On the Rayleigh-Ritz Method, Gorman?s Superposition Method and the exact Dynamic Stiffness Method for vibration and stability analysis of continuous systems

For calculating the natural frequencies, critical loads and associated modes of structures and structural elements such as beams and plates, three powerful analytical methods are commonly used. These are the Rayleigh-Ritz Method, Gorman?s Superposition Method and the exact Dynamic Stiffness Method. This paper is an attempt to compare these methods and bring to light the ways in which they differ, some of which are obvious but others are not well understood. The paper also addresses the meaning of exact method, which is sometimes incorrectly used in literature to refer to methods that give accurate (but approximate) solutions. Where applicable, any boundedness of the method is also discussed.