# Energy Approximations Applied to Problems of Structural Equilibrium, Stability and Vibrations

*THE paper discusses the general energy basis of structural problems of equilibrium, stability and vibrations making use of Hamilton’s principle of least action as a starting point. The forms which the energy takes in the various cases are shown and the analytical method of solution is then followed. This is compared with the functional approximation methods of Rayleigh-Ritz, Lagrange and Galerkin. The useful property of orthogonality is briefly discussed. A number of examples are then given which demonstrate the use of the above methods to some simple problems of structural
mechanics.
P.B. Morice*

Author(s): Morice, P B

Keywords: analysis;stability;vibration;approximate methods;energy methods