ABSTRACT. The classical 3D beam element has been modified and developed as a new finite element for vibration analysis of frame structures with flexible connections and cracked mem hers. The mass and stiffness matrices of the modified elements are established basing on a new form of shape functions, which are obtained in investigating a beam with flexible supports and crack modeled through equivalent springs. These shape functions remain the cubic polynomial form and contain flexible connection (or crack) parameters. They do not change standard procedure of the finite element method (FEM). Therefore, the presented method is easy for engineers in application and allows to analyze eigen-parameters of structures as functions of the connection (or crack) parameters. The proposed approach has been applied to calculate natural frequencies and mode shape of typical frame structures in presented examples.

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Abstract. In this paper, after analysing deformations of loading ball-bearing it is able to investigate vibrations of rotor-bearing system as the system with non-linear and periodically varying stiffness. The modelling of the systems is depent on properties of the shaft (rigid or flexible) and on measurement techniques for system vibrations (by eddy current proximity probe for rotating shaft or on non-rotating parts of the rotor-bearing systems) it can be described by a single degree-of-freedom or two-degree-of freedom nonlinear systems subjected to parameteric and external excitations. Therefore it is possible to obtain different characteristics of system vibrations with respect to different defects of ball-bearing. These symptoms help us to identify and estimate the bearing quality by measurement and analysis of system vibrations.

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