Browsing by Author "Bennett, J. G."

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    A study of a dynamical finite element analysis for application to axial wave propagation problems in semi-infinite and finite membranes and shells of revolution
    Bennett, J. G. (Virginia Polytechnic Institute and State University, 1970)
    The method known in the literature as dynamical finite element analysis is investigated and applied to wave propagation problems occurring in membranes and thin shells of revolution. Both semi-infinite and finite versions of cylindrical and conical membrane shells are studied and a finite membrane shell having a meridional curve which is parabolic is solved. A thin cylindrical shell is also considered in order to determine the effect of including shear and rotary inertia. The source excitation is generally considered to be the constant velocity motion of one end, but the results for a stress pulse input to one end of a semi-infinite cylindrical membrane shell are also given. The thin cylindrical shell is considered as an initial value problem. The difference in the solutions resulting from prescribing an axial or tangential velocity excitation at the end of a semi-infinite conical membrane shell is presented. The method itself requires a careful ordering of the calculations and the principles for determining the correct order are discussed. The rules for handling the boundary conditions for finite shells are shown to follow logically from this ordering of the calculations. An energy balance check on the computations is shown to be an effective independent check on the correctness and stability of the solution, and a discussion of the conditions used to verify that the numerical results are the solutions is included. The results for the finite problems are new results and the semi-infinite problems are discussed with respect to previously published results.