In this paper, we set up a nonlinear equation of motion of quasi-one-dimensional lattice vibration; which includes dissipative terms, random distributional force (thermal), and periodic force and strain-force terms. Using small-perturbation method to solve the nonlinear equation, we get the vibrational frequency distribution, which is divided into two kinds of spectrum -discrete and continuous spectrum. The two kinds of spectrum relate to elastic and plastic strain, respectively. Through numerical calculation, the curves of damped oscillation of lattice are depicted and also the profile of shock wavefront produced by external perturbing field are shown. In shock wavefront, there is a high density region of phonon - thermal region, and also strong stress in there. Finally, our theory can well explain the pictures given by Xu Chenfa's experiment and also be useful to explanation of mechanism of some kind of defect and dislocation.
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