Chapter 2 - Dynamic Response of Beams and Other Structures to Deterministic Excitation

Abstract

The basic formulas describing the behavior of the slender beam can be derived from the basic rules of the theory of elasticity, by neglecting terms that are derived for phenomena that do not contribute to the general understanding of the beam's behavior. There are many practical methods to obtain the resonance frequencies and the modes of a cantilever beam or of a general structure. The main purpose of a structural analysis in a design process is to predict the stresses in the structural design. Most of the design criteria in engineering applications are related to stresses or to a structural behavior that is an outcome of the stress fields in the structure. Stresses in an elastic system are a direct outcome of the relative displacement and are obtained by using the material constitutive relations and the compatibility equations. The effect of the dynamic load factor (DLF), or the amplification factor, is introduced into the system when the deflections are calculated. The stress behavior of a dynamic response is better understood when “stress modes” are used. The stresses at the finite elements nodes of the cantilever beam can also be computed using the postprocessor of the finite element solution. The mode shapes can give the designer more insight into the behavior of the structural system and may lead to some conclusions about the response behavior of the system and to direct design changes, if required.