球形沼气池模具结构振动响应的黏弹性解

VISCOELASTIC ANALYTICAL SOLUTION FOR DYNAMIC RESPONSE OF DIE STRUCTURE OF A SPHERICAL BIOGAS DIGESTER

考虑土和模具结构的动力相互作用,在频率域内研究了深埋球形沼气池模具结构的动力特性。根据黏弹性理论,通过引入势函数得到了黏弹性土体的位移、应力等的解析解。将模具结构等效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了模具结构振动响应的完全解析解。根据界面连续性条件,确定了待定系数的具体表达式。将不同类型的黏弹性模具结构动力响应进行了对比,并考察了分数导数本构参数、土体和模具结构各参数对系统动力特性的影响。结果表明:模具结构的黏性对系统动力响应有显著影响。随着壁厚的增加,模具结构振动响应幅值减小;随着阶数的增加,系统共振效应逐渐减弱;随着材料参数比Tσ/Tε的增加,系统响应幅值减小。

Considering the dynamic interaction between a die structure and its soil, the dynamic characteristics of a die structure with a deeply embedded spherical biogas digester is presented in the frequency domain. Based on the viscoelastic theory, the analytical solutions for the displacement and stress of the soil are derived by the potential functions. The die structure is treated as a viscoelastic medium with a fractional derivative constitutive relation. Based on the viscoelastic theory, the analytical solution for the dynamic response of the die structure is obtained. The specific expressions of undetermined coefficients are determined based on continuity conditions. The dynamic responses of different types of viscoelastic die structures are compared, and the influences of the parameters for fractional derivative constitutive parameters, the soil and the die structure on the system dynamic characteristics are analyzed. The results show that the viscous of a die structure has a significant influence on the dynamic response of the system. The response amplitudes of a die structure decrease gradually as the thickness of the die structure increases. With the order increasing, the system-resonance effect is weakening. With the material parameter ratio Tσ/Tε increasing, the system-response amplitudes are decreasing.