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该文采用解析方法在频率域内对黏弹土层和衬砌结构简谐振动特性进行了研究。首先,将土骨架视为具有分数阶导数本构关系的黏弹性体,根据黏弹性理论,推导得到了简谐荷载作用下分数导数型黏弹性土层的位移和应力等解析表达式。其次,建立了两种类型的衬砌运动方程:第一,将衬砌结构视为均匀弹性介质,研究了分数导数黏弹性土中弹性衬砌结构的动力特性;第二,将衬砌等效为薄壁壳体结构,利用Flügge薄壳理论,得到了衬砌结构的运动方程,并对分数导数黏弹性土和壳体衬砌的动力相互作用进行了分析。根据连续性边界条件,得到了相关待定系数的表达式。再次,与以往的解析解进行了对比。最后,通过算例分析了土体和衬砌各参数对系统动力特性的影响,结果表明:薄壁壳体衬砌结构条件下系统的动力响应大于均匀弹性衬砌结构条件下系统的动力响应;随着土体和衬砌模量比的增加,响应幅值逐渐减小。分数导数本构参数对系统的动力特性有较大影响。
In this paper, the analytical method is used to study the harmonic vibration characteristics of viscoelastic soil and lining structures in the frequency domain. First, the soil skeleton is regarded as a viscoelastic body with fractional derivative constitutive relation. According to the viscoelastic theory, the analytical expression of the displacement and stress of fractional derivative viscoelastic soil under simple harmonic loading is derived. Secondly, two types of lining motion equations are established. First, considering the lining structure as a uniform elastic medium, the dynamic behavior of the elastic lining structure in fractional-derivative viscoelastic soil is studied. Secondly, the lining is equivalent to the thin- The body structure of the lining structure is obtained by using the Flügge shell theory. The dynamic interaction between the fractional derivative viscoelastic soil and the shell lining is analyzed. According to the continuity boundary conditions, the expression of the related undetermined coefficients is obtained. Again, compared with the previous analytical solution. Finally, the influence of parameters of soil and lining on the dynamic characteristics of the system is analyzed by means of a numerical example. The results show that the dynamic response of the system under thin-wall shell lining is greater than that of the system under uniform elastic lining. Body and lining modulus ratio increases, the response amplitude decreases. Fractional derivative constitutive parameters have great influence on the dynamic characteristics of the system.