Frequency formula for a class of fractal vibration system

Four fractal nonlinear oscillators (The fractal Duffing oscillator, fractal attachment oscillator, fractal Toda oscillator, and a fractal nonlinear oscillator) are successfully established by He’s fractal derivative in a fractal space, and their variational principles are obtained by semi-inverse transform method. The approximate frequency of the four fractal oscillators are found by a simple frequency formula. The results show the frequency formula is a powerful and simple tool to a class of fractal oscillators.

Vibration Analysis of Cylindrical with Splitter Plates under Different Deflection Angles at High Reynolds Number

In order to study the influence of the splitter plate in the elastic support system, the SST k-omega turbulence model is used to solve the problem, and the cylindrical system with splitter plate is numerically simulated by overset mesh. This paper studies the effect of the splitter plate on the vibration system at different deflection angles. The results show that the splitter plate has little effect on the system when the deflection angle is low. When the deflection angle is about 10 degrees, the system vibration characteristics will have a sudden change, the amplitude will decrease, and the vortex frequency will increase. Between the deflection angle of 10 degrees and 45 degrees, as the deflection angle increases, the amplitude increases and the vortex frequency decreases. It can be seen from the motion trajectory that the deflection angle changes suddenly after 10 degrees, and the system has a very small amplitude between 10 degrees and 25 degrees. In this declination interval, the splitter plate controls the vibration of the cylindrical system better.

Stability and synchronous characteristics of a two exciters vibration system considering material motion

Nowadays, two exciters vibration system played an indispensable role in a majority of machinery and devices, such as vibratory feeder, vibrating screen, vibration conveyer, vibrating crusher, and so on. The stability of the system and the synchronous characteristics of two exciters are affected by material motion. However, those effects of material on two exciters vibration system were studied very little. Based on the special background, a mechanical model that two exciters vibration system considering material motion is proposed. Firstly, the system's dynamic equations are solved by using Lagrange principle and Newton's second law. Then, the motion stability of the system when material with different mass move on the vibrating body is analyzed by [Formula: see text] mapping and numerical simulation methods, and the motion forms of the material are also studied. Meanwhile, the frequency responses of the vibrating body are analyzed. Finally, the influence of material on the phase difference of the two exciters is revealed. It can be concluded that with the mass ratio of the material to the vibrating body increasing, the system's motion evolves from stable periodic motion to chaotic state, the synchronization ability of two exciters decline, and the unpredictability of abrupt change about the phase difference increases. Further, the uncertainties of both the abrupt change of phase difference and the collision location affect each other and eventually lead to the instability of the system.

A Simple Frequency Formulation for the Tangent Oscillator

The frequency of a nonlinear vibration system is nonlinearly related to its amplitude, and this relationship is critical in the design of a packaging system and a microelectromechanical system (MEMS). This paper proposes a straightforward frequency prediction method for nonlinear oscillators with arbitrary initial conditions. The tangent oscillator, the hyperbolic tangent oscillator, a singular oscillator, and a MEMS oscillator are chosen to elucidate the simple solving process. The results, when compared with those obtained by the homotopy perturbation method, exhibit a good agreement. This paper introduces a very convenient procedure for attaining quick and accurate insight into the vibration property of a nonlinear vibration system.