The vibration characteristics of thick rectangular multilayered plates

We develop the analysis and numerical calculations for the exact free vibration characteristics of simply-supported, rectangular, thick, multilayered composite plates. We assume that each layer of the composite plate is of arbitrary thickness, is perfectly bonded to adjacent layers, possesses up to orthotropic material symmetry and that its material crystallographic axes are oriented either parallel or perpendicular to the plate's boundaries. Exact formal solutions are obtained for the individual layers which are, in turn, used to relate the field variables at the upper and lower layer surfaces. The solution is carried through by the successive application of appropriate interfacial continuity conditions between adjacent lamina. We facilitate our analysis and its numerical implementation by making use of the matrix transfer technique, thereby rendering the order of the resulting eigenproblem independent of the number of lamina. Numerical results are given in the form of scaled natural frequency versus nondimensionalized mode numbers. The effect of the plate's microstructure on its vibrational characteristics is investigated by examining changes in natural frequency and modal response for selected laminate lay-ups and material combinations.