Natural vibrations of reinforced viscoelastic cylindrical shells with a viscoelastic filler. Part 1

Reinforced viscoelastic cylindrical shells with deformable fillers are used in rocketry, aircraft construction, shipbuilding, and construction. To give greater rigidity, the thin-walled part of the shell is reinforced with ribs, while a slight increase in the weight of the structure significantly increases its strength, even if the ribs are of low height. The purpose of this work is to develop a technique, algorithm and programs for finding resonant frequencies and modes of vibration for circular ribbed viscoelastic cylindrical shells under various boundary conditions. The paper deals with vibrations of longitudinally reinforced cylindrical shell structures with a filler. The variational principle is used to study the vibrations of a thin longitudinally reinforced viscoelastic cylindrical shell under dynamic influences. Oscillatory processes of the filler and the bonded shell satisfy the Lamé equations. At the contact between the shell and the filler, the conditions of rigid contact are fulfilled. The relationship between stresses and strains, for a linear viscoelastic material, is represented in the form of the Boltzmann-Voltaire integral. To solve this problem, the following are used: the method of separated variables, methods of the theory of potential functions (special functions) and the Gauss method. The dependence of the change in the dynamism coefficient on the relative weights of the ribs is plotted for different weights of the transverse rib.