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.