Dynamic Stability of a Cylindrical Shell Made of a Material of Different Modulus Plased on a Viscous-elastic Foundation

The problem of stability of a cylindrical shell with various modules on a viscoelastic base is investigated. It is assumed that the shell of a circular cross section is subjected to force and loses stability in an axisymmetric form. It is believed that one end of the shell remains motionless, while the other changes its location (moves) at a certain speed. It is assumed that the transverse displacement is greater than the longitudinal one. When solving the problem, the resistance of the external environment was taken into account, and it was also read that the cylindrical shell was made of a material of different modularity. Relationship equations are obtained between the critical force and the characteristic parameters for a cylindrical shell located on a base, characterized, in turn, as a viscoelastic base and the Pasternak model. From the equations obtained and the results presented, it can be seen that serious errors are allowed if, when solving stability issues, the resistance of the external environment and different modularity are not taken into account. The calculation results show that the value of the critical force in the case under consideration differs significantly from the values corresponding to classical problems, and depends on the parameters characterizing the base resistance. The results obtained can be used in calculations of multi-modulus cylindrical shells for strength, stability, and frequency-amplitude characteristics, taking into account the resistance of the external environment.