Energy Methods of Structural Dynamics

This chapter presents energy methods of structural dynamics. Differential equations of motion can be obtained using energy principles and the calculus of variations, i.e., these are the same differential equations that are obtained using the static method. The main goal of energy principles is to find very effective approximate solutions to dynamic problems. Energy methods are associated with integration operations, allowing approximate solutions to have greater accuracy than using differentiation operations. Thus, the conditions for applying integration are better than the same for differentiation. Energy methods can also be considered as methods of approximating functions, since their application solves the problem of the best approximation of given functions in advance to the actual ones. Energy methods belong to the category of applied mathematical methods and can be used in many fields and problems of mechanics. In this chapter, we will discuss the following: derivation of equations of motion using D’Alembert Principle, static method, energy method, applicable problems and solutions, Rayleigh, Ritz, and Bubnov–Galerkin methods.