Dissertation > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Deformation solid dynamics

Study on Propagation of Solitary Waves in Nonlinear Bars and Its Complex Dynamic Behavior

Author ZhaoGuangHui
Tutor YangGuiTong;ZhangNianMei
School Taiyuan University of Technology
Course Solid Mechanics
Keywords Peierls-Nabarro force Sine-Gordon equation Solitary wave Melnikov method Build- coordinates Chaos
CLC O347
Type PhD thesis
Year 2005
Downloads 133
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Nonlinear metallic rod member is an essential component of many structures and lattice deformation resistance must be overcome , when the metallic rod force deformed , wherein Peierls-Nabarro (PN) force is very basic many impaired barrier very important one . Study one-dimensional metal bars, taking into account the the PN force of effect and material viscous effect in the the different disturbances role under vibration and nonlinear wave propagation problems . Description rod by Hamiltonian variational principle of nonlinear differential equations of motion of the waves , which is disturbed by the Sine-Gordon (SG) equation . Two ways to describe and predict system dynamic response under different disturbance from the numerical calculation and theoretical analysis , found that the metal rod not only kink wave , and under certain conditions , the motion of the rod showing the characteristics of chaos . By numerical calculation , the system studied taking into account the PN force and material viscous effect of a one-dimensional finite-length metal thin rod strain zero initial conditions, boundary conditions and displacement along the space unimodal distribution space by along the uniform distribution of the dynamic response of the axial external force changes over time harmonic disturbances . -Time curve of the state variables , time and space surface , the power spectral density function the largest Lyaounov index , Poincaré map , phase trajectories and other means , given the magnitude and frequency of the periodic disturbance , the amplitude of the initial conditions , the PN force and frequency , viscous effects , rod length factors on system dynamic response . Found rod geometry conditions and material properties change , shows four kinds of typical power behavior : simple harmonic motion has nothing to do with the spatial position of the single wave simple harmonic motion , a single wave of quasi-periodic motion and single- space modal chaotic movement . Irregular movement given system geometry and material properties. The drillstring simplify Petroleum Engineering for the semi-infinite pole , included in the rod the PN force effect and the material viscous effects , values ??change over time harmonic external force applied to the rod end , the amplitude and frequency of the external force PN force of nonlinear wave propagation characteristics and the vibration characteristics of the various points in the rod

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