Abstract:In this review article, the growth and related academic communications in the dynamics of multibody systems are firstly surveyed. Then, the recent advances in the numerical algorithms for solving the dynamic equations of flexible multibody systems, the contact/impact dynamics of flexible multibody systems and the deployment of flexible space structures are systematically reviewed, together with several open problems of concern. Finally, some suggestions are made for the prospective researches on the dynamics of flexible multibody systems.

Abstract:When the mechanical system is coupled with the constraints, it is very convenient for the transition from the rectangular coordinates to the generalized coordinates, and it is also very necessary. The introduction of generalized coordinates is one of the major features of analytical mechanics, and the Lagrange equation is based on the generalized coordinates. In this paper, some relevant history data of the formation of generalized coordinates are provided, and some propositions are given.

Abstract:The stability of singular points and their trajectories in phase space of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator are studied. Firstly, the singular points of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator are obtained. Based on the Lyapunov indirect method and the gradient method, the stability of equilibrium points of this system are then discussed. Finally, numerical simulations are performed by the software Matlab, and Poincare surface of the section are used to study the trajectories of the system in phase space. It is found that, with the increase of energy, the chaos appears finally through two stages of regular motion as well as the coexistence of regular motion and chaos.

Abstract:In this paper, the dynamic behaviors and synchronization is investigated for a three-mode system of Couette-Taylor flow, and the corresponding evolution of Couette-Taylor flow is also explained. By constructing a family of generalized radically infinite and positive definite Lyapunov functions, the globally attractive set and positively invariant set of the Couette?Taylor flow system are obtained. It is found that the designed linear feedback controller are effective in globally synchronizing two identical chaotic systems. Eventually, a numerical example is provided to validate the feasibility of the results.

Abstract:The software of Matlab is used in this paper to simulate the whole process of dynamic behavior for the system divergence and chaos. The simulation results, such as the maximum Lyapunov exponent spectrum and bifurcation diagram, Poincare cross section, power spectrum and return map, are described to investigate the characteristics of system chaotic behavior. Meanwhile, the globally exponentially synchronization of the chaotic system is achieved by linear feedback synchronization control. The validity of the synchronous method is then theoretically performed by Lyapunov second method. Moreover, the simulation of synchronous system also verifies the effectiveness of the synchronous method.

Abstract:This paper presents the nonlinear dynamical analysis of a multilayer d31 piezoelectric macro-fiber composite (MFC) laminated shell under the transverse excitations, and the effect of the piezoelectric properties on structure vibration response is also studied. The nonlinear dynamic equations of the MFC laminated shell is firstly established. Based on the known geometrical and material properties of its constituents, their electric field dependence was presented. The vibration mode-shape functions are then obtained according to the displacement boundary conditions, and the Galerkin method is employed to transform the partial differential equation into two nonlinear ordinary differential equations. Subsequently, numerical simulation examines the effect of the transverse excitations and the piezoelectric coefficients on the nonlinear vibration of MFC laminated shell. The two-dimensional phase portraits, three-dimensional phase portraits, waveform phase, frequency spectrum phase, and bifurcation diagram are presented and used to investigate the different kinds of the periodic and chaotic motions of (MFC) laminated shell. The results indicate that piezoelectric parameters have a strong effect on the vibration response of the MFC laminated shell.

Abstract:The oblique impact dynamic analysis for a flexible manipulator system with large overall motion is studied in this paper. Based on the rigid-flexible coupling dynamic theory of flexible multibody system, the coupling deformation item is considered to reflect the coupling effect of the large overall rigid body motion and the small elastic deformation motion. The rigid-flexible coupling continuous dynamic equations of the system are then derived through the use of the Lagrange dynamic method. The oblique impact dynamic model for the system is developed by introducing a oblique impact model which includes the normal impact model and the tangential impact model. Meanwhile, the impact forces are added to the system dynamic equations in form of the generalized forces. A nonlinear spring damper model based on the continuous contact force method is set as the normal impact model, while a modified Coulomb friction model, which describes the friction force of the whole process with a unified equation, is set as the tangential impact model. The contact separation criterion is also established to identify the dynamic status and realize the transformation between the continuous dynamic model and the oblique impact dynamic model. Moreover, the impact dynamic simulation examples are given to verify the oblique impact dynamic modeling method, and the dynamic behaviors in the global simulation process are discussed. The results show that the impact makes a great effect on the large overall motion and the small deformation motion both in the impact process and the un-impact process. The dynamic parameters, such as the displacement, the deformation, the mechanical energy and the impact force are also compared at different impact angels.

Abstract:Although each rotor is balanced well, unbalance vibration fault still exists for the shafting with three supports (i.e., steam turbine, compressor unit, etc.). The effect of residual unbalance phase difference on vibration characteristics of shafting with three supports is investigated in this paper. A finite element model is developed for shafting with two spans and three supports to analyze the steady-state response. Additionally, the combination of residual unbalances phase difference among multi rotors is presented. The relationship between the supports vibration and the residual unbalance phase difference among multi rotors are confirmed. The phase difference of shafting with residual unbalance mostly affects the shafting vibration in the high speed, and the minimum vibration amplitude for the shafting is from 0-180. Obviously, it is different from the traditional shafting with four supports. Finally, the vibration experiment for the phase difference of shafting residual unbalances is performed to validate the simulation predictions. It is a new way to suppress the unbalance vibration fault for this kind of shafting with multi rotors.

Abstract:An interval analysis method of rotor transient response based on interval mathematics, Taylor expansions and perturbation theory is proposed to analyze the transient response of flexible rotors with uncertain parameters. As the specific probability distribution of uncertain parameters is not required, the interval analysis method is more suitable for practical use in comparison with traditional probability methods when dealing with the uncertain problems. Transient dynamic balancing method of flexible rotors based on transient response information was then introduced, and the simulation of a double-disc rotor with elastic supports was carried out. The influence of uncertainties on the balancing efficiency was analyzed by introducing uncertainties into the transient dynamic balancing process. The results show that the uncertainties can cause significant reduction in dynamic balancing efficiency and increasing of the residual vibration.

Abstract:A 2-dimensional rigid airfoil with a control surface is simplified to 3-DOF aeroelastic model. This 3-DOF aeroelastic model took a cubic nonlinear stiffness in heaving and pitching displacement directions, and employed bilinear stiffness for the clearance in the control surface. Based on the principle of target energy transfer, a single degree of nonlinear energy sinker is coupled with the airfoil structure for suppressing the flutter of the system. Considering the quasi steady aerodynamic theory, the motion equations of the two systems (with and without NES) are established. Meanwhile, the peak-peak amplitude diagrams show that the global dynamic property of the system is changed by attaching a NES. Bifurcation diagrams is also constructed by using numerical continuation method for both systems. The Comparison of the bifurcation diagrams exhibits the suppressing effect of the NES, and it is find that aeroelastic instability was partially or even completely suppressed by passively transferring vibration energy from the wing to the NES in a one-way irreversible fashion.

Abstract:This paper studied the sloshing stability of a liquid-filled cylindrical tank subjected to longitudinal excitation. A pendulum model is used to obtain equivalent dynamics Mathieu equation of the liquid sloshing under the longitudinal excitation. Based on the perturbation method, the stability boundaries are then obtained with the variation of the damping, liquid height and diameter of the tank. The results show that the damping, the liquid height and the diameter of tank have an important effect on stability boundaries.

Abstract:Dynamic blood disease appears in a wide range of fluctuations on the number of blood cells, which is primarily abnormal changing in the hematopoietic stem cell number. In a Fourth Order hematopoietic system, a changing parameter leads to different oscillation modes of the number of blood cells in the dynamic blood disease oscillations. Through two-parameter bifurcation analysis on the hematopoietic system, we can push a oscillatory mode into a stable equilibrium state by adjusting another parameter to maintain the stability of the number of blood cells.

Abstract:This paper investigates the stability control of body-fixed hovering orbit over the near-Earth asteroid 433 Eros. Its gravitational field is approximated simulated by using the triaxial ellipsoidal model. Dynamical equations of the spacecraft near 433 Eros are derived. The time-varying sliding mode control with the same acceleration and variable intercept is adopted to design the hovering controller. Meanwhile, the sliding surface in this method is different from the conventional sliding mode control, where there is no reaching phase. Numerical simulations are then carried out with different initial conditions and hovering conditions to evaluate the effectiveness of the designed controller. The maximum values of spacecraft velocity and acceleration are analyzed by varying the switching time of sliding surface.