GBT-based local and global vibration analysis of thin-walled members

This chapter discusses the use of numerical techniques to perform vibration analysis, the concepts of finite element analysis (FEA) and finite strip analysis (FSA). The literature review in the chapter has been organized according to the particular methodology employed: there are separate sub-sections dealing with investigations carried out by means of (1) the finite element method (mostly shell element discretizations), (2) the finite strip method and (iii) the generalized beam theory (GBT) – because the aim of the chapter is to present the fundamentals and illustrate the application of a GBT formulation to analyze the vibration behavior of thin-walled members, the last sub-section also includes a brief outline of its content. Silvestre and Camotim (2003) formulated, implemented, and validated an efficient beam finite element intended to perform GBT-based buckling analyses in the context of arbitrarily orthotropic thin-walled members. The most relevant steps involved in the formulation of this finite element, specialized for the vibration analysis of isotropic thin-walled members, are described briefly in the chapter.