Dynamic Stiffness and Substructures models a complex dynamic system and offers a solution to the advanced dynamical problem associated with the effects of wind and earthquakes on structures. Since the system matrices are inevitably frequency dependant, those are exclusively considered in this publication. The relation between the frequency matrices by the Leung's theorem is most important in the development of efficient algorithms for the natural modes. This new approach was developed by the author over the past 15 years. It offers practising engineers and researchers a wide choice for structural modelling and analysis. Abundant numerical examples enable the reader to understand the theorem and to apply the methods.

Contenuti

1 Harmonic Analysis.- 1.1 Steady State.- 1.2 Multiple Degrees of Freedom.- 1.3 Modal Analysis and Acceleration.- 2 Finite Elements and Continuum Elements.- 2.1 Formulation.- 2.2 Bar Elements.- 2.3 Beam Elements.- 2.4 Continuous Mass Model.- 2.5 Rectangular Plate.- 2.6 Interaction Between Beams and Plates.- 2.7 Leung’s Theorem.- 2.8 Simpson’s Hypothesis.- 2.9 Sturm’s Theorem.- 2.10 Wittrick-Williams Algorithm.- 2.11 Derivatives of the Dynamic Stiffness.- 3 Dynamic Substructures.- 3.1 Exact Dynamic Condensation.- 3.2 Dynamic Substructures.- 3.3 Dynamic Flexibility.- 3.4 Dynamic Transformation.- 3.5 Damped Substructures.- 3.6 Multilevel Substructures.- 3.7 Non-conservative Substructures.- 3.8 Substructure Response.- 3.9 Periodic Structures.- 3.10 Derivatives of Substructure.- 4 Dynamic Stiffness.- 4.1 Follower Force.- 4.2 Parametrically Excited Members.- 4.3 Effects of In-Plane Moment.- 4.4 Reponse Analysis.- 4.5 Non-conservative Modal Analysis.- 4.6 Exponentially Varying Harmonic Excitations.- 5 General Formulation.- 5.1 Initial Stress Formulation.- 5.2 Finite Element Method.- 5.3 Dynamic Stiffness Method.- 5.4 Thin-Walled Beam.- 5.5 Shear Deformable Thin-Walled Beam.- 5.6 Analytical Dynamic Stiffness.- 5.7 Curved Thin-Walled Beam.- 5.8 Helix.- 5.9 Curvature Effect.- 5.10 Extensions.- 5.11 Symmetry of the Dynamic Stiffness Matrix.

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