Abstract:Traditionally,analytical mechanics is described by means of dynamics,and the common foundation for structural mechanics and optimal control is analytical mechanics.So,under the framework of structural mechanics or optimal control theory,there should also be a whole set of analytical mechanics theory,which we define as analytical structural mechanics.A conservative system can be described with the Hamilton system methodology,and its characteristic is the symplectic conservation,which is the most important feature of conservative system.The finite element method was initiated from structural mechanics,and its element stiffness matrices should be symmetric,which is,in fact,the symplectic conservation.Based on the fact that the interval deformation energy depends only on the two end displacements vector,we derive the Lagrange and Poisson brackets analytically,the symplectic duality system,the canonical equations,and the canonical transformations,etc.

Abstract:Solution of the nonlinear vibration in conservation system by using the target function method is studied in this paper. The motion of pendulum is taken as an example problem. The relevant governing equation is integrated on the variable for time with the vanishing initial velocity and non-vanishing initial displacement. In this case, the velocity is a function of time, and it is in turn called the target function. Since the pendulum completes a periodic motion from the right side to the left side and then to the right side, the second zero of the target function becomes the period of the motion. In addition, in the time of numerical integration the displacement is also obtained. The suggested method depends on the numerical integration of the ordinary differential equation and the half-division technique for finding the zeros of a function. Solutions for some nonlinear differential equations are also evaluated. Finally, numerical examples and results are given.

Abstract:This letter gives a method that can achieve chaos synchronization of chaotic systems. This method makes synchronization problems changed into the asymptotic stability questions of the 0 solution of the linear systems, then gives the control variable according to the control theory of linear system. This method is simple and it can achieve chaos synchronization of two chaotic systems efficiently. The synchronization is overall asymptotic stable.　The basic theory and the numerical experiments of two identical and nonidentical chaotic systems are performed. The numerical example is a new system.

Abstract:A technique coupling with the parameter transformation method and the multiple scales method is presented for determining the primary resonance response of strongly non-linear Duffing-Rayleigh oscillator to random narrow-band excitation. By introducing of a new expansion parameter, the multiple scales method is employed to determine the equations describing the modulation of the amplitude and phase. The dynamical behaviors of the primary resonance response are analyzed in detail. The effect of the random excitation on the stable periodic response is analyzed as a perturbation and stationary mean-square response is obtained by the moment method. Sufficient and necessary condition for stability of the steady-state response is obtained by Routh–Hurwitz criterion. Theoretical analyses in addition to numerical calculation show that under some conditions the system may have two steady-state solutions. Theoretical results are verified by numerical ones and good agreement is found. The results obtained for strongly non-linear oscillator complement previous results in the literature for weakly non-linear oscillator.

Abstract:This paper presents a study on the chaotic transient phenomena of a controlled electromechanical system with a time delay in the feedback path. A few case studies, with help of possible explanations, show that the occurrence of multiple chaotic transients exists not only with respect to the initial system states, but also to the values of time delay.

Abstract:A new kind of Lagrange function by variational principle of liquid sloshing in pitching tank is build. Based on this, the analytical solution of liquid nonlinear sloshing in pitching tank can be investigated. In the paper, the Taylor series about wave elevation function in the liquid free surface of velocity potential function is derived. After this, the nonlinear equations of free surface kinetic boundary condition and dynamic boundary condition is gained. Then, by supposing the solution in the form of the superposition of each dominated harmonic wave, the corresponding algebraic equations about unknown coefficients by Harmonic Balance Method (HBM) is derived. Last, the algebraic equations are solved by Broyden method. By the example of a two-dimensional, rigid, rectangular, open tank without baffles, the liquid large amplitude sloshing problem is investigated. As for the amplitude of liquid sloshing, comparison between theory and experiment show good agreement at certain frequency range. And at the same time, the phenomenon of zero shift at the liquid surface is found evidently.

Abstract:In this paper, the non-linear ultraharmonic resonance of a conductive beam plate in a magnetic field subjected to some mechanical loadings is studied. Base on nonlinear electro-magneto-elastic equations of the plate and the expression of electromagnetic forces, the vibration equations of thin beam plate under uniform transverse magnetic field and mechanical loadings are obtained. By use of the Galerkin’s method, the differential equation of the nonlinear vibration is derived consequently. By mean of multiscale method, the amplitude and frequency resonance equations in steady state are arrived at. By some examples, the amplitude-frequency curves, time history curves are derived. The influences of plate thickness, magnetic field and excitation amplitude on vibration properties of system are analyzed.

Abstract:The idea and method of controlling complex dynamic behavior of a rotor-bearing system, i.e. bifurcation and chaos, is given in this paper. A controller of the controlling bifurcation and chaos is designed by washout-filter feedback method. Characters of the bifurcation and chaos are improved according to above method. The stability of a rotor system is controlled by modulating the parameters of this controller. Numerical simulation result show that, the dynamic behavior is changed rapidly along with the rotate speed of the rotor-bearing system increase continued. The washout-filter feed back method has a good effect on controlling bifurcation and chaos in above condition.

Abstract:In this proposed paper, based on the dynamic equation of linear gyroscopic system,the differential equation in Lagrange system is transformed into Hamilton system, and then the weighted adjoint symplectic orthogonal relations between the eigenvectors and the expansion theorem for arbitrary state vector are given in state space. Based on the above relations, the equations for modal perturbation analysis and the sensibility computation of eigenvectors are established, and a new effective algorithm for modal perturbation analysis and the sensibility computation is proposed, which can eliminate the traditional difficulties in perturbation analysis and sensibility computation in Lagrange system. An example shows the effectiveness of the numerical method of this paper.

Abstract:In allusion to the specific features of a non-linear rolling element bearing-rotor system with pedestal looseness at one support, The dynamical equations of roll element bearing - rotor system are derived using the theories of Hertz theory，non-linear dynamics and rotor dynamics after the nonlinear condition of looseness is taken into account. After simulating the dynamic equation of the system numerically, the complex motions including the period doubling and chaotic motions and the transformational laws are showed with the increase of the rotating speed and the augment of the clearance by means of the phase maps, the bifurcate maps, the Poincaré maps and the correlation dimension. The bifurcation, chaotic motions and their laws of changes roll element bearing - rotor system with pedestal looseness are analyzed based that. The valuable conclusions for engineering are acquired. The analysis results in this paper provide some reference for diagnosing the fault of Pedestal looseness.

Abstract:In this paper, an attempt was made to extend the Differential Quadrature Method (DQM) to establish the nonlinear vibrations of a cantilevered pipe conveying fluid with motion-limiting nonlinear constraints. The partial differential equation of motion of the pipe was transformed to an ordinary differential equation by DQM. Based on this，attention was concentrated on the vibration behaviour of the free end of the pipe, and several vibrations were found by numerical calculations. Calculations of the bifurcation diagram, phase portraits of the motion, time histories and Poincaré maps establish definitively the existence of chaotic vibrations. The route to chaos is shown to be via period-doubling bifurcations of specific parameters. The represented results show reasonably good agreement with other classical ones. Thus it is demonstrated that the present method is valid and applicable for studying the dynamic response (including chaotic vibrations) of some other structures.

Abstract:This work proposes a modified Bingham model for describing magneto-rheological fluid (MRF) damping force by experimental data. The model parameters have direct physical significance to the MRF damper properties. In addition, the primary resonance reduction in a single-degree-of-freedom (SDOF) skyhook controlled system is investigated. An analytical solution for the system’s primary resonance is obtained, which is verified by numerical solution. The effect of changing physical model parameters on the system’s primary resonance is also studied.

Abstract:APFSDS is the main weapon that killed the armor target in the ground. During the discarding sabot, the interference between sabot and long rod is complicated and the dispersion of APFSDS is affected. on the basis of expression form of particle movement and the theorem of moment of momentum on systems of coordinates and the law of APFSDS movement and separation process out of bore, This text make asymmetry dynamics model of separation which it can describe the sabot motion out of bore accurately, and the process of discarding sabot was calculated. This module of movement and separation of APFSDS is worthy of analyzing the discarding process and movement out of bore.

Abstract:The control of a semi-active suspension of the full-vehicle model has been investigated. According to the Lagrange equation of the second type, a special Lagrange equation of the second type for the semi-active suspension of the full-vehicle model is obtained. Then the equation of motion and its state space form for the system are established, considering the comprehensive coupling of the vertical motion, the pitch motion and the roll motion of the sprung mass. The semi-active suspension of the full-vehicle model is controlled with some on-off control laws, using four MR dampers as actuators for the system. The simulation results demonstrate that the on-off control is just of little use for the control of the vertical acceleration and the roll angular acceleration of sprung mass, the pitch angular acceleration is even deteriorated. However, it can effectively control the dynamic deflection of the suspension, the dynamic deflection of the tire and the vertical acceleration of unsprung mass. Furthermore, the rear suspension is much better controlled than the front one. Here, the No.4 control law is the best on-off control law and easy to be realized. The results can be the reference of the more advanced control law for the semi-active suspension of the full-vehicle model.

Abstract:From a convolution type constitutive model of viscoelastic solids with damage, the equations governing the static-dynamic behaviors of viscoelastic Timoshenko beams with damage are presented under the case of finite deflections. The Galerkin method was firstly applied to simplify the set of equations and a set of ordinary-differential equations were obtained. The numerical methods in nonlinear dynamics, such as Phase-trajectory figures and Poincare sections were used to solve the simplified system. The influences of the load parameters on the dynamic behavior of nonlinear viscoelastic Timoshenko beams with damage were investigated. In particular, the effects of the damage on the dynamical behaviors of viscoelastic Timoshenko beams were considered.

Abstract:The effects of wind speed, attack angle, bundle, magnetic force and weight hammer on galloping are analyzed by utilizing 3D finite element method. The results show that the effects of wind speed, attack angle and bundle are great, but the effect of magnetic force is very small. It is also shown that it is effective for guarding against galloping to fix weight hammers at the 1/3 and 2/3 span of the line.

Abstract:Hydroelastic instability of blades in flowing passageway is one of important factors which induce hydraulic vibrations of a huge hydro turbine machinery. An objective of this paper is to establish a mathematical methodology to analyze the characteristics of the dynamical instability of the blades of huge Francis Hydro Turbine. To do that, theory of the arbitrary thin shell and arbitrary Lagrangian-Eulerian (ALE) formulation are applied in an orthogonal streamlines coordinate system to get a nonlinear parametric model describing vibration along the normal of the blade surfaces, and the dynamical instability conditions on the Bessel function expansion with the frictional velocity in the near-walled region of the blade was obtained.