NATURAL FREQUENCIES AND MODE SHAPES OF MULTI-DEGREES OF FREEDOM SYSTEMS ON A PROGRAMMABLE CALCULATOR.

The Holzer tabulation method for determining the natural frequencies of multi-degree of freedom torsional systems is relatively easy to automate on a computer or a programmable calculator. The Holzer method has been extended to translational systems consisting of masses and springs configured so that the model starts with a mass and ends with a mass. For example, the method has been used to determine the natural frequencies of freight trains with an engine in the front and a caboose in the rear. The method presented here extends the basic Holzer theory further to accommodate lumped parameter structural models. A program is developed for a programmable calculator for determining the natural frequencies and mode shapes of multi-degree of freedom systems.