Numerical modeling of the stability of parametric vibrations of a high thin-wall shell of negative Gaussian curvature
DOI:
https://doi.org/10.32347/2410-2547.2018.101.45-59Keywords:
dynamic stability, parametric vibrations, finite element method, high thin-wall shell, hyperboloidAbstract
A numerical simulation of the stability of parametric vibrations of a high thin-wall shell in the form of hyperboloid under the action of the external surface pressure and axial compression was performed. The equation of dynamic stability of the shell was presented in the form of a static equilibrium equation with the addition of the D'Alambert forces of inertia, dissipative forces, and some components of the unexcited stress-strain state of the shell were depending on time. The reduced mass, damping, stiffness, and geometric stiffness matrixes of the shell were formed using the procedures of the finite element analysis software program. The problem of nonlinear statics was solved by the modified Newton-Raphson method. The stability of the shell under the action of the static component of parametric load of the two types are solved by the Lanczos method. A modal analysis of the shell without loads in a linear formulation was performed by Lanczos method. The frequencies and modes vibrations of the shell, which was loaded with the static component of the parametric load, were calculated. When were forming the models of the stability of parametric vibrations the features of the static and dynamic behavior of the thin-walled shell of negative Gaussian curvature under different types of load were taken into account. The research of the static and dynamic characteristics of the shell showed that the wall deformation shape have a large number of half-waves both in the radial and axial directions. Such a deformation of the wall in the form of bulges and dents is more dangerous than the deformation of Shukhov hyperboloid wall consisting of the rods.
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