AXISYMMETRIC VIBRATIONS OF CONCENTRIC DISSIMILAR ORTHOTROPIC COMPOSITE ANNULAR PLATES

The axisymmetric vibrational behaviour of two concentric dissimilar orthotropic composite annuli is investigated. Sixth order systems of equations of motion for each annulus are presented together with the matching conditions at their interface. The common frequency of vibration of the structure is determined numerically using a finite difference method. Bi-layered, triple-layered and bi-+triple-layered material compositions were considered. Computed results for a wide range of possible orthotropic material combinations indicate the complex role the material orthotropies play in determining the annuliʹs vibrational response. It is shown that the frequency increase factor (defined as the ratio between the highest and lowest frequencies obtained for all inner and outer material combinations considered) is very sensitive to the geometric, heterogeneity and orthotropy parameters of the composite annular plates. Unfortunately, no simple rule of thumb formula for estimating the effect of the material composition on the frequency appears to be deducible. However, in keeping with previous results for concentric dissimilar isotropic annuli, the geometry (expressed via the radii of the inner and outer annuli) and the different material compositions were found to exert a considerable influence on the natural frequency of vibration. In the absence of appropriate analytical expressions, optimization and, thereby, control of the natural frequency of composite plate-like structures, through geometry and material composition, must make use of parametric studies similar to the current one.