## 1 Introduction
However, in the previous studies, cantilever-type composite plate structures were treated as thin plates and the classical lamination theory (CLT) was used to analyze the free vibration of such plates. The CLT does not consider the through-thickness shear deformation so it is only suitable for the analysis of thin plates. In fact, the thicknesses of many cantilever-type plate structures used in different industries are generally relatively large so the classical lamination theory becomes inappropriate for modeling the vibration behavior of such plate structures. Therefore, in order to have more realistic predictions of the vibration characteristics of relatively thick cantilever-type composite plate structures, there is a need to develop an appropriate method that can take the through-thickness shear deformation into consideration. Recently, detailed reviews on different shear deformation theories for modeling composite plate deflection have been conducted [50; 51]. Among the shear deformation theories, the commonly used theory for plate analysis is the conventional first-order shear deformation theory (FSDT) [52; 53]. In the conventional FSDT, five independent displacement components (three displacement components at the mid-plane and two shear rotations) are required to describe the displacement field of a thick plate. Furthermore, shear correction factors are needed to correct the effects of uniform shear stress distribution over the plate thickness on the strain energy of the plate. Several methods studying the calculation of shear correction factors for composite laminates have been reported in the literature [54; 55; 56; 57; 58]. Besides the conventional FSDT, another type of FSDT, which is termed simple first-order shear deformation theory (SFSDT),has been used for engineering applications. Contrary to the conventional FSDT, the simple first-order shear deformation theory (SFSDT) only uses four displacement components to describe the displacement field of a composite plate. Hence, with respect to computational efficiency, the SFSDT seems to be more advantageous than the conventional FSDT. Recently, a number of researchers have attempted to apply SFSDT to plate analysis [59, 60, 61, 62, 63, 64, 65]. For instance, [PERSON] and his associates [59, 60, 61] used SFSDT-based methods to analyze various functionally graded/laminated composite/sandwich plates and beams with different boundary and loading conditions. In their studies, they adopted a shear correction factor of 5/6 to analyze very thick plates with a length-to-thickness ratio (a/h) as small as 2 in the numerical examples for illustration. [PERSON] [62] developed an SFSDT-based finite element method to analyze thick plates with a/h \(\geq\) 5 using a shear correction factor equal to 5/6 or 0.8667. [PERSON] and [PERSON] [65] applied the SFSDT to study the bending, buckling, and free vibration of isotropic plates with the consideration of the in-plane rotation and the use of a shear correction factor of 5/6. In applying the SFSDT, some researchers have introduced warping functions to approximate the deformed shapes of the plane cross-sections after deformation and satisfy the shear stress boundary conditions on the top and bottom plate surfaces [66, 67, 68, 69, 70]. It is noted that all the above works formulated on the basis of SFSDT have derived the governing equations or equations of motion for plate analysis. The use of the above SFSDT-based methods for free vibration analysis of thick cantilever composite plates may be computationally expensive or not simple enough for engineering applications. By contrast, the incorporation of the advantages of the Ritz method and the SFSDT may produce a useful technique for plate analysis. Hence, it is worth putting effort into developing the method formulated on the basis of the Ritz method and SFSDT for the vibration analysis of composite cantilever plates with the consideration of engineering applications.