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The in-plane free vibration of a rectangular plate made of functional graded materials (FGM) is studied based on the two-dimensional linear elasticity theory. The material parameters of FGM rectangular plates are assumed to vary along with the length and width directions according to an exponential law. The governing equation of motion for the FGM rectangular plate is derived using the D' Alembert principle. Subsequently, the equation of motion is solved by the Differential Quadrature Method (DQM), and the natural frequencies for in-plane free vibration of FGM rectangular plate are obtained accordingly. The effects of gradient index, length-width ratio and stiffness of elastic boundary on the natural frequency of FGM rectangular plates are discussed, and the modes for in-plane free vibration are provided.

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Nowadays, numerous supervised deep learning models have been applied to bearing fault diagnosis. However, labelling the health states of the bearing vibration data is a time-consuming work and dependent on expert experience. In order to tackle this problem, a novel unsupervised bearing fault diagnosis method named adversarial flow-based model is explored in this paper. Flow-based model is a type of generative models that is proved to be better than other types in many aspects. This paper introduces the flow-based model into the field of machinery fault diagnosis, and designs an appropriate model architecture so as to train the model in unsupervised and adversarial ways. The proposed model contains an autoencoder (AE), a flow-based model, and a classifier. Firstly, the AE maps the vibration data from signal space to latent vector space. Then, the flow-based model aligns the distributions of the latent vectors of different bearing states with specific prior distributions. Finally, the classifier tries to discriminate the aligned latent vectors from the vectors sampled from the prior distributions. With the help of distinguishable prior distributions and the adversarial training mechanism between the classifier and the flow-based model together with the AE, the bearing data with the same health states are clustered into the same areas. The good clustering performance of the adversarial flow-based model is verified by a dataset with 10 health states from a bearing test rig.