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<p>Problems of the dynamics of solid bodies with internal degrees of freedom are always of significant theoretical and practical interest for the researchers. The complexity of investigation of these objects is explained, in the first turn, by the necessity of analysis of the behavior of systems in combined statement. Serious problems are encountered in the case where the internal degrees of freedom are determined by the components with continual structure. Moreover, for the description of the behavior of the analyzed system, it is necessary to use a mathematical model with inhomogeneous mathematical structure (a system of ordinary differential equations for the motion of the solid body and a partial differential equation for the description of the continual component), which is quite complicated. Additional complexities appear in the case of motion of solid bodies containing liquids because the motion of solid body is described in the Lagrange variables, whereas the motion of liquid is described in the Euler variables. Moreover, the problem of determination of the forces of interaction between the components is also quite complicated. We study the problem of motion of a carrier body containing liquid with a free surface, which is one of the most important theoretical and practical problems. Our main attention is focused on the cases of motion of a “cylindrical vessel– liquid with free surface” mechanical system in the nonlinear range of perturbations of the free surface of liquid for significant manifestations of the combined character of motion and for the angular motions of the carrier body. Based on the performed research, we reveal specific features of the development of resonance processes in the system. For the vibrations of the system on a pendulum suspension, it is shown that the decrease in the length of suspension leads to changes in the order of location of the normal modes of vibrations placed in the order of increase in eigenfrequencies. For all types of resonances, we reveal the absence of transition of the system into the steady-state mode of motion (in the classical sense) confirmed by the experimental data.</p>

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Dynamics of a Solid Body with Internal Degrees of Freedom Caused by a Liquid with a Free Surface

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • Oleg Limarchenko

摘要

Problems of the dynamics of solid bodies with internal degrees of freedom are always of significant theoretical and practical interest for the researchers. The complexity of investigation of these objects is explained, in the first turn, by the necessity of analysis of the behavior of systems in combined statement. Serious problems are encountered in the case where the internal degrees of freedom are determined by the components with continual structure. Moreover, for the description of the behavior of the analyzed system, it is necessary to use a mathematical model with inhomogeneous mathematical structure (a system of ordinary differential equations for the motion of the solid body and a partial differential equation for the description of the continual component), which is quite complicated. Additional complexities appear in the case of motion of solid bodies containing liquids because the motion of solid body is described in the Lagrange variables, whereas the motion of liquid is described in the Euler variables. Moreover, the problem of determination of the forces of interaction between the components is also quite complicated. We study the problem of motion of a carrier body containing liquid with a free surface, which is one of the most important theoretical and practical problems. Our main attention is focused on the cases of motion of a “cylindrical vessel– liquid with free surface” mechanical system in the nonlinear range of perturbations of the free surface of liquid for significant manifestations of the combined character of motion and for the angular motions of the carrier body. Based on the performed research, we reveal specific features of the development of resonance processes in the system. For the vibrations of the system on a pendulum suspension, it is shown that the decrease in the length of suspension leads to changes in the order of location of the normal modes of vibrations placed in the order of increase in eigenfrequencies. For all types of resonances, we reveal the absence of transition of the system into the steady-state mode of motion (in the classical sense) confirmed by the experimental data.