Nonlinear liquid motion in a longitudinally excited container with elastic bottom.

Abstract

This paper is concerned with theoretical investigation of liquid motion in a circular cylindrical container subjected to longitudinal excitation of sinusoidal form. The basic equations are derived for an incompressible and nonviscous liquid. The motion of the liquid is considered to be irrotational. The container bottom is treated as a thin elastic plate, while the dynamic and kinematic conditions of the liquid free surface are represented by nonlinear equations. Depending on the excitation parameters, the free surface will exhibit a plane surface or oscillate with a finite amplitude. The finite amplitude can be a one-half subharmonic, harmonic, or superharmonic of the excitation frequency. Both one-half subharmonic and harmonic responses have been treated in more detail. It was found that the influence of the elastic bottom upon the response of the liquid is more significant as the tank diameter increases. Furthermore, as the bottom thickness decreases, the elastic effect is more obvious. The liquid height is also a factor affecting the liquid response. As the liquid height decreases, the influence of the elastic bottom upon the liquid response plays an important role. A comparison of the responses of the liquid in a container with an elastic bottom to that of a container with a rigid bottom has been made. The free surface elevations due to the liquid motions are obtained also.