Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method

Based on the homotopy analysis method, this paper studies the nonlinear vibration of FGM pipeline with pores under generalized boundary conditions. Based on the power-law distribution of FGM, the physical properties of the material are distributed along the radial direction of the pipe. For the mathematical model of the pores of the pipe, we choose Voigt model to describe the material properties of FGM pipes with pores. Based on Euler Bernoulli beam theory and the influence of von-Kármán nonlinearity, using Hamilton variational principle, the dynamic control equations and generalized boundary conditions of functionally graded fluid transmission pipelines with pores are established. The homotopy analysis method is used to solve the nonlinear vibration characteristics of functionally graded flow pipelines under generalized boundary conditions. The numerical results show that the translation spring has little effect on the critical velocity of instability, while the rotation spring can increase the critical velocity of instability, making the system more stable;In the nonlinear system, the viscoelastic coefficient does not change the critical velocity; pipe length, power-law exponent and porosity all affect the nonlinear free vibration of FGM porous flow pipeline.