Abstract
KEYWORDS:
Transmission, vibration, symmetrical systems, eigenvalue, eigenvector
ABSTRACT:
There are many technical applications where the studied system can be considered composed by two or many identical parts or systems that present some symmetries. These symmetries can be used to simplify the analysis of such systems in order to reduce the dimension of the equations that describe the motion. In the paper are identified, for these special systems with certain symmetries, some properties to vibrations. The use of the above mentioned properties permit to simplify the steady state analysis of the model.
In the case of mechanical systems showing certain symmetries, the differential equations describing their evolution in time display a series of specific properties - a consequence of the very existence of these symmetries. The present work sets forth some of these properties which may be used in the numerical resolution of these systems.
Some interesting properties of the systems showing symmetries concerning the eigenvalues and the eigenvector are proved and it is presented how these properties to simplify the calculus of the mechanical systems can. The transmission of a car is a very significant sample.