Static bifurcation and nonlinear vibration of pipes conveying fluid in thermal environment

In practical engineering, changes of environment temperature can significantly alter natural characteristics of a pipe system. In current work, the exact non-trivial equilibrium configuration of the pipe conveying fluid in a thermal environment is investigated for the first time, including the effect of temperature on natural frequencies and bending vibrations. Firstly, the partial-differential-integral governing equation for bending vibrating pipes subjected to changing temperature is established based on the Euler-Bernoulli beam theory, by means of the generalized Hamilton's principle. Exact solutions for non-trivial equilibrium configurations and critical flow velocities are obtained analytically. Stability of these configurations is discussed and reveals that just the first one is stable. The nonlinear resonance properties of the pipe conveying fluid in a thermal environment are analyzed by the harmonic balance method (HBM) on the basis of Galerkin truncation. The analytical results are verified by the differential quadrature element method (DQEM). It is found that an increasing temperature leads to a larger non-trivial equilibrium configuration and a lower critical flow velocity, with a consequent decrease in the stability of the system. High temperature and high flow velocity reduce the resonant frequency in the subcritical region. In the supercritical region, they increase the resonant frequency. Unlike pipes in the subcritical region, the response in the supercritical region has more resonant peaks and exhibits soft characteristics due to the quadratic nonlinearity. Besides, the asymmetry of the response caused by the zero drift is more pronounced at low temperatures or flow velocities. This study provides theoretical guidance for the vibration design of pipes conveying fluids in a thermal environment.