This book attempts to cover the fundamentals of the vibration of engineering systems, focusing at a later stage on how symmetry affects vibration behaviour. Symmetry is a common property in many engineering systems and has been studied for many years in several areas of physics and chemistry, as, for example, crystallography and quantum or molecular mechanics. The book provides the civil engineer with the basics of vibration analysis and structural dynamics first, and then with well-established methods applied to several problems of symmetry in physics and chemistry harnessed for the study of vibration problems in engineering.
The book comprises two parts. The first of these covers, in a concise and yet thorough way, the fundamentals of vibration analysis and structural dynamics intended for all civil, structural and mechanical engineering students and practitioners. The theory is accompanied by certain fully worked out numerical examples and tutorial questions; considerations are also extended to continuous systems and the application of the finite-element method in vibration analysis.
The second part concerns the introduction of a novel method to analyse vibrations of a symmetric system. By using the group theory mathematical concepts, the method is developed and applied to the treatment of a range of structural vibration problems. This approach provides valuable insights into the vibration analysis of symmetric systems, as well as logical explanations for certain phenomena that dominate vibration behaviour; for instance, the coincidence of frequencies, similarity of modes and stationarity points. The latter topics make the book of interest not only to the aforementioned readership, but also to researchers working with the development of computational approaches in structural vibration analysis.
The first five chapters provide information and guidance on vibration analysis and structural dynamics. Chapter 1 is a general introduction to structural vibrations, including computational modelling of discrete systems and lumped parameter models. Chapter 2 deals with the free vibration response of both damped and undamped single-degree-of-freedom systems, as well as their treatment in the case of the forced response to harmonic excitation. Chapter 3 considers the structural vibration of systems with two or more degrees of freedom. The theoretical formulation of vibration problems in continuous systems and finite-element formulation are dealt with in chapters 4 and 5, respectively.
The next six chapters concern a novel approach to the vibration analysis of symmetric systems. Chapter 6 outlines group theory basics, symmetry groups and representation theory. In chapters 7–9 the computation of natural frequencies and mode shapes of several discrete systems are proved to be simple enough within the group theory framework. In chapter 10 a relevant theoretical formulation of the finite-difference method is presented and applied to the vibration analysis of plates. In the last chapter, a group theory formulation for finite elements is developed and appropriately illustrated.
Overall, the book provides comprehensive guidance for students, practitioners and researchers interested in the essentials and group-theoretic formulations of vibration analysis and structural dynamics.
