Dynamic stability and linear vibration analysis of functionally graded axially moving pipes via the finite element approach

This paper presents a finite element-based numerical investigation of the dynamic stability and linear vibration characteristics of an axially moving functionally graded pipe system. Functionally graded materials (FGMs) provide gradual variation in material properties, which can influence the structural response under axial motion. This study addresses the effects of axial speed and material gradation indices on natural frequencies and stability boundaries across five vibration modes. Numerical simulations show that increasing axial speed and gradation index leads to a reduction in natural frequencies with lower vibration modes being more sensitive due to combined geometric and material softening effects. A flutter instability is observed sharply beyond an axial speed of 40 m/s, indicating a dynamic instability threshold dependent on system parameters. Thermal stability analysis reveals that the system maintains robust resistance to temperature variations and changes in gradation indices. Harmonic response analysis identifies a dominant resonance peak near 5 Hz, characteristic of a lightly damped structure. These findings provide valuable guidance for the design and safe operation of advanced axially moving pipe systems in applications such as aerospace, mechanical conveyance and energy transport where stability and vibration control are critical.