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Here, the large amplitude axisymmetric vibration of a circular plate having a circumferential crack is studied considering the simply supported and clamped boundary conditions. Exact modal functions are generated by satisfying the boundary conditions and constraints along the crack. The inplane or membrane forces resulting from the large deflection are derived from the Berger's formulation. Next, the Galerkin's method is used to transform the differential equation into the Duffing equation with cubic nonlinearities. The amplitude and phase curves are generated using the Method of multiple scales. Natural frequency variations of axisymmetric modes are studied for a change in crack depth and crack position, considering both boundary conditions. Some natural frequencies are also compared with the finite element results and they are found to be in good agreement. For clamped boundary conditions, the natural frequency of a cracked plate is shown to approach that of an uncracked plate for a particular crack position independent of different crack depths. The amplitude and phase curves are shown for different crack parameters. Finally, the phase plane plot variations are presented for different crack depths, positions and boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, vibration analysis of a rectangular thin isotropic plate with a part-through surface crack of arbitrary orientation and position is performed by using the Kirchhoff plate theory. Simply supported (SSSS), clamped (CCCC) and simply supported–clamped (SCSC) boundary conditions are considered for the analysis. First, the governing differential equation of a cracked plate is formulated. A modified line spring model is then used to formulate the crack terms in the governing equation. Next, by the application of Burger's formulation, the differential equation is transformed into the well-known Duffing equation with cubic and quadratic nonlinearities. The Duffing equation is then solved by the method of multiple scales (MMS) to extract the frequency response curve. Natural frequencies are evaluated for different values of length, angle and position of a part-through surface crack. Some results are compared with the published literature. Amplitude variation with different values of length, angle and position of a part-through surface crack are presented, for all three types of the plate boundary conditions. [Copyright &y& Elsevier]

Faults in a rotor-bearing system due to bearings and unbalance have been classified using support vector machines (SVMs). Vibration signals on a rotor-bearing system were measured simultaneously at five different rotating speeds using seven transducers. The most sensitive feature of the vibration signals has been determined using compensation distance evaluation technique. Multi-class SVMs classification algorithm was then implemented for classification of the faults by considering SVMs created by the possible combinations of the most two sensitive features for each type of fault. By using optimal SVM parameters, the effective location of transducer among seven transducers for best classification of the faults has been investigated and found that any transducer provides a classification of 75% or better and this classification rate increases when more transducers are considered. This paper provides a robust SVM based technique using only time domain data without any additional preprocessing for classifying bearing and unbalance faults. [ABSTRACT FROM AUTHOR]