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Vibrations of axially traveling plates partially coupled with a viscous, orthogonally flowing liquid

A semi‐analytical method is presented to study the free vibration of an axially traveling plate partially submersed in viscous and orthogonally flowing liquid. The method is based on the classical thin plate theory and the finite element theory. The Navier‐Stokes equation, Bernoulli's equation and the velocity potential function are used to express the liquid. The formulation of the dynamical liquid‐induced force is derived by kinematic boundary conditions of the plate‐liquid interfaces. The governing equations of the partially immersed traveling plate are obtained via the Hamilton's principle. Numerical calculations show that as the plate thickness increases, the liquid viscosity effect on natural frequencies of the plate becomes weaker and weaker. Besides, the magnitude of the liquid viscosity effect is found to be positively related to the distance between the plate and rigid wall, and the width of liquid domain. The plate is easier to reach the critical speed when the orthogonal liquid velocity is larger. Moreover, liquid viscosity plays important role on the vibrational behavior of the immersed traveling plate when the liquid velocity is relatively large. Several verifications have been conducted to test the effectiveness and accuracy of the developed method.