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MECH 375 Experiment 5 Characteristics of a Two Degrees-of-Freedom System Concordia University
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MECH 375 Experiment 5 Characteristics of aTwo Degrees-of-Freedom System Concordia
University
, On
Characteristics of a Two Degrees-of-Freedom System
Concordia University
5.1 Characteristics of a Two Degrees-of-Freedom Semi-Definite System
Objective
, The objective of this laboratory is to determine the natural frequencies and mode shapes
occurring in a two degree-of-freedom semi-definite system.
Introduction
To study a two degree-of-freedom system such as the one in this laboratory, we need
two independent coordinates to describe its motion. These two coordinates are often the two
discrete masses or inertias of the rotors attached to a shaft. Furthermore, these systems
exhibit two distinct natural frequencies that are of upmost importance for engineers when
given the task to design or optimize machinery or devices that incorporate them.
In the following figure, two rotors are coupled together by a massless shaft where the
system rotates freely with the usage of frictionless bearings at both ends [1]:
Fig. 1 [1]: Semi-Definite Two Degree-Of-Freedom System Schematic
Fig. 2 [1]: Two Degree-Of-Freedom Free Body Diagram
The previous illustration, Fig. 2, shows the free body diagram of a two degree-of-
freedomset-up that is similar to the one used in this laboratory. From this free body diagram,
we may deduce the following equations of motions [1]:
The natural frequencies of this system is determined by
[1]:where we obtain
From the natural frequencies, the mode shapes are [1]:
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