Nonlinear dynamical model of hyperelastic pipes conveying fluid with finite deformation: roles of hyperelasticity and nonlinearity

In recent years, there has been a growing trend in the application of hyperelastic pipes across several engineering fields, especially in bioengineering and biomedical engineering. For further understanding the dynamic behavior of hyperelastic pipes conveying fluid, this study proposes a mathematical model for the nonlinear forced vibrations of simply supported hyperelastic pipes based on the Yeoh's hyperelastic model. Some numerical methods are employed for verification purposes and to solve the dynamical system. In the discussion part, a series of significantly different results can be drawn about the hyperelastic pipe compared with linearelastic ones. Particularly, compared with the linearelastic pipe system with cubic nonlinearity only, the coupled effect of the nonlinear geometric relations and hyperelastic constitutive relations lead to the simultaneous existence of different order nonlinearities in the hyperelastic pipe model, including quadratic, cubic, quartic or quantic nonlinearities. Softening behaviors of the hyperelastic pipe can be observed, which are mainly caused by the combined influence of nonlinear constitutive relation (used hyperelastic model) and nonlinear geometric relation. Additionally, linear and low-order nonlinear terms in the hyperelastic pipe model play much more important roles in influencing nonlinear dynamic responses than high-order nonlinear ones. Furthermore, it is clarified that fluid-structure interactions (FSIs) between the internal fluid and the hyperelastic pipe have a significant influence on nonlinear dynamic responses by dominating the linear characters instead of the nonlinear ones.