Study On Nonlinear Dynamics Of A Nanocomposite Buckling Beam Under Parameter Excitation

Nanocomposites as new material, are widely used in aerospace engineering, national defence, transportation, sports and other fields because of the designability. Viscoelastic materiel performances ample nonlinear phenomenon from the research of the materiel and nanocomposites are viscoelastic material, so the dynamic properties have important practical applications.In this paper, the buckling of beam of nanocomposites with parametric exctitation is analysed. It's impossible to use the theory constructe the dynamical equation, because the material parameters and constitutive relation are unknown. Through building experimental device of the nonlinear vibrating beam with parametric exctitation and using experimental modeling method, we constitue the dynamical equation of the vibrating beam. The main contents include the following content:Firstly, the 1/2 subharmonic resonance is analysed with multiscale method. The amplitude-frequency response at the steady-state response and bifurcation behavior with the excitation amplitude or damping changed and other parameters fixed are discussed.Secondly,the dynamic characteristics of beams are studied with Runge-Kutta numerical methods, by use of poincare map, phase diagram and power spectrum, the dynamical behaviors are identified based on the equation. The bifurcation diagram are presented in the case of excitation amplitude and damping is respectively varied while other parameters are fixed. The the maximum Lyapunov exponent is calculated to identify chaos. The roads leading to chaos is also discussed.Finally,the incremental harmonic balance nonlinearity identification (IHBNID) is applied to parametric identification of nonlinear systems. Considering the Mathieu-Duffing equation as an example, the effectiveness of the IHBNID can be verified on bifurcate and chaos.