Laminated composite plates are being increasingly used in the aeronautical and aerospace industry as well as in other "elds of modern technology. To use them e!eciently a good understanding of their structural and dynamical behaviour is needed. The Classical ΒΈaminate Plate ΒΉheory [1] which ignores the e!ect of transverse shear deformation becomes inadequate for the analysis of multilayer composites. The "rst order theories (FSDTs) based on Reissner [2] and Mindlin [3] assume linear in-plane stresses and displacements, respectively, through the laminate thickness. Since FSDTs account for layerwise constant states of transverse shear stress, shear correction coe$cients are needed to rectify the unrealistic variation of the shear strain/stress through the thickness and which ultimately de"ne the shear strain energy. In order to overcome the limitations of FSDTs, higher order shear deformation theories (HSDTs) that involve higher order terms in Taylor's expansions of the displacement in the thickness co-ordinate were developed. Hildebrand et al. [4] were the "rst to introduce this approach to derive improved theories of plates and shells. Kant [5] was the "rst to derive the complete set of variationally consistent governing equations for the #exure of a symmetrically laminated composite plate incorporating both distortion of transverse normals and e!ects of transverse normal stress/strain by utilizing the complete three-dimensional generalized Hooke's law and presented results for isotropic plate only.
Later Mallikarjuna [6], Mallikarjuna and Kant [7] and Kant and Mallikarjuna [8,9] presented a set of higher order re"ned theories and presented formulations and solutions for the free vibration analysis of general laminated composite and sandwich plate problems based on "nite element methods. In this investigation, analytical solutions for the free vibration analysis of laminated composite and sandwich plates based on two higher order re,ned theories already developed by the ,rst author for which analytical formulations and solutions were not reported earlier in the literature are presented. After establishing the accuracy of the present results with three-dimensional elasticity solutions for isotropic, orthotropic and composite plates, benchmark results and comparison of solutions using various theories are presented for multilayer sandwich plates.
The displacement models under various theories considered in the present investigations are listed below [10}14]: