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研究了桩侧土为4元件粘弹性模型（分别采用两个Voigt体串联或两个Maxwell体并联）及其简化条件下（可简化成多种三元件粘弹性模型）桩土系统的振动特性,并求得了桩顶在瞬态半正弦脉冲荷载作用下,桩的时域纵向响应的半解析解,同时结合基桩完整性检测的机械阻抗法和反射波法研究了各主要模型参数对时域及频域响应曲线的影响。试算分析表明,当采用两个Voigt体串联模型时,桩的振动特性主要受参数较小的一个控制,较大的一个则起辅助作用。而当采用双 Maxwell体并联上模型时,在Maxwell体中,串联的弹簧和阻尼器通过相互耦合发挥作用,即弹簧系数的增加可表现为传统Voigt模型下阻尼作用的增强,而阻尼系数的增加则也可表现为传统Voigt模型下土刚度作用的增强,其中一个元件（弹簧或阻尼器）系数增加的极限状态（趋于无穷大）等效于另一个元件单独存在时的作用结果。研究结果表明,本文得到的理论成果相比于已有理论更加完善并能更好地反映客观实际。
The vibration characteristics of the pile-soil system with 4-element viscoelastic models (two Voigt-body cascades or two Maxwell-body cascades respectively connected in parallel) and its simplified condition (which can be simplified into a variety of three-element viscoelastic models) The semi-analytical solutions of the longitudinal response of pile in time domain under transient half-sine pulse loading are obtained. The mechanical impedance method and reflection wave method of pile integrity detection are used to study the influence of the parameters of the main model on the time domain And frequency response curve. Trial analysis shows that when two Voigt body series models are used, the vibration characteristics of the pile are mainly controlled by a smaller parameter, and the larger one plays an auxiliary role. However, when the dual Maxwell model is used in parallel with the model, the spring and the damper in series function through the mutual coupling in the Maxwell body. That is to say, the increase of the spring coefficient can be expressed as the increase of the damping effect under the traditional Voigt model, while the increase of the damping coefficient The increase in soil stiffness under the traditional Voigt model can also be shown. The limit state (toward infinity) in which the coefficient of one element (spring or damper) increases is equivalent to the effect of the other element alone. The results show that the theoretical results obtained in this paper are more perfect than the existing theories and can better reflect the objective reality.