Vol. 2, No. 1 (2018): Regular Issue

The effects of combined DC and fast AC electromagnetic actuations on the dynamic behavior of an excited cantilever beam is studied considering a single mode approximation. Analytical investigation is performed to extract the equation of motion describing the slow dynamic of the system. The influence of the fast AC actuation and the air gap on the nonlinear behavior of the system is examined. It is shown that the nonlinear characteristic of the system can be controlled by appropriately tuning the AC actuation or the air gap. This can be useful in certain engineering applications where the operating frequency range includes one or several critical frequencies that should be avoided.

In this paper, we investigate the existence, uniqueness and Ulam stability of solutions for impulsive type pantograph equations with Katugampola fractional derivative. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem.

Based upon an asymptotically reduced coupled model, nonlinear forced vibrations of a non-horizontally suspended cable is investigated in this paper, which is coupled with a flexible oscillating tower. The cable’s nonlinear coupled dynamics is a modulated version of cable’s uncoupled dynamics, i.e., the cable dynamics with fixed rigid towers. Nonlinear frequency responses of the cable-tower coupled system are found, with saddle-node bifurcations, Hopf bifurcations, and quasi-periodic behaviors detected. Special attentions are paid to the dynamic effects caused by cable-tower coupling, boundary damping, and the inclinations.

In this paper, we discuss the existence, uniqueness and stability of nonlinear neutral pantograph equation with ψ -fractional derivative. The arguments are based upon Schauder fixed point theorem and Banach contraction principle. Moreover, we discuss the Ulam-Hyers type stability.

Addressing the impact of quantization error in analog-to-digital converter (ADC) for signal processing, a Discrete Fourier Transform (DFT) based method for the generation of dithering signals is presented. Effective in reducing quantization error, the dithering signal generated using the method is not only independent of the input signal but also can improve the performance of the ADC. To illustrate the advantages of the dithering signal reconstructed using the method, three kinds of typical dithering effects, namely, Triangular Distribution Dithering, Gaussian Distribution Dithering and Uniform Distribution Dithering on the quantization error in an ADC are considered. The properties of three practical dithering signals are investigated. It is shown that while these typical dithering may be useful they are some potential problems. The dithering signals reconstructed using the DFT based generation scheme is shown to contribute significantly to reducing quantization error. Numerical experiments and theoretical analyses demonstrate that the DFT based dithering reconstruction can obtain prominent performance for ADC in comparison to typical dithering signals.

This study investigates the non-linear dynamic scaling laws for a rotating thin-wall short cylindrical shell. By introducing the geometric non-linear term, corresponding governing equations are employed to establish the non-linear scaling laws. Both the natural frequency and single-point excitation response of the rotating cylindrical shell are investigated. The applicability of the scaling laws of the rotating thin-wall short cylindrical shell is verified numerically. In addition, the scaling laws for linear and non-linear vibrations are compared. Analytical results indicate that the scaled model designed by the non-linear scaling laws are more restrictive than that of using the linear scaling laws. In addition, they predict the characteristics of the prototype with good accuracy.

The attention is confined to the vibration suppression of rotor unbalance in this paper. A method to control synchronous vibration due to rotor unbalance in rotor-bearings system is proposed which uses active magnetic actuator (AMA) to produce active control force to suppress rotor’s vibration. A model reference adaptive control strategy based on self-adjusting of Proportional and Differential gain is adopt for producing active electromagnetic force. First the model of rotor-bearing system with AMA and the ideal reference model are established using the finite element and the state space method. Then on the basis of PD feedback, the adaptive control of feedforward and unbalance compensation is considered. An active vibration control scheme for controlling transverse vibration of rotor due to unbalance excitation is designed. Finally, numerical example and simulated analysis for controlling synchronous vibration of rotor are carried out. The simulation results indicate that the proposed approach can effectively suppress the synchronous vibration caused by rotor unbalance using the electromagnetic force.

Combining transient blade row (TBR) method with stationary inverse Fourier transformation (IFT), an effective method for numerical simulation of flow-induced force on the blade at the last stage of steam turbine is proposed in this study. Using this method, only a single flow channel needs simulating transiently to obtain the force on blade. Then, the numerical simulation of flow-induced force using this method is carried out on the last stage of a real steam turbine, and the feasibility of this method is also verified via this example. Comparing with traditional transient computation, a remarkable amount of computing time and resources can be saved by this method.