| Nonlinear metallic bar is the basic part of many structures. When the metallic bar deforms after being loaded, resistance of lattice to motion have to be overcome. Peierls-Nabarro(P-N) barrier is not only a basic one but also an important one in many barriers happened in deformed lattices. Considering P-N effect and viscosity of solids, vibration of the bar and propagation of nonlinear wave have been researched under different driving. Governing equation is derived through Hamiltonian variational principle, and dynamic responses of these systems have been described and forecasted through numerical computation and theoretical analysis:1. Under strainless boundary conditions, one-dimensional finite metallic bar subjected to periodic field is simulated systematically with the initial displacement taken as single-hump along the bar.Various diagnostic tools such as time history, power spectrum density function, maximum Lyapunov exponent, Poincare map, phase trajectory portrait have been used to show dynamical responses. Influences of factorssuch as driving amplitude and frequency, initial condition, amplitude and frequency of P-N force, viscous effect and length of the bar have been researched.We find that for different sizes and physical characters, spatial structure will show flat state or single-hump distribution along the bar, and temporal behavior will show periodic, quasi-periodic or chaotic responses respectively.2. Drillstring in oil drilling is simplified as a half-infinite bar. Taking account of P-N force and viscous effect of solid, propagation of nonlinear wave and vibrating of particles are investigated under periodic exciting at the end of the bar. Influences of factors including amplitude and frequency of driving, amplitude of P-N force on the nonlinear responses are researched. We find that all the points of the bar have the same qualitative characters, but vibrating amplitude decreases along the bar. 1-period, 2-period, 3-period, 13-period motion, quasi-periodic motion and chaotic motion would appear under certain driving force and physical properties. Equilibrium point and limit cycle are presented to show transition to periodic and quasi-periodic motion through Poincare mapping section.3. Propagation of soliton in one-dimensional infinite metallic thin bar, which is subjected to axially periodic load and in which P-N effect and viscous effect of metal are taken into account, is investigated qualitatively. Collective coordinate method is employed to reduce the perturbed system into ordinary differential system.Using Melnikov method, thresholds for chaos are given. We find that the critical ratio of the amplitude of external force to damping coefficient (fla)cfor chaos increases along with driving frequency. There is not ultrasubharmonic and even order subharmonic bifurcation orbits in this perturbed system, and a series of odd order harmonic bifurcations will occur before Smale horseshoe mapping appears. By studying the effect of P-N force on the transition to chaos, we find that (fla)c increases with P-N amplitude under small driving frequency. Inversely, (fJa)c decreases with P-N amplitude under large diving frequency.4. In view of P-N force and viscous effect of material, dynamic responses of one-dimensional infinite metallic bar exerted with axial load that is correlative with space and time are investigated. The accurate expressions of librating periodic orbits, rotating periodic orbits and heteroclinic orbits of the perturbation-free system are derived.Melnikov method is utilized to show thresholds for chaos and bifurcations of periodic orbits. It appears that librating periodic orbits reach chaos through odd order subharmonic bifurcation, and rotating periodic orbits reach chaos through even order subharmonic bifurcation. Analysis about effect of P-N force on the onset of chaotic motion denote that chaotic critical value would decrease rapidly and then rise with the parameters values increasing continuously, so as to create a minimum point along every curves.
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