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Abstract <p>The free vibrations of a conical shell with elastic elements and longitudinally reinforced ribs located in an elastic medium are investigated. The discrete arrangement of the reinforcing ribs is taken into account. The natural frequencies of the shell vibrations are determined by the energy method. In the solution process, an infinite homogeneous algebraic system of equations is obtained. The determinant of the system is set equal to zero and an equation is obtained that allows determining the natural frequencies of the oscillations of the shell with an additional mass. At certain values of the parameters, calculations are made and graphs are constructed. Analysis of the calculation results shows that the minimum natural frequency of the system increases with increasing mass.</p> <p>As a result, analysis of the curves shows that the effect of the added mass on the minimum natural frequency of the shell oscillations is quite significant. This effect increases with a decrease in the stiffness of the connections between the mass and the shell.</p>

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Study of Free Oscillations of a Ribbed Conical Shell Containing an Elastically Suspended Mass in an Elastic Medium

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • G. A. Mammadova,
  • M. A. Rustamova,
  • S. A. Piriev

摘要

Abstract

The free vibrations of a conical shell with elastic elements and longitudinally reinforced ribs located in an elastic medium are investigated. The discrete arrangement of the reinforcing ribs is taken into account. The natural frequencies of the shell vibrations are determined by the energy method. In the solution process, an infinite homogeneous algebraic system of equations is obtained. The determinant of the system is set equal to zero and an equation is obtained that allows determining the natural frequencies of the oscillations of the shell with an additional mass. At certain values of the parameters, calculations are made and graphs are constructed. Analysis of the calculation results shows that the minimum natural frequency of the system increases with increasing mass.

As a result, analysis of the curves shows that the effect of the added mass on the minimum natural frequency of the shell oscillations is quite significant. This effect increases with a decrease in the stiffness of the connections between the mass and the shell.