Affiliations: Institute of Applied Mechanics, College of Science,
Northeastern University, Shenyang, Liaoning, China
Note: [] Corresponding author: J. Li, Institute of Applied Mechanics,
College of Science, Northeastern University, Shenyang 110819, Liaoning, China.
Tel.: +86 024 8368 1645; E-mail: jianli@mail.neu.edu.cn
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.
