Random vibrations of composite beams and plates
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The response characteristics of beams and plates made from composite laminates are strongly affected by the shear deformations of their layers. However, incorporation of the shear deformation further complicates the equations of motion and their analysis. As a result the vibration analysis of such structures have been limited to simple free vibration studies such as determination of their frequencies. The forced vibration problems of these structures have been solved by exact methods for only some very simple cases. In this study, a generalized modal approach is presented to solve more general vibration problems of composite beams and plates. The coupled systems of partial differential equations, representing the equations of motion, are uncoupled into modal equations by utilizing the eigenfunctions of the system and its adjoint. A method is presented to obtain these eigenfunctions for beams with arbitrary boundary conditions and for plates with Levy-type boundary conditions. The forced vibration solutions obtained by this method are then used to calculate the random response characteristics of beams and plates subjected to spatially and temporally correlated random loads.
- Doctoral Dissertations