| Composite material has its centuries-old history and expansive applicationbackground, the use of it is a significant milestone of human development.Because each of its component can supplement each other, composite materialshows excellent characteristics in respects of rigidity, intensity, etc. It can beseen that composite material is now in widespread use as building materials suchas FRP, reinforced concrete, etc and it is also widely used in aviation andaerospace field. It has been a long time for buckling stability, post-buckling pathdevelopment and nonlinear dynamic performance of composite structure to bestudied in the area of solid-bifurcation and chaos as a key point and researchesof them are concerned by more and more researchers. In present paper, severalaspects are investigated in the following:1.Taking stress wave propagation into account, the governing equations ofcomposite beam with the clamped-fixed boundary conditions considering FSDTare derived on the basis of Reddy’ theory and solved by the variable-separatedmethod. The analytic expression of the critical buckling load is acquired andcompared with that without taking FSDT into consideration. By numerical calculation, the effects of FSDT on dynamic buckling of composite beamconsidering the difference of ply sequences, layer angle and boundary conditionsare discussed.2.Based on Hamilton Principle, the nonlinear dynamic post-bucklinggoverning equations of composite bar without initial imperfection can bededuced by substitution of equilibrium equations taking account of inertia andFSDT and solved by using finite difference method. The effects of impactvelocity, small amplitude parameters, different modes, etc on post-buckling pathof composite single bar are discussed.3.Influencing factors of Duffing equations’ coefficients can be obtained bytransforming governing equations of composite beam into Duffing equations.Furthermore, subharmonic orbit and heteroclinic orbit of Duffing system withthe clamped-fixed boundary conditions are discussed and chaos thresholds ofthese two orbits are solved by the method of Melnikov. As the result, thecharacteristics of chaos can be described by using the displacement-time curvegraph, the space trajectory, the Poincaré map, the power spectrum chart and theLyapunov exponent spectrum. By numerical calculation, the effects ofcomposite parameters on chaos threshold can be analyzed when takinggraphite-epoxy composite material as an example. At last, chaos of compositebeam can be controlled by method of OGY and results show that the chaoticphenomena of this system will degenerate when amplitude0under tinydisturbance is increasing. 4.The composite beam with the clamped-fixed boundary conditions underexcitation of cross-direction can be simplified as general dynamic modelequations of random Duffing system. Effects of random parameters such asstiffness coefficient, damping coefficient, quality coefficient and effects ofrandom excitation such as Gaussian white noise, bounded noise are respectivelyanalyzed and discussed. It can be obtained that these three coefficients have theirdifferent influences to the bifurcation of the system regarding periodic incentiveamplitude as its bifurcation parameter by the method of Chebyshev polynomialapproximation and colored noise is more likely to reach chaotic state than whitenoise under calculation settlements of this paper according to the method ofrandom Melnikov.5.Based on Ritz-Galerkin Method, the governing equations of compositebeam with the clamped-fixed boundary conditions can be simplified to thetypical formal of Duffing Equations as taking geometric nonlinear intoconsideration. The Duffing-Van Der Pol System is also introduced, and itobtains parameter values of these two systems when they reach the chaotic statecommonly according to their bifurcation diagrams. The Duffing System and theDVP System (short for Duffing-Van Der Pol) can achieve accuratesynchronization by generalized projective synchronization method and monitorof them can be also acquired. Finally, numerical simulation of chaoticsynchronization is done by Matlab and synchronous error curve diagrams,2D-phase-trajectory diagrams,3D-phase-trajectory diagrams can be gotten in order to verify the accuracy of chaotic synchronization. |
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