## 1 Introduction  
A rectangular orthotropic plate has many applications in designing different components in the engineering field, such as aerospace, mechanical, and civil. The orthotropic response of a given material is due to the existence of its constitutive relations. Various composite plates have been modeled analytically as orthotropic plates in recent years. So, one should have knowledge of the free vibration of such structures for efficient dynamic structural analyses. Starting from the earlier works on natural vibration of the plate by [PERSON] [1] and [PERSON] [2], the past few decades have witnessed different numerical and analytical methods, such as the Kantorovich method, the superposition method, the Rayleigh-Ritz method, and the iterative reduction method, for the investigation of natural vibrations of rectangular orthotropic plates [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. The usually adopted finite element method (FEM) has also proved its popularity in the dynamic analysis of orthotropic rectangular plates [21, 22, 23]. However, the main drawback of traditional FEM and other approximate methods is the discretization technique of the given structure, which depends on the number of elements taken. The dynamic stiffness method (DSM) provides accurate results independent of the number of elements implemented in the investigation. The DSM has proven its efficiency in the dynamic analysis of bars, beams, rings, and shells [24, 25, 26, 27, 28, 29, 30, 31], and the W-W algorithm [24, 25, 26, 27, 28] is implemented as a solution technique to the final dynamic stiffness matrix to find out the natural vibration frequencies of beams. [PERSON] and [PERSON] [32] are probably the earliest researchers who developed DSM for isotropic simply supported plates, applying CPT. [PERSON] and [PERSON] extended the DSM and applied the first-order deformation theory (FSDT) for isotropic [33] and composite plates [34; 35]. [PERSON] et al. [36] further formulated the DSM for rectangular anisotropic plates using the higher shear deformation theory (HSDT) with the W-W algorithm. Further, [PERSON] and [PERSON] [37] developed DSM by applying the sophisticated layer-wise first-order theory to investigate laminated composite plates. Continuing this work, [PERSON] et al. [38] developed an exact dynamic stiffness (DS) matrix for an isotropic rectangular plate. [PERSON] et al. [39] used DSM for free vibration analyses of thick composite plates resting on non-homogeneous foundations. Recently, [PERSON] et al. developed DSM for an isotropic rectangular plate with arbitrary boundary conditions undergoing in-plane free vibration [40], which was further exploited for out-of-plane free vibration of the rectangular Mindlin plate element [41] and later on for isotropic plate assemblies [42]. [PERSON] et al. formulated DSM for both out-of-plane [43] and in-plane [44] free vibrations of the rectangular orthotropic plate, taking advantage of the symmetry and Gorman-type decomposition of the free boundary conditions. [PERSON] et al. [45] developed DSM for analyzing the free vibration response of the functionally-graded material plate using the classical plate theory with the physical neutral surface concept. [PERSON] et al. [46] used the classical plate theory to formulate a dynamic stiffness matrix to compute the natural frequencies of the rectangular plate with the considered Levy-type boundary conditions. Moreover, [PERSON] and [PERSON] developed an exact spectral-dynamic stiffness method (S-DSM), which combines the spectral method with classical DSM for free vibration analyses of orthotropic composite plates and their assemblies [47; 48] and, subsequently, for isotropic rectangular plates [49] with arbitrary boundary conditions. This work reports the out-of-plane free vibration response of a thin rectangular orthotropic plate for Levy-type boundary conditions based on CPT using the exact DSM method with the Wittrick-Williams algorithm.