Vibration Analysis and Structural Dynamics for Civil Engineers Essentials and Group-Theoretic Formulations

Appeals to the Student and the Seasoned Professional While the analysis of a civil-engineering structure typically seeks to quantify static effects (stresses and strains), there are some aspects that require considerations of vibration and dynamic behavior. Vibration Analysis and Structural Dynamics for Civil Engineers: Essentials and Group-Theoretic Formulations is relevant to instances that involve significant time-varying effects, including impact and sudden movement. It explains the basic theory to undergraduate and graduate students taking courses on vibration and dynamics, and also presents an original approach for the vibration analysis of symmetric systems, for both researchers and practicing engineers. Divided into two parts, it first covers the fundamentals of the vibration of engineering systems, and later addresses how symmetry affects vibration behavior. Part I treats the modeling of discrete single and multi-degree-of-freedom systems, as well as mathematical formulations for continuous systems, both analytical and numerical. It also features some worked examples and tutorial problems.
Part II introduces the mathematical concepts of group theory and symmetry groups, and applies these to the vibration of a diverse range of problems in structural mechanics. It reveals the computational benefits of the group-theoretic approach, and sheds new insights on complex vibration phenomena.
The book consists of 11 chapters with topics that include: * The vibration of discrete systems or lumped parameter models * The free and forced response of single degree-of-freedom systems * The vibration of systems with multiple degrees of freedom * The vibration of continuous systems (strings, rods and beams) * The essentials of finite-element vibration modelling * Symmetry considerations and an outline of group and representation theories * Applications of group theory to the vibration of linear mechanical systems * Applications of group theory to the vibration of structural grids and cable nets * Group-theoretic finite-element and finite-difference formulations Vibration Analysis and Structural Dynamics for Civil Engineers: Essentials and Group-Theoretic Formulations acquaints students with the fundamentals of vibration theory, informs experienced structural practitioners on simple and effective techniques for vibration modelling, and provides researchers with new directions for the development of computational vibration procedures.

PART I: ESSENTIALS Introduction Definitions, aims and general concepts Basic features of a vibrating system, and further concepts Tutorial questions Single degree-of-freedom systems Basic equation of motion Free vibration response Equivalent spring stiffnesses for various structural and mechanical systems Response to harmonic excitation Tutorial questions Systems with more than one degree of freedom Introductory remark Equations of motion Techniques for assembling the stiffness matrix The flexibility formulation of the equations of motion and assembly of the flexibility matrix Determination of natural frequencies and mode shapes The flexibility formulation of the eigenvalue problem Worked examples The modal matrix Orthogonality of eigenvectors Generalized mass and stiffness matrices Worked examples Modal analysis Worked example Tutorial questions Continuous systems Introduction Transverse vibration of strings Axial vibration of rods Flexural vibration of beams Orthogonality of natural modes of vibration Dynamic response by the method of modal analysis Finite-element vibration analysis The finite-element formulation Stiffness and consistent mass matrices for some common finite elements Assembly of the system equations of motion References PART II: GROUP-THEORETIC FORMULATIONS Basic concepts of symmetry groups and representation theory Symmetry groups Group tables and classes Representations of symmetry groups Character tables Group algebra Idempotents Applications References Rectilinear models Introduction A Shaft-disc torsional system A Spring-mass extensional system Conclusions Plane structural grids Introduction Rectangular configurations Square configurations Conclusion High-tension cable nets Basic assumptions and geometric formulation Outline of computational scheme Illustrative examples Symmetry-adapted functions Symmetry-adapted flexibility matrices Subspace mass matrices Eigenvalues, eigenvectors and mode shapes Summary and concluding remarks References Finite-difference formulation for plates General finite-difference formulation for plate vibration Group-theoretic implementation Application to rectangular and square plates Finite-difference equations for generator nodes of the basis vectors Symmetry-adapted finite-difference equations and system eigenvalues Concluding remarks References Finite-element formulations for symmetric elements Group-theoretic formulation for finite elements Coordinate system, node numbering and positive directions Symmetry-adapted nodal freedoms Displacement field decomposition Subspace shape functions Subspace element matrices Final element matrices Concluding remarks References

Alphose Zingoni is professor of structural engineering and mechanics in the Department of Civil Engineering at the University of Cape Town. He holds an M.Sc in structural engineering and a Ph.D in shell structures, both earned at Imperial College London. Dr. Zingoni has research interests encompassing shell structures, space structures, vibration analysis, and applications of group theory to problems in computational structural mechanics. He has written numerous scientific papers on these topics, which have been published in leading international journals and presented at various international conferences worldwide.