## Transient response of shells of revolution by direct integration and modal superposition methodsThe results of an analytical effort to obtain and evaluate transient response data for a cylindrical and a conical shell by use of two different approaches: direct integration and modal superposition are described. The inclusion of nonlinear terms is more important than the inclusion of secondary linear effects (transverse shear deformation and rotary inertia) although there are thin-shell structures where these secondary effects are important. The advantages of the direct integration approach are that geometric nonlinear and secondary effects are easy to include and high-frequency response may be calculated. In comparison to the modal superposition technique the computer storage requirements are smaller. The advantages of the modal superposition approach are that the solution is independent of the previous time history and that once the modal data are obtained, the response for repeated cases may be efficiently computed. Also, any admissible set of initial conditions can be applied. |

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admissible set axisymmetric calculated circumferential computer storage conical shell cylinder cylindrical shell data are obtained DATA FROM FIGURE defined in equation diagonal matrix direct integration approach direct integration scheme DISP S/L Effects of rotary eigenvalues eigenvector element stiffness matrix equation C18 equation C27 freely supported frequencies Gaussian elimination Geometry high-frequency response increments inertia and transverse initial conditions initial velocity integration and modal kinetic energy kth element Langley Research Center LINEAR SEC EFF matrix defined ment meridional coordinate meridional moment resultant middle surface modal data modal stress modal superposition approach MODAL SUPERPOSITION METHODS modal superposition technique mode shapes nth harmonic appendix number of elements once the modal OOOZ previous time history quadratic form reference RESPONSE OF SHELLS S/L Figure S/L W DISP set of initial shear stress shell having L/r shell meridian shells of revolution stiffness and mass strain energy thin-shell structures transient response transverse shear deformation trapezoidal rule