deve10p an electrical analogy for the action of a been
under load it is necessary to replace the differential equations which
govern the stresses and deflections by difference equations. The rela-
tions between voltages and currents in an electrical circuit may also be
expressed by difference equations. An analogous electrical circuit for
a beam is one in which the voltages and currents are related by difference
equations which have a form identical to that of the structural equations,
2including the boundary conditions. When such a circuit is designed and
constructed the physical circuit, with its components, is called an '
analog computer.