A REDUCTION OF THE EQUATIONS OF THE LINEAR STATIONARY VIBRATING SYSTEMS WITHOUT LIMITATIONS OF DISSIPATION USING THE METHOD OF MODAL TRUNCATION

Abstract

A method for reduction of differential equations describing linear stationary vibrating systems with a finite number of degrees of freedom usable for shortening the time of digital integration of such equations, when the dynamic model of the vibrating system has a wide spectrum of natural frequencies and the investigator takes an interest in the range of low natural frequencies within the said spectrum only, is proposed herein. For this purpose, the equations are formed in the state variables of the system using the normal Bulgakov's coordinates and then are reduced by rejecting the equations bound with higher natural frequencies according to the method of modal truncation. The method does not require any limitations of damping of the systems under the investigation. In the example, it is shown that in case of a system of 168 degrees of freedom, the time of digital integration was reduced after simplification about 100 times upon small reduction errors.

http://dx.doi.org/10.5755/j01.mech.17.5.728