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    Theme Articles on Nonlinear Control of Engineering Vibration

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    Chinese Journal of Theoretical and Applied Mechanics    2019, 51 (2): 322-323.  
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    Muqing Niu, Bintang Yang, Yikun Yang, Guang Meng, Liqun Chen
    Chinese Journal of Theoretical and Applied Mechanics    2019, 51 (2): 324-332.   DOI: 10.6052/0459-1879-18-254
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    The actuation system, which is composed of magnetostrictive actuator and compliant displacement amplifier, has the advantages of high precision and large actuation force. It is connected in parallel with passive vibration isolator. The resulting active and passive vibration isolator can make up for the deficiencies of passive isolator on low-frequency and micro-amplitude conditions. In this paper, a nonlinear magnetostrictive actuation model is proposed based on Jiles-Atherton model. Magneto-mechanical effect is comprehensively characterized by being decomposed into stress related effects on effective field, magnetization, magnetostriction and Young's modulus. A dynamic model of the isolator is established considering the coupling effects between active isolator and passive isolator. With the coupling effect, the performance of actuation system is related to passive isolator parameters. With higher passive isolator stiffness, the actuation displacement decreases and the required actuation force increases. The coupling effect also leads to the change of equivalent stiffness of the isolator due to the ?E effect of magnetostrictive material. The influence of coupling effects can be weakened by parameter design of compliant amplifier. The performances of the active and passive vibration isolator are validated by numerical simulation. Three kinds of vibration frequencies are used, which are below, around and beyond natural frequency of the isolator, respectively. Compared to passive vibration isolator, better vibration isolation performances are acquired by adding active vibration isolator on all three conditions. And the calculation results show that the proposed model considering magneto-mechanical effect can reach a higher accuracy.

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    Chuyuan Liu, Zesen Liu, Hanwen Song
    Chinese Journal of Theoretical and Applied Mechanics    2019, 51 (2): 333-340.   DOI: 10.6052/0459-1879-18-265
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    The aerodynamic flutter of aerospace vehicle Rudder-airfoil structure is a catastrophic dynamic behavior. In the aeroelastic dynamic model that is on the basis of doublet lattice theory, aerodynamic load can be expressed as a closed-loop control force that is a kind of state feedback based on structural dynamic response. In fact, the aerodynamic forces received by each node are derived from the complex coefficient proportional feedback of the displacement response and velocity response of all nodes. The control law of feedback is dependent on the geometric parameters, material parameters, dynamic characteristics of the structure, flight altitude, air density and inflow velocity etc. It usually needs to be identified and validated by actual flight or wind tunnel testing. Under laboratory conditions, with the premise of equivalent modal characteristic in system dynamic responds, a strategy is put forward that is based on active control in order to track the eigenvalues of self-excited flutter in Rudder-airfoil structure under aerodynamic load. The process of solving the non-self-adjoint dynamic differential equation and its characteristic equation of the equivalent system is established and discussed. The comparison between the computed results and those results from the common software shows good consistency. Through optimization search, the optimal feedback point for displacement and velocity, the optimal actuation point, and the optimal feedback-gain factor can be obtained respectively. The fitting of the wind velocity-displacement gain curve and wind velocity-velocity gain curve can help to realize the real contribution control of the aerodynamic force of the equivalent system. Simulation example shows that the first two modal are the main modal of flutter and higher order modals do not participate in flutter, so the active control strategy focuses on the main modal of flutter. The result also shows that the predicted experimental process does not need identification or reconstruction of the unsteady aerodynamic force in time domain. Ground simulation experiment can be achieved without any other meddles. The active control reaches satisfied effects, ensure the variation characteristics of eigenvalue, achieves preliminary eigenvalue tracking of self-excited flutter, and provides a basement to further promote the active control simulation experiment and flutter parameter identification.

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    Jin Wei, Dengqing Cao, Tao Yu
    Chinese Journal of Theoretical and Applied Mechanics    2019, 51 (2): 341-353.   DOI: 10.6052/0459-1879-18-356
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    With the scale enlarging and flexibility of the actual engineering structures utilized in aerospace and other fields, the issues on the study of nonlinear vibration and active vibration control of the structure become more and more important. The key process of dealing with the vibration and control for such a kind of structure is to establish the nonlinear dynamic model and formulate the state space model of the system. For composite flexible structures composed of flexible components, rigid bodies and flexible joints, because of the vibration coupling between each part of the structure, the modes of an individual flexible component with the cantilever, simply supported and free stationary boundary are different from the real mode of the structure. In this paper, an analytic extraction method of global modes of composite flexible structures is presented, and the nonlinear dynamic model and the state-space model of the system can be obtained by the global mode discretization. Adopting the Cartesian coordinates to describe the motion of the system, establishing the motion equations of the system, and combining with the partial differential equation of the flexible part, the ordinary differential motion equation of the rigid body, the matching condition of force, moment, slope of the deflection curve and displacement at the interface, and the boundary condition of the system, the frequency equation of uniform form is given by using the separating variable method. Consequently, the natural frequencies and the global mode representation of the analytic function of the system are obtained. The global mode extraction method presented here not only facilitates the parametric analysis of the natural frequencies and global modes of composite flexible structures, but also provides an effective way to establish the low dimensional nonlinear dynamic model and the state space model of the composite flexible structure, which is of great significance for the study of nonlinear dynamic responses and the design of active vibration control of this kind of structures.

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    Hao Li, Fagang Zhao, Xubin Zhou
    Chinese Journal of Theoretical and Applied Mechanics    2019, 51 (2): 354-363.   DOI: 10.6052/0459-1879-18-266
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    A quasi-zero stiffness (QZS) vibration isolator has zero stiffness at its equilibrium position, and is efficient in isolating the low amplitude micro vibrations. Therefore, the QZS vibration isolators have excellent potential in applying on the micro vibration isolation of space structures, e.g. satellite structures. Normally, a QZS vibration isolator composes of a positive stiffness element and a negative stiffness element. In many concepts of QZS vibration isolators, the negative stiffness elements are inefficient in weight and volume, because they are normally combined by several components, and external restrains or forces are needed to stress certain components. As a result, the volume and weight of the QZS vibration isolators are unacceptable in some applications, such as space technology and aviation technology. In order to improve the weight and volume of QZS vibration isolators, in this study a novel QZS vibration isolator is put forward by applying the bistable composite laminates as negative stiffness element. The system of this QZS vibration isolator is greatly simplified because of the inherent negative stiffness of bistable laminates. The principle of this novel QZS vibration isolator is illustrated, and the performance of which is analyzed by finite element method. A prototype of the novel QZS vibration isolator is fabricated and is tested in experiment. Experimental results indicate that the acceleration transmission rate of the proposed QZS vibration isolator is much improved comparing with a linear spring isolator. Nevertheless, the tested results of the isolator are not as good as predicted via the finite element analysis. The in practice performance of the proposed QZS vibration isolator is analyzed and discussed. Finite element analysis illustrates that both manufacturing error and assembly error have significant negative influence on the practical performance of the proposed QZS vibration isolator, and the robustness of the isolator should be improved in the future work.

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    Zhongwen Pan, Jianwei Xing, Lei Wang, Shenyan Chen
    Chinese Journal of Theoretical and Applied Mechanics    2019, 51 (2): 364-370.   DOI: 10.6052/0459-1879-18-285
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    Whole-satellite vibration isolation is an effective measure to improve the satellite vibration environment. Traditional Whole-Satellite vibration isolation schemes mainly insert flexible and high-damping structures between satellite and rocket. Due to the series of flexible components, the scheme achieves vibration reduction, and also causes a significant decrease in the modal frequencies of satellite branches (satellite, satellite brackets, transition brackets) and the entire launch vehicle with a remarkably increase in satellite vibration displacement. The former seriously affects the flight stability of launch vehicle, especially the stability of final stage, while the latter greatly reduces the dynamic clearance between satellite and fairing, which may lead to collision between satellite and fairing in severe cases. In order to solve the problem of series whole-satellite vibration isolation, this paper presents a whole-satellite vibration isolation scheme with parallel dampers in the original main bearing structure (transition support). This scheme does not change the form and connection relationship of satellite branch structure, and does not affect the strength and stiffness of satellite branch main bearing structure. According to the characteristics of flexible spacecraft, a multi-degree-of-freedom system dynamics model is established. The effects of different damping characteristics on the transmission characteristics near the resonance frequencies of the system are analyzed by simulation. It is concluded that increasing damping can effectively improve the vibration transmission characteristics near the resonance frequencies of the system. A viscous damper and its mounting bracket are designed according to the external excitation characteristics of a launch vehicle, the structural form of transition support and vibration reduction requirement of satellite. By evenly distributing eight vibration reduction units in the transition support, a whole satellite vibration isolation scheme with Parallel bearing and vibration reduction is constructed. Finite element analysis and experimental results show that the variation of satellite branch frequencies is less than 5% and the transmission characteristics at resonance frequencies are improved by 30%~40% compared with the non-vibration state.

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    Xingtian Liu, Shuhai Chen, Jiadeng Wang, Junfeng Shen
    Chinese Journal of Theoretical and Applied Mechanics    2019, 51 (2): 371-379.   DOI: 10.6052/0459-1879-18-302
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    In vibration isolation field, nonlinear vibration isolation system catch more attention than linear system because of the better vibration isolation performance. In this paper, a novel nonlinear vibration isolation system with geometric nonlinear friction damping is proposed by add two friction damper that perpendicular to the movement direction of the isolated object. The absolute and relative displacement transmissibility of such kind of vibration isolation system are studied in this paper. Different from the friction damper which usually assuming that the friction force is constant, the friction force studied in this paper is proportional to the displacement of the isolated mass by configuring two linear friction dampers perpendicular to the moving direction of the mass. The mathematical model of the friction damping and the forced vibration of the system are established. The dynamic equation is solved by using Harmonic Balance Method (HBM) subsequently by making some simplification. The result solved by HBM is verified numerically. The performance of the nonlinear vibration isolation system is compared with that of a linear one by the performance index defined by absolute and relative transmissibility. The geometric nonlinear friction can offer small or large friction damping depends on the relative displacement, therefore, the nonlinear friction force can improve the transmissibility for both absolute and relative displacement at resonance and the higher frequencies region if the damping values are chosen carefully which surpass a traditional Kevin vibration isolator model. Meanwhile, the nonlinear vibration isolation system can enlarge the application region for different excitation amplitude and avoid the system failure though the responses of the isolated mass is amplified at low frequency. The vibration isolation system with the configuration of the friction damper proposed is very suitable for both resonance and higher frequencies vibration control. The conclusions given are of importance when design and choosing the friction damping parameters.

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