Parameter resonance analysis of pipes conveying fluid with shape memory alloy constitutive relation

The parametric resonance of moving elastic pipelines was investigated. Boundary conditions were assumed, and the elastic properties of the pipelines were described using the constitutive relationship of shape memory alloys. Based on Newton's second law, the transverse vibration equation for shape memory alloy axial motion pipelines were derived. when assuming that the viscosity coefficient has a minimal impact on the unperturbed system, the characteristic functions and natural frequencies were studied, followed by numerical validation.