The paper investigates the process of pulsation of a spherical cavity (bubble) in a liquid under the influence of a source of ultrasonic vibrations. The pulsation of a spherical cavity is described by the Kirkwood-Bethe equations, which are one of the most accurate mathematical models of pulsation processes at an arbitrary velocity of the cavity boundary. The Kirkwood-Bethe equations are essentially non-linear, therefore, to construct solutions and parametric analysis of the bubble collapse process under the influence of ultrasound, a numerical algorithm based on the Runge-Kutta method in the Felberg modification of the 4-5th order with adaptive selection of the integration step in time has been developed and implemented. The proposed algorithm makes it possible to fully describe the process of cavitation pulsations, to carry out comprehensive parametric studies and to evaluate the influence of various process parameters on the intensity of cavitation. As an example, the results of calculating the process of pulsation of the cavitation pocket in water are given and the influence of the amplitude of ultrasonic vibrations and the initial radius on the process of cavitation of a single bubble is estimated.
During the operation of a solid-propellant rocket engine, the combustion products of a powder charge create an increased pressure in the combustion chamber. In addition, the combustion of gunpowder is accompanied by a large release of heat, which, despite the thermal insulation, causes the appearance of deformations in the engine cowling. This leads to the need to investigate the durability of the shell under the influence of internal pressure and temperature fields. The aim of the paper is to determine the complex dynamic deformed state and vibrations of the engine cowling under the action of force and temperature loads. The problem of a complex axisymmetric stress-strain state and vibrations of a thin cylindrical shell with a dynamically breaking internal elastic foundation, obeying Winkler’s hypothesis, is approximately solved. The shell is under the action of internal pressure and temperature fields on a part of its length free from an elastic base. The resolving equation of the problem of the shell deflection is solved by the Bubnov-Galerkin method, reducing the problem to a system of linear algebraic equations. The examples are considered, in which the basic frequencies of natural vibrations of the structure are determined depending on the conditions of shell fastening. Parametric studies are carried out.
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