Dynamics of axially moving viscoelastic panels immersed in fluid

The vibration of axially moving panels immersed in fluid are widely concerned in engineering problems. In this paper, free vibration characteristics and dynamic stabilities of an axially moving viscoelastic panel immersed in fluid are investigated. The governing equation is given by applying the generalized extended Hamilton principle. The axial tension per unit width is related to the axial speed and the axial acceleration, changing continuously in the axial direction, which is the innovation point and key problem of this paper. However, they were independent of each other in most previous studies. The fluid is assumed to be an ideal liquid, that is, inviscid, homogeneous and incompressible. By using the velocity potential function, the Bernoulli equation, the dynamic pressure and the boundary conditions of the fluid are derived and incorporated into the governing equation in the form of an additional mass. The Galerkin method is used to discretize the governing equation and convert it into a matrix form. The influences of the truncation order numbers and the immersion depths on the first four natural frequencies are analyzed. We found an interesting phenomenon that the fluid has an effect on both the inertia term and the damping term of the system and the effect of damping force generated by fluid is greater than that of inertia. Another innovation is that the immersion depth has little effect on the natural frequency. Moreover, the subharmonic resonance and the combination resonance are analyzed by using the averaging method. The influences of system parameters including truncation order numbers, axially supported stiffness parameters, viscoelasticity coefficients, mean axial speeds, fluids and immersion depth on the stability boundaries are considered. The stability boundaries of three models, namely the vacuum model, the material derivative model, and the partial derivative model, are compared. The results show that the material derivative model is more reasonable. The results are verified by the Runge-Kutta algorithm. The results of the analytical and numerical methods of the subharmonic and combination resonances are in good agreement with each other. In this paper, the dynamic stability of an axially moving viscoelastic panel immersed in fluid is studied by means of the average method. It extends the application range of the averaging method and provides a reference for the study of axially moving structures immersed in fluid.