On the Sensitivity of Derived Elastic Constants to the Utilized Modes in the Vibration Testing of Composite Plates

This paper investigates how the accuracy of the elastic constants of an orthotropic material depends on the vibration modes that are used to derive such constants from plate vibration test data. The behavior of four independent elastic constants - the longitudinal and transverse Young’s modulus, the shear modulus and Poisson’s ratio in the plane are examined. The elastic constants are derived by a method earlier proposed by the author in which the transverse vibration displacement of a completely free plate is represented by contributions from three optimally selected characteristic normal modes. Results are shown for graphite/epoxy (orthotropy ratio about 13). The results suggest that the in-plane elastic constants are most sensitive to the fundamental torsional mode of the completely free plate. As illustration, the in-plane elastic constants of an orthotropic plate are extracted from modes with different sensitivities. The sensitivities appear to bear faithful correlations to the goodness of the results. A major contribution of this paper is that it underscores the importance of using modes with significant sensitivity to the elastic constants desired, and gives guidance for the most advantageous selection of modes for deriving elastic constants. Although the case studied concerns a thin orthotropic plate with four independent elastic constants, this idea may readily be extended to more complex cases where more elastic constants than the four involved in this case are extracted.