ABSTRACT
The simulation of physical phenomena has been much simplified and extended by the use of numerical methods, which avoid limitations and simplifying assumptions frequently inherent in analytical solutions of mathematical representations. There are many ways in which this can be done. The equations can be solved by replacing integrals and derivatives by finite sums and finite differences. An alternative strategy involves the replacement of the equations by analogue models, which express the same behavior, on the basis that these may be easier to solve numerically in particular circumstances. Perhaps the best-known example is the equivalent electrical network. The use of electrical network models in mechanics is well established. There are direct analogues between springs, masses, and dampers on one side and capacitors, inductors, and resistors on the other. The solution to the mechanical problem can then be obtained using conventional circuit analysis techniques with results in either the time or frequency domains. As will be seen, in the case of transmission line matrix (TLM), the equivalent electrical analogue has the further major advantage that it leads directly to a simple and natural numerical discretization scheme.
