Date of Award
MS in Aerospace Engineering
The purpose of this study is to develop an analytical solution for modal analysis of actively damped orthotropic composite plates in bending and to verify it with experimental analysis.
The analytical modal analysis solution for composite plate dynamics is derived using Euler theory. This analysis applies to structures with orthotropic lamina of uniform material properties at any lamination angle. The bending-extensional coupling can be neglected for plates that are symmetric or approximately symmetric, which allows an exact solution for natural frequency and mode shape to be obtained. An exact solution can be found for natural vibration and in general.
The active control is modeled analytically by combining the Lagrange equation with the Ritz Assumed Mode method. This analysis produces a generalized coordinate vector that correlates the assumed mode to the particular amplitude of a particular case. The kinetic energy dissipated by the piezoelectric actuator from the system over one oscillation can be calculated from the generalized coordinate vector and the assumed mode. The equivalent damping ratio of the active control system is calculated as the ratio between the kinetic energy absorbed by the piezoelectric actuator from the system in one oscillation and the maximum strain energy of the system during that oscillation.
A point mass on the plate, such as an accelerometer mass, can also be modeled as a single layer of uniform mass, that is an isotropic layer, by equating the potential energy of the point mass with the potential energy of the uniform mass layer. It is important to note that the mass of the isotropic layer is frequency dependent, and it has no effect on the plate stiffness.
The analytical model is validated by comparison to experimental work. The samples studied were aluminum and composite plates of various lengths. The active control predictions were also validated using previous experimental work completed at California Polytechnic State University in San Luis Obispo. These cases included active control of an aluminum beam with a patch of piezoelectric material and an aluminum sailplane with a patch of piezoelectric material.
Results indicate that while the analytical mode solutions are in good agreement with the experimental results, they are also systematically higher than the experimental results. The analytical active control solutions match previous work when the piezoelectric effects are linear. The main result of adding an active control system is approximately a 5-10% increase in modal frequencies and a 200-800% increase of damping ratio.