An approximate method of calculating the oscillations of a liquid in inclined elastic cavities and channels

Abstract

Small oscillations of an ideal incompressible liquid, which partially fills an inclined elastic container (a mobile cavity or channel) of arbitrary form and having a longitudinal plane of symmetry, are considered. The integral condition of continuity of the liquid is obtained by integrating the differential condition of incompressibility and exact satisfaction of the kinematic boundary conditions on the wetted side walls. Using this equation, systems of coordinate functions are constructed which represent the kinematically possible displacements of the liquid, for calculating the oscillations by the Ritz method and the finite-element method. The basic unknown functions, which describe the displacements of the liquid in cross-sections, are approximated by power functions and Legendre functions. Transverse layers of liquid, within the limits of the thickness of which a linear approximation for the unknown functions can be used, are considered as finite elements.