Structural Dynamics

Dynamics is increasingly being identified by consulting engineers as one of the key skills which needs to be taught in civil engineering degree programs. This is driven by the trend towards lighter, more vibration-prone structures, the growth of business in earthquake regions, the identification of new threats such as terrorist attack and the increased availability of sophisticated dynamic analysis tools.

Martin Williams presents this short, accessible introduction to the area of structural dynamics. He begins by describing dynamic systems and their representation for analytical purposes. The two main chapters deal with linear analysis of single (SDOF) and multi-degree-of-freedom (MDOF) systems, under free vibration and in response to a variety of forcing functions. Hand analysis of continuous systems is covered briefly to illustrate the key principles. Methods of calculation of non-linear dynamic response is also discussed. Lastly, the key principles of random vibration analysis are presented – this approach is crucial for wind engineering and is increasingly important for other load cases.

An appendix briefly summarizes relevant mathematical techniques. Extensive use is made of worked examples, mostly drawn from civil engineering (though not exclusively – there is considerable benefit to be gained from emphasizing the commonality with other branches of engineering). This introductory dynamics textbook is aimed at upper level civil engineering undergraduates and those starting an M.Sc. course in the area.

Table of Contents

Introduction to Dynamic Systems

What Is Dynamics and Why Is It Important?

Basic Definitions

Describing Oscillatory Motion

Dynamic Properties of Physical Systems

Dynamic Loads

Key Points

Tutorial Problems

Single-Degree-Of-Freedom Systems

Introduction

Equation of Motion

Free Vibration

Response to Dynamic Loads

Transfer Functions and Block Diagrams

Key Points

Tutorial Problems

Multi-Degree-Of-Freedom Systems

Introduction

Equations of Motion

Free Vibration of MDOF Systems

Vibration Analysis of DOF Systems

Response of MDOF Systems to Dynamic Loads

Key Points

Tutorial Problems

Continuous Systems

Introduction

Vibrations of Beams

Equivalent Single-Degree-Of-Freedom Systems

Key Points

Tutorial Problems

Non-Linear Dynamics

Introduction

Non-Linearity in Structural Properties

Time-Stepping Algorithms

Approximate Treatment of Non-Linearity

Key Points

Tutorial Problems

Fourier Analysis and Random Vibrations

Introduction

Properties of Random Variables and Processes

Autocorrelation

Fourier Analysis

Power Spectral Density

Impulse Response and Transfer Function

Key Points

Tutorial Problems

Appendices

Background Mathematics

Further Reading