An analytical formulation for the vectors of contact forces and the stiffness matrix of the non-linear friction contact interface is developed for the analysis of multi-harmonic vibrations in the frequency domain. The contact interface elements provided here an exact description of friction and unilateral contact forces at the interacting surfaces, taking into account the influence of the variable normal load on the friction forces, including the extreme cases of separation of the two surfaces. Initial gaps and interferences at the contact nodes, which affect the normal force, as well as the unilateral action of the normal force at the contact surface, are all included in the model. The accurate calculation of the force vector and the tangent stiffness matrix provides a very reliable and fast convergence of the iteration process used in the search for the amplitudes of nonlinear vibrations of bladed discs. Numerical investigations demonstrate excellent performance with respect to speed, accuracy and stability of computation.
This paper surveys the state of the art of modal testing or experimental modal analysis of rotating structures. When applied to ordinary, non-rotating structures, modal testing is considered to be well established. Rotating structures, on the other hand, impose special difficulties when one seeks to obtain the parameters of the dynamical model experimentally. This paper focuses on the necessary experimental techniques and their relationship to the current state of the existing theory. Existing modal analysis methods, models and techniques, and their advantages, limitations and relevance are outlined and compared. In addition, some new developments allowing us to circumvent some of the above-mentioned difficulties are presented.Rotating machines appear in almost every aspect of our modern life: cars, aeroplanes, vacuum cleaners and steam-turbines all have many rotating structures whose dynamics need to be modelled, analysed and improved. The reliability, stability and the response levels of these machines, predicted by analytical models, are generally not satisfactory until validated by experimentally obtained data. For this purpose, modal testing has to be employed and further advance is essential in order to overcome the difficulties in this area.In this paper, the differences between the mathematical models used for dynamic analysis of non-rotating and rotating structures are clarified. The implications of the model structure, in the latter case, on the application of modal testing are presented, as this is a point of great importance when experimental modal analysis is employed for rotating structures. Models with different degrees of complexity are being used for different types of rotating machines. A classification of such models is outlined in this work and the underlying assumptions and features are described in terms of a hierarchical complexity. Several applications of modal testing are reported here and some experimental evidence to support the validity of the theory is presented. Desired future activities, which are required to advance the theory and practice of this field, are summarized in conclusion.
In this paper, a review is presented of the various methods which are available for the purpose of performing a systematic comparison and correlation between two sets of vibration data. In the present case, the application of interest is in conducting this correlation process as a prelude to model correction or updating activity.
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