Catastrophic failures of turbomachines have been reported due to resonant vibration of its blades. Thus, it is important to estimate the natural frequencies of such structures. Towards this end, finite element method based simulation is the prevalent industrial practice. However, this process can be time consuming and computationally inefficient at the design stage. In the present work, the turbomachinery blades are modelled as rotating, curved and twisted cantilever beams. In this work, novel analytical formulae to determine the natural frequencies of such structures are derived. The complications of curvature, twist and rotation are treated as perturbation parameters. The present work begins by individually analyzing the effects of curvature, twist and rotation. The subsequent chapters combines two of these complications. In the final chapter, the effects of all the three complications are considered together. In some cases, the analytical form of the Lagrangian is unavailable in the literature. In such cases, the Lagrangian is derived from first principles. Rayleigh-Ritz method is employed to derive low order matrix equations corresponding to the problems solved in each chapter. Towards this end, aningeniouschoiceofshapefunctionsisused. Theseshapefunctionsarethesimplified mode shapes of the curved beam. These are obtained by simplifying the exact mode shapes through asymptotic argument. The roots of the determinant of the above matrix represent the natural frequencies of the system. These roots are found using a regular perturbation method. The derived perturbation formulae are in the form of a reference solution to which the corrections due to the complications (viz. curvature, twist and rotation) are added. The reference solution corresponds to the well-known caseauniform,non-rotatingstraightcantileverbeam. Theresultsobtainedfromthederived formula correlate with FEM simulation results (performed in a commercial FEM package). Comparisons are also made with experimental results available in the literature. It is shown that the perturbation-based formula yield results comparable with FEM simulation for a large range of perturbation parameters. It is envisioned that the availability of the simple analytical formulae will expedite design iterations, aid uncertainty quantification and ease the computational implementation by replacing the sophisticated FEM simulations with simple spreadsheet calculations. Further, interesting physical insights can be derived from the perturbation-based formulae.