Shijian Zhu

Analysis of non-linear dynamics of a two-degree-of-freedom vibration system with non-linear damping and non-linear spring

In this paper, the non-linear dynamics of a two-degree-of-freedom vibration system with non-linear damping and non-linear spring is studied. The analytic results show that the purposes of reducing amplitude and oscillation can be realized by adjusting properly the system parameters and considering the value of exciting frequency. The conclusions can provide some available evidences for the design and improvement of the non-linear absorber. Numerical simulations show the system exhibits periodic motions, quasiperiodic motions and chaotic motions.

Modelling of the stiffness of elastic body

Abstract It is necessary for designing vibration-isolation systems to know the components’ static stiffness, dynamic stiffness and shock stiffness, which are obtained through experiment at present. If the stiffness model of (viscous) elastic body is set-up, the essence of stiffness will be clearer and the experiment simpler. This paper presents a new method for modelling the stiffness of elastic body with viscoelastic theory. The parameters of the model set-up by using this method can be determined easily and present the characteristics of the elastic bodys static stiffness, dynamic stiffness and shock stiffness.

Nonlinear Normal Modes for Multi-Degree-of-Freedom Nonlinear Vibration Isolation System

Nonlinear vibration isolation system (VIS) plays an important role for improving the capability of hydroacoustic stealth of naval vessels. In engineering, Nonlinear VIS is generally a multi-degree-of-freedom system and its mathematical model is a set of coupled differential equations. Nonlinear normal mode (NNM) is an effective tool for decoupling and analyzing the dynamics of this coupled system. In this paper, taking the flexibility of the base into consideration, the equations of motion of an on-board VIS with quadric and cubic nonlinearities is formulated. The NNMs of this multi-degree-of-freedom nonlinear VIS are constructed by using the invariant manifold approach. The invariant surfaces of the NNMs and the decoupled oscillators are presented.Copyright

Numerical and Experimental Research on Dynamics of Two DOF Vibration System with Piecewise Stiffness

In this paper, the two dof vibration isolation system with piecewise linear vibration isolators under force excitation is analyzed. Isolators with asymmetric restoring forces are considered, and the results of periodic-n and chaotic motions are calculated by numerical simulation. These motions are described by phase plane diagram, spectrogram and Poincaré mapping. The simulation results are experimentally verified. The results that are obtained in this paper would be significant for chaos method to line spectra reduction.

The Application of Cell Mapping Method to High-Dimensional Nonlinear System

After analyzing the inefficiency of the conventional Cell Mapping Methods in global analysis for high-dimensional nonlinear systems, several principles should be followed for these methods’ implementations in high-dimensional systems are proposed in this paper. Those are: appropriate selection of investigating plane, reduction of data size, and projection of attractors to the investigating plane. According to these, the idea of dynamic array is introduced to the method of Point Mapping Under Cell Reference (PMUCR) to improve computing efficiency. The comparison of the CPU time between the applications of this modified method to a 2-dimensional system and to a 4-dimensional one is carried out, and the results confirm this modified method can be utilized to analyze high-dimensional systems effectively. Finally, as examples, the periodic and chaotic motions of a coupled Duffing system are investigated through this method and some diagrams of global characteristics are presented.Copyright

Study on Application of Neural Network in Chaotic Vibration Isolation System

The paper studies the application of neural network in chaotic vibration isolation system. Because the dynamical characteristics of the isolation system change with working state of the isolated object, the control system must have the ability to adjust the system parameters online to obtain the designated target. During the controlling process, chaotic vibration signal identification is the first step. New technology, however, is needed to identify the category of the signals because the traditional methods such as Lyapunov exponent and correlation dimension are time-consuming. The incompact wavelet neural network is trained to classify different signals effectively in this paper, and it is beneficial to adjust the nonlinear isolation system parameters timely. Hence the system works in a chaotic state, and the linear spectrum in the waterborne noise can be reduced.Copyright

Research on active vibration isolation based on chaos synchronization

To improve warship capability of concealment, the key problem of the design of the chaotic vibration isolation system is how to keep the chaotic response in different working condition. The existing isolation systems, however, are designed based on linear system theory, and thus it is difficult to generate chaos; but if the isolation system is designed according to nonlinear theory, it is difficult to realize in practical engineering. The main reason is that the element of isolation system should be calculated accurately. The controller based on the Lyapunov stability theory is designed, and the aim is to make the output variable of the isolation system track the output variable of the chaos system, i.e. the output of two systems are synchronized by choosing the output matrix of chaos system suitably. Results show that the response of the double layer vibration isolation can track the output of the Duffing driven system, and the force transferred to base is reduced effectively. The performance of the vibration isolation is improved.

A VOF based numerical simulation of initial flow field of underwater gas jet

Underwater gas jet produces a complex unstable multiphase flow field, which is involved in different technological fields. The VOF multiphase flow model and the RNG κ - ε turbulence model were adopted to predict the structure of underwater gas jet flow field and to reveal the development of transient flow. The features of the developing process of the two phase flow, and the basic characteristics of the jet flow under the influence of the complex compression and expansion waves were revealed. The simulated results are in good agreement with experimental data, and thus indicate the accuracy of the proposed method.

Analysis of the cord layer's influence on the air spring's lateral stiffness

Stiffness is one of the most important factors to vibration isolation system. Paper established a finite element model of the air spring, used nonlinear finite element method to analysis the rectangular shape air springs stiffness. By considering the nonlinearity of the rubber-cord composite material, the geometric nonlinear process caused by large deformation and the nonlinear contact between the rigid base plate and the flexible capsule, paper calculated and plotted the characteristic curve of air springs, and analyzed the influence of cord angle, cord spacing and number of cord layers on the air springs lateral stiffness characteristics. The finite element method results are consistent with the test results, which proved the method is feasible.

Design and simulation on nonlinear rubber isolator based on ANSYS software

In order to meet the requirement of vibration and shock isolation simultaneously, a nonlinear rubber isolator is designed and analyzed. The stiffness of the rubber isolator can be changed with the displacement. The ANSYS software is set as simulation platform, and the finite element model of the nonlinear rubber isolator is built based on the hyperelastic and viscoelastic theory. The stiffness of the isolator is obtained by static and transient analysis. The results show that the vibration and shock isolation can be achieved by the nonlinear isolator simultaneously. This design would be significative for vibration and shock isolation.