Abstract
The theory of singuarity functions is introduced to present an analytical approach for the natural properties of a unidirectional vibrating steel strip with two opposite edges simply supported and other two free, partially submerged in fluid and under tension. The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the steel strip. The effect of fluid on vibrations of the strip may be equivalent to added mass of the strip. The math formula of added mass can be obtained from kinematic boundary conditions of the strip-fluid interfaces. Singularity functions are adopted to solve problems of the strip with discontinuous characteristics. By applying Laplace transforms, analytical solutions for inherent properties of the vibrating steel strip in contact with fluid are finally acquired. An example is given to illustrate that the proposed method matches the numerical solution using the finite element method (FEM) very closely. The results show that fluid has strong effect on natural frequencies and mode shapes of vibrating steel strips partially dipped into a liquid. The influences such as tension, the submergence depth, the position of strip in the container and the dimension of the container on the dynamic behavior of the strip are also investigated. Moreover, the presented method can also be used to study vertical or angled plates with discontinuous characteristics as well as different types of pressure fields around.
Highlights
Problems of interaction between thin plates and fluid have received extensive attention in recent decades
The main objective of the investigation described in this paper is to put forward a new analytical method for the inherent properties of a tensioned, unidirectional vibrating plate partially submerged in liquid
The results show that the calculations based on the proposed approach are in very good agreement with the data of finite element method (FEM)
Summary
Problems of interaction between thin plates and fluid have received extensive attention in recent decades. The objective of this article is to provide a new analytical method to investigate flexural vibration of a rectangular plate partially immersed in fluid. The motivation of this work is to find an analytical approach for real time computation of a vibrating steel strip partially immersed in liquid zinc during the continuous hot-dip galvanizing process (Fig. 1). The field test results in a continuous hot-dip galvanizing line had revealed that the wind load induce flexural vibrations in the axial direction of the strip. These two parts have the same rigidity but a different mass surface density In this way, the partially submerged plate may be treated as a non-immersed plate with discontinuous characteristics. Singularity functions are good tools to solve the problem on discontinuous characteristics. They are generally considered a family of functions as follows [21]
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