Об устойчивости колебаний упругого основания жесткого прямоугольного канала c идеальной жидкостью

Abstract

In a linear formulation, the joint natural vibrations of the elastic bottom of a rigid rectangular channel and an ideal incompressible fluid are investigated. The rectangular channel has an elastic bottom in the form of a clamped rectangular plate. It is shown that the frequency equation splits into two equations describing even and odd frequencies and can be written in a single form for these frequencies. An approximate formula for high frequencies is obtained from which it follows that the dependence of the square of the frequency on the bending stiffness and restressing is linear in nature and the highest frequency value is achieved for the inertia-free plate. The approximate stability conditions for joint vibrations of the elastic bottom and liquid are derived. These conditions are independent of the depth of the liquid and the mass of the plate. In the absence of plate pretension, the exact conditions for the stability of the vibrations of the elastic base and fluid are obtained. It is shown that the approximate value of the critical dimensionless bending stiffness for asymmetric frequencies is underestimated by 0.952 times, and for symmetric ones, by 0.930 times