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 APPENDIX D TABLE axisymmetric BETAMAX Bk+1 computer storage conical shell cylinder cylindrical shell data are obtained DATA FROM FIGURE defined in equation direct integration approach direct integration scheme DISP S/L displacement components Effects of rotary eigenvalues eigenvector equation C18 equation C27 Equation C31 finite-element frequencies Gaussian elimination increments inertia and transverse initial conditions integration and modal kinetic energy kth element Langley Research Center matrix defined meridional coordinate MERIDIONAL DISTANCE middle surface modal data modal stress modal superposition approach MODAL SUPERPOSITION METHODS modal superposition technique mode shapes MX/MXMAX MXMAX normal displacement W/r nth harmonic appendix NX/NXMGX NXMAX once the modal previous time history quadratic form reference RESPONSE OF SHELLS S/L Figure S/L W DISP SEC EFF set of initial shell having L/r shell meridian shells of revolution strain energy stress resultant thin-shell structures transient response transverse shear deformation trapezoidal rule UMAX WMAX WMGX