## 1 Introduction  
Modal characteristics (natural frequency and mode shape) have found different applications in the areas of structural engineering and solid mechanics. For instance, for safety reasons, modal characteristics are important parameters to be dealt with in the design, system identification, and health monitoring of a structure. Regarding the design of a structure subject to dynamic loads, the natural frequencies of the structure must be taken into consideration to prevent resonance from occurring. Therefore, to avoid the occurrence of resonance, many papers have been devoted to the optimal design of structures with the consideration of natural frequency constraints [1; 2; 3; 4; 5]. Regarding health monitoring/assessment, the modal characteristics of a damaged structure are important information for assessingstructural damage. For instance, many papers have been devoted to the use of natural frequencies/mode shapes for detecting damage in structures [6; 7; 8; 9; 10; 11; 12]. In the area of system identification, many researchers have used natural frequencies/mode shapes to identify the system parameters of composite structures [13; 14; 15; 16; 17; 18; 19; 20]. For instance, [PERSON] and [PERSON] [17] used natural frequencies in a Ritz-based method to identify the material constants of flexibly restrained plates. In the acoustic area, modal characteristics information has been used to modify the vibration behavior of flat-panel sound radiators for enhancing their sound radiation efficiency [21; 22; 23]. For instance, [PERSON] et al. [23] used the information of modal characteristics to mitigate sound pressure level dips for smoothing the sound pressure level curves of composite panel-form speakers. Therefore, the above literature review has shown that modal characteristics are important structural parameters that have found many different engineering applications. Cantilever-plate/beam-like structural parts such as turbine blades, fighter spoilers, aircraft stabilizers, and missile fins are subject to dynamic loads which can cause them to vibrate. Furthermore, because of their importance, many research papers have been published to focus on the free vibration analysis of cantilever-plate/beam-like structural parts and different methods have been proposed to determine their modal characteristics [24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37]. Therefore, from the engineering application point of view, it is still desirable to develop more efficient and effective methods for predicting the actual vibration behavior of these types of structures. On the other hand, advanced composite materials have many attractive properties such as high strength in the fiber direction, ease of being tailored to make fibers coincide with the direction of stress flow, light weight, and super corrosion resistance capability. Recently, they have been used to fabricate vibration-susceptible composite plate structures in the wind power, aerospace, aircraft, and defense industries, among others. The wide application of composite plates in different industries has led to the development of different methods for determining the modal characteristics of composite plates [38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49]. In particular, due to its simplicity of implementation, effectiveness in producing reliable results, and computational efficiency, the Ritz method has been widely used for the free vibration analysis of plates. For instance, [PERSON] et al. [46] used Legendre polynomials as characteristic functions in the Ritz method to study the free vibration and sound radiation of elastically restrained shear deformable stiffened composite plates. Regarding the use of the Ritz method in vibration analysis, it is noted that the appropriateness of the chosen characteristic functions can have significant effects on the accuracy of the modal characteristics. When the thickness of a plate increases, the effects of through-thickness shear deformation on the plate deflection may become too significant to be neglected.