A Dividing Analysis of the Principal Vibrations of Multi-Degree-of-Freedom Linear Vibrating Systems

Abstract

"A dividing differential equation method" to analyze the principal vibrations of multi-degree-of-freedom linear vibrating systems is proposed. By this method, an overall sytem is divided into several partial systems in order to make the principal vibrations of the overall system correspond one-to-one and continuously to those of the partial systems, and a first-order differential equation with an independent variable expressing the degree of connectivity among the partial systems is introduced. The theory is developed for studying the natural frequencies and the normal modes of vibration simultaneously and also for another care when only the natural frequencies are treated.A way of setting up an auxiliary system is presented. The numerical computations of the principal vibrations of an overall system can easily be executed by making use of a suitable numerical method and an electronic computer, the programming for which is very easy.