Waves in a liquid between two coaxial cylindrical shells induced by vibrations of the inner cylinder
The authors examine the problem of waves between two coaxial surfaces with the deformating inner surface. The equations for the velocity potential \(\varphi\) of the liquid and for the function of the displacement of free surface \(\zeta\), both being the parameters governing the flow of the liquid, are presented. The \(\varphi\) and \(\zeta\) are expanded in natural modes. For parametric resonance, the approximation for \(\zeta\) and the trigonometric-polynomial form of parameters included in \(\zeta\) are proposed. The decomposition parameters for \(\varphi\) as well as the system of first-order linear equations for coefficients in the trigonometric polynomials in parameters included in \(\zeta\) are obtained. Such equations are typical for dynamic systems with parametric resonances. These systems are usually smooth and locally unstable. The numerical calculations for the natural frequencies show that two types of resonances are realized at frequencies deviating only by about 2\% from the experimental values.
scientific article; zbMATH DE number 553525
scientific article