Vibrations of a Layered Conical Shell Under Nonstationary Load*.

A method for determining the nature of vibrations and stress–strain state of ribbed orthotropic conical shells with asymmetric layers interacting with masses under dynamic loads is developed using the theory of shells and the Tymoshenko hypotheses. The equations of vibrations of a shell formulated for the displacements of points of the midsurface are obtained using the Hamilton principle. To solve the system of equations of motion of the shell, trigonometric series in spatial coordinates and an explicit finite-difference scheme with respect to time are used. The accuracy of calculations by the finite-difference method depending on the number of time steps is estimated for a layered cylindrical shell as an example. The stress–strain state of a conical orthotropic shell with symmetric and asymmetric layers, longitudinal ribs, and masses under a short-term axisymmetric external load distributed over a portion of the shell and moving from the minor base to the major base is analyzed. [ABSTRACT FROM AUTHOR]