Open AccessBiharmonic Modulated Axially Symmetric Shapes of Cylindrical Shells and the Critical Lines and Points on the Loading Path on the Linear Theory
Author(s) -
E. Z. Korol
Publication year - 2010
Publication title -
izvestiâ mgtu "mami"
Language(s) - English
Resource type - Journals
eISSN - 2949-1428
pISSN - 2074-0530
DOI - 10.17816/2074-0530-69703
Subject(s) - biharmonic equation , orthogonality , axial symmetry , rotational symmetry , mathematical analysis , line (geometry) , physics , trajectory , shell (structure) , mathematics , geometry , classical mechanics , boundary value problem , quantum mechanics , materials science , composite material
The article examanies a generalized formulation of the conditions and an analysis of the critical state of shells under the action of external parameter evolving axisymmetric longitudinal loads. Generalized formulation includes a task in the space of coefficients of differential equation of the trajectory of loading and critical states. Critical states of the shell associated with the loading trajectory reach of the characteristic lines and points. The characteristic lines and points include the line dividing the modulation, level lines of squares of natural frequencies (wavelength) and the points of orthogonality or isogonality (isocline).