Thermoelastic Vibration Analysis Of Functionally Graded Fluid-conveying Pipes At Different Scales

As the carrier of fluid transport and storage,functionally graded fluid-conveying pipe is widely used in engineering field.The vibration governing equation of functionally graded fluid-conveying pipes in different scales is established based on the theory of Euler-beam model.The vibration governing equation is solved by galerkin method,differential quadrature method and dynamic stiffness method,and the vibration problem of the functionally graded fluid-conveying pipes in different scales is studied.The research contents and main conclusions of this paper can be summarized as the following five aspects:1.The thermoelastic vibration of the macroscopic FGM fluid-conveying pipe in the elastic matrix is analyzed in this paper.The influences of the volume fraction,length-diameter ratio,elastic coefficient of the elastic matrix and external radius on the natural frequency and critical velocity of the pipe are studied.From results we can see that the natural frequency of the pipe increases and the critical velocity of the pipe decreases with the increases of the volume fraction of the metal material.With the temperature increases,the natural frequency of the system and its corresponding critical velocity decrease,and the stability of the pipe decreases.With the length-diameter ratio decreases,the natural frequency of the pipe decreases significantly.The natural frequency of the system decreases with the increases of the external radius and decreases more slowly with the increases of the radius.The natural frequency of the pipe increases with the increase of the elasticity coefficient.2.The vibration of multi-span aluminum-based functionally graded material fluid-conveying pipe reinforced by carbon nanotubes(CNTs)is studied.Taking a two-span pipe as an example,the influence of the volume fraction of CNTs on the natural frequency,critical velocity,critical pressure and stable state of the pipe of a two-span pipe is analyzed.The influence of different span combinations on the natural frequency,critical velocity and stability is analyzed,and the effect of the radius of the pipe on its natural frequency is also analyzed.The results show that the stability state of the pipe changes from stability to static instability and finally to dynamic instability with the increase of flow velocity.With the increase of the volume fraction index,the first three order natural frequency,critical velocity and critical pressure of the system will increase,and the greater the volume fraction index is,the smaller the rate of change will be.The increase of the pressure inside the pipe will lead to the decrease of the natural frequency of the pipe,and the continuous increase of the pressure inside the pipe will eventually lead to the static instability of the pipe.The smaller the ratio between the length of the first and the length of the second span of the pip,the greater corresponding natural frequency when the flow rate is zero,and the greater corresponding damping value when the flow velocity is the same.If the thickness of the pipe is unchanged,the natural frequency will increase with the increase of the radius of the pipe.3.The thermoelastic vibration problems of microscale functionally graded pipe embedded in elastic matrix are studied,and the microscale effect of microscale functionally graded pipe and the influence of microfluid effect on its natural frequency and critical velocity are analyzed in detail.The influence of volume fraction on its natural frequency and critical velocity are analyzed.The influence of the elastic coefficient on the natural frequency of the elastic matrix is studied,and the influence of external radius on natural frequency of pipeline is also analyzed.The results show that with the increase of temperature,the natural frequency of the pipe and its corresponding critical velocity decrease,and the stability of the pipe decreases.The scale effect of the microscale functionally gradient material pipeline will obviously improve the critical velocity of the system.The microfluid effect will reduce the critical flow velocity of the system.The stability of the system is higher than that of the system calculated by the macroscopic model when considering the size effect of micropipe and microfluid.With the increase of the volume fraction index,the natural frequency of the system decreases,and the decreasing speed becomes slower and slower.The natural frequency of the system decreases with the increase of the radius of the pipe,and the decreasing speed becomes slower with the increase of the radius.4.The vibration and stability of the cantilever functionally graded nanotube under thermo-magnetic coupling effect are studied,and the influence of magnetic field and temperature on the vibration and stability of the pipe is analyzed.The effects of nonlocal parameters,mass ratio,Knudsen number,elasticity coefficient of elastic matrix,and volume fraction on critical velocity of instability are also analyzed.The results show that the longitudinal magnetic field will increase the overdamped interval of the real part of the first-order eigenvalue of the system,increase the appear flow rate of the second-order and third-order overdamped interval,increase the critical flow rate of the system,and reduce the frequency corresponding to the instable flow rate,but have no effect on the length of the second-order overdamped interval.The increasing temperature will increase the critical velocity of the system and make the system more stable.The increase of the elastic coefficient of the elastic matrix will lead to the increase of the critical instable velocity of the system,and with the increase of non-local parameters,the critical instable velocity of the system will decrease.The increase of Knudsen number will lead to the decrease of critical velocity of instability of the system.The increase of the volume fraction index will reduce the critical velocity of instability.5.The vibration and stability of a two-segment constructed nanotube embedded in elastic matrix are studied.The influence of length ratio,elastic model ratio,mass ratio and elastic coefficient of elastic matrix on the vibration and stability of the two sections are analyzed in detail.The analysis results show that changing the elastic coefficient,the length ratio and elastic modulus ratio will not change the instability mode of the tube.Changing the mass ratio will change the instability mode of the combined pipeline.The elastic coefficient mainly affects the natural frequency and critical velocity of the combined tube in the first mode.The length ratio mainly affects the natural frequency and the flow velocity in the second mode.The influence of the elastic modulus ratio on the natural frequency and the dynamic instable velocity in the second order mode is greater than that on the critical velocity and natural frequency in the first order mode.The mass ratio mainly affects the natural frequency of the combined nanotube,but has little effect on its critical velocity.