Vibration Analysis of Continuous Systems by Dynamic Discretization

An equivalent mass matrix may be defined, for a segment of a continuous system, as one which retains precisely the dynamic properties of the original segment in discretized form. Dynamic Discretization, which makes use of a particular form of Stodola iteration, progressively generates the equivalent mass matrix in ascending powers of frequency squared, whilst simultaneously generating deformation functions in a similar power series. The method is quasi-static and readily copes with shear deformation, rotary inertia and quite complex segment geometry. Accurate vibration analysis in terms of frequencies, mode shapes and corresponding stress distributions is achieved using an extremely coarse system subdivision for a variety of geometries.