Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton’s principle, the nonlinear governing equation of an axially functionally graded (AFG) pipe is established. The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam. Via the direct multi-scale method, the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method (DQEM). The influence of Young’s modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions. In general, the pipe in the supercritical region is more sensitive to the pulsating excitation. The nonlinearity changes from hard to soft, and the non-trivial equilibrium configuration introduces more frequency components to the vibration. Besides, the increasing Young’s modulus gradient improves the critical pulsating flow velocity of the parametric resonance, and further enhances the stability of the system. In addition, when the temperature increases along the axial direction, reducing the gradient parameter can enhance the response asymmetry. This work further complements the theoretical analysis of pipes conveying pulsating fluid.