Nonlinear vibration of axially moving plates partially in contact with liquid via Chebyshev collocation method

Abstract

This paper analyzes nonlinear free vibration of plates that move axially and in partial contact with liquid. The von Kármán nonlinear plate theory is employed in the theoretical model. The fluid is characterized as an ideal fluid and represented using the velocity potential and Bernoulli's equation. The fluid pressure exerted on the plate is equivalent to a virtual additional mass, which is considered as part of the total mass of the structure. Employing the Hamilton's principle to derive the immersed moving plates’ governing equations. Afterward, the nonlinear frequencies of plates moving axially and contacting with liquid are evaluated by the Chebyshev collocation method combined with the direct iterative technique. The results indicate that the Chebyshev collocation method exhibits excellent convergence and exceptional accuracy. It has been observed that the immersed moving plates’ nonlinear frequencies gradually increase with the decrease of the axial velocity. The increase of immersion level or fluid density reduces nonlinear frequencies, but has little influence on nonlinear to linear frequency ratios.