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A Numerical (Matrix) Solution For The Vibration Frequencies And Modes Of A Nonuniform Rectangular Plate With Arbitrary Edge Conditions, F. David Utterback
"The material presented in this thesis is designed to provide the practicing engineer with a practical, approximate method of solution for the increasingly important problem of plate vibrations. The technique presented herein is basically an application of the use of generalized coordinates to describe the elastic and inertial properties of a finite element representation of a nonuniform rectangular plate. The plate will be idealized by utilizing a modification of the grid work technique developed by Hrennifkoff as a lattice work of interconnecting beams. By employing the elastic displacements as generalized coordinates, the only required compatibility conditions are that the displacements ...