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In this paper, a nonlocal Bernoulli-Euler beam model is established based on the theory of nonlocal elasticity. Frequency equations and modal shape functions of beam structures with some typical boundary conditions are derived based on the model. The corresponding dynamic properties are presented and discussed in detail, which are shown to be very different from those predicted by classic elasticity theory when nonlocal effects are significant. The results can be applied to modeling and characterization of size-dependent mechanical properties of micro- or nanoelectromechanical system (MEMS or NEMS) devices.

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Two improved Elman network models, output-input feedback (OIF) and output-hidden feedback (OHF), are proposed based on the modified Elman network. A recurrent backpropagation control (RBPC) network model is developed by using the OIF Elman network as a passageway of the error back-Propagation. The stability of the improved Elman