Effect of the stiffness of ribs on the vibrations and stability of open cylindrical shells

Abstract

The effect of the stiffness of ribs on the minimum natural frequencies and critical stresses of axially compressed open cylindrical shells reinforced with a quasiregular set of longitudinal ribs is analyzed by way of numerical examples. It is shown that the earlier discovered phenomenon of abrupt decrease in the minimum frequencies is independent of rib stiffness for certain modes and a small number of ribs Keywords: open cylindrical shell, minimum natural frequencies, critical stress, quasiregular arrangement of ribs Introduction. As in [3, 4], we will consider hinged open cylindrical shells reinforced with quasiregular sets of longitudinal ribs. A set of ribs is quasiregular if all the geometrical and mechanical characteristics of all ribs are equal, the ribs are equally spaced, and the distance from the edges of the shell to the closest ribs is equal to half the distance between ribs. The exact solution of the equations of motion of such shells was found in [3]. This solution was used in [4] to examine the influence of the number and arrangement of ribs on the natural frequencies and critical stresses in such shells under axial compression.The stiffness of ribs was kept constant in [4]. Here, we will vary it to analyze in more detail the effect of ribs on the stress-strain state of the shell. The equations to be used to determine the minimum natural frequencies and critical stresses are borrowed from [3,4].We will show that the phenomenon (first discovered in [4]) of significant decrease in the minimum natural frequencies for certain vibration modes and number of ribs is independent of their stiffness.Similar problems of statics, dynamics, and static stability of shells were solved in [5][6][7][8].

Numerical analysis of edge effects in laminated composites under uniaxial compression

“…Note that the numerical analysis of edge effects in structural members made of composites involves mathematical and mechanical models and criteria for the evaluation of edge-effect zones [2,9]. The problems addressed here are inadequately elucidated in the literature [5][6][7] because it is difficult to solve them. The present paper gives a problem statement, governing equations, and a method for the numerical analysis of edge effects in two-component laminated composite under uniaxial compression.…”