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

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 increasing, the system-response amplitudes are decreasing.