Fiber-reinforced polymer composite materials have gained extensive application in aerospace, automotive, marine, and civil infrastructure owing to their exceptional specific strength, stiffness, and design flexibility. However, delamination - a critical interlaminar failure mode compromises structural integrity and dynamic performance. This comprehensive study investigates the vibration behavior of carbon fiber-reinforced polymer (CFRP) composite plates subjected to varying delamination extents, laminate stacking sequences, and boundary constraints through integrated analytical and finite element methodologies. The governing differential equations are derived using the Rayleigh-Ritz energy method based on classical laminated plate theory, and numerical simulations are performed using ANSYS finite element software. The investigation examines delamination sizes ranging from 0% to 56.25% of plate area, three distinct stacking configurations ([0/90/45/90], [0/45], [0/90]), and all sides clamped (CCCC), simply supported (SSSS), cantilever (CFFF), and free edges (FFFF) boundary conditions. Results demonstrate that natural frequencies decrease systematically with increasing delamination size, with maximum reduction of 5-8% occurring for the largest delamination extent (56.25%) across all boundary condition.. Furthermore, CNT integration enhances both natural frequencies (up to 29.8% increase at 2.5 wt% CNT loading) and damping characteristics (42.1% improvement). These findings support improved design and vibration control of advanced composite structures.