Structural Dynamics

Franklin Y. Cheng

Curators' Professor Emeritus of Civil Engineering, University of Missouri, Rolla, MO

3.1 Dynamic Forces and Structural Models 3-2

Characteristics of Dynamic Forces • Mathematical Models of Structural Systems

3.2 Response Analysis of Single d.o.f. Systems 3-3

Definition of d.o.f. • Undamped and Damped Free Vibration • Undamped and Damped Forced Vibration

3.3 Response Analysis of Multiple d.o.f. Systems — Lumped-Mass Formulation 3-11

Nature of Spring-Mass Model • Normal Modes, Modal Matrix, and Characteristics of Orthogonality • Response Analysis and Relevant Parameters • Proportional and Nonproportional Damping • Various Eigensolution Techniques

3.4 Response Analysis of Continuous Systems — Dynamic-Stiffness Formulation 3-18

Characteristics and Formulation of the Model • Derivation of Dynamic Stiffness Based on Bernoulli-Euler Equation • Dynamic System Matrix and Eigensolutions • Response Analysis • Effects of Rotatory Inertia as well as Bending and Shear Deformation on Frequencies • Coupling of Longitudinal and Flexural Vibration • Effects of Elastic Media, Torsion, and Axial Force on Vibration

3.5 Response Analysis of Finite Element Systems —

Consistent-Mass Formulation 3-28

Introduction • Formulation of Stiffness and Mass Matrices • Frequency Comparison for Lumped-Mass, Dynamic-Stiffness, and Consistent-Mass Models • Axial, Torsional Vibration, and Flexural Vibration with Timoshenko Theory • Dynamic Motion Equation with P-A Effect

3.6 Elastic and Inelastic Response Analysis Methods Based on Nature of Exciting Forces 3-31

Nature of Exciting Forces • Modal Analysis • Direct Integration Methods • Stability Condition and Selection of Time Interval • Nondeterministic Analysis • Comments on Wave Propagation Analysis

3.7 Hysteresis Models and Nonlinear Response Analysis 3-39

Introduction • Elasto-Plastic Stiffness Formulation • Bilinear Stiffness Formulation • Elasto-Plastic and Bilinear Response Comparisons • Effects of P-A, Material Nonlinearity, and Large Deformation on Response • Hysteresis Models and Stiffnesses for Steel Bracings and for RC Beams, Columns, and Walls of

Building Systems

3.8 Concluding Remarks 3-49

Glossary 3-50

References 3-51

Further Reading 3-52

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