THE VIBRATION AND BUCKLING CHARACTERISTICS OF CYLINDRICAL SHELLS UNDER AXIAL LOAD AND EXTERNAL PRESSURE
AIR FORCE FLIGHT DYNAMICS LAB WRIGHT-PATTERSON AFB OH VEHICLE DYNAMICS DIV
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The Galerkin method is applied to Flugges differential equations for the vibration of a cylindrical shell under axial load and external pressure to obtain a 3N x 3N characteristic equation in matrix form. N is the number of terms in the assumed series of displacement functions for the u, v, and w displacements which can be selected to satisfy various boundary conditions. For the freely-supported cylinder an exact solution exists, and the various assumed modes uncouple, reducing the problem to the solution of a 3 x 3 characteristic equation for each mode. The third order characteristic equation for the freely- supported cylinder was solved for a wide range of shell parameters. The natural vibration frequencies and buckling values for axial load and external pressure for all three eigenvalues associated with each mode, are presented in a series of figures. The square of the vibration frequency for any mode was found to vary linearly with axial load, and approximately linearly with a pressure loading for modes with two or more circumferential waves.