Determination of the spectrum of regions of dynamic instability of three-layer cylindrical shells

Abstract

1. Analysis of the results obtained for the example of boron-plastic and hybrid three-layer shells leads us to conclude that the kinematically uniform model cannot be used to calculate the PRDS of three-layer shells with bearing layers having a stiffness three to four times greater and a density roughly one order greater than the stiffness and density of the filler material. 2. The replacement of the rigid fiber-reinforced material of the middle layer of the shell by a “soft” and light material such as foam plastic leads to a situation whereby the initial sections of the RDI connected with vibrations of the shell as a whole in the x, y, and z directions are shifted toward smaller frequencies θ. Here, the number of regions ηp(l, n)\((p = \overline {1,{\text{ 3}}} )\) forming the RDI is greater, at least on the initial sections, due to the fact that regions corresponding to different modes of parametric vibration are brought closer together. The width of these regions of dynamic instability is decreased by several factors compared to the width of the corresponding ηp of the RDI spectrum of a shell having all of its layers made of a stiff material. 3. Calculated results obtained in the present study but not reported in this article show that the RDI's connected with vibration of the middle layer in the transverse shear planes and in the direction of the z axis change in a manner similar to that described in Part 2 (compressive vibrations). The remaining six RDL's connected with the same vibrations of the bearing layers of the shell are shifted toward larger θ. The width of all of the regions of the nine RDI's indicated here is negligibly small.