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Considering viscosity of one-dimensional finite metallic bar,the effect of Peierls-Nabarro(P-N) force on nonlinear vibration is investigated under strainless boundary conditions and singlehump initial displacement condition.Governing equation is derived as perturbed Sine-Gordon(SG) type equation.With the size and physical properties specified, the spatial modes and long-time asymptotic states evolve as a function of P-N force.Different dynamic responses are shown numerically: x-independent simple harmonic motion;harmonic motion with single wave;quasi-periodic motion with single wave and chaotic motion with single spatial mode.It’s found that P-N force is also an important factor in affecting the motion of this system.
Considering the viscosity of one-dimensional finite metallic bar, the effect of Peierls-Nabarro (PN) force on nonlinear vibration is investigated under strainless boundary conditions and singlehump initial displacement condition. Governing equation is derived as perturbed Sine-Gordon (SG) type equation. With the size and physical properties specified, the spatial modes and long-time asymptotic states evolve as a function of PN force. Different dynamic responses are shown numerically: x-independent simple harmonic motion; harmonic motion with single wave; quasi-periodic motion with single wave and chaotic motion with single spatial mode. It’s found that PN force is also an important factor in affecting the motion of this system.