Twelve Lectures on Structural Dynamics





Preface

Nowadays, with the amazing computing capability of computers and the

availability of sophisticated, user-friendly computer-aided analysis software,

the main difficulty for the analyst is to interpret the results and to make sure that

the analysis includes all the relevant physical phenomena. The majority of

structural failures occur because physical phenomena are overlooked, or greatly

underestimated, rather than as a result of computational errors (e.g., the flutter of

the Takoma suspension bridge, or the recent Fukushima tsunami disaster). To

build confidence in the design, the analyst first develops a crude model, a model of

minimum complexity which still reflects the main physical phenomena. What

minimum complexity means depends on the problem; for example, a point mass

with two degrees of freedom is sufficient to explain the stable operation of a rotor

at supercritical velocities, but it is impossible to account for the dependency of the

natural frequencies on the rotor speed without including the gyroscopic effects;

the effect of prestresses on the natural frequencies cannot be accounted for without

the inclusion of nonlinear strains (Green strain tensor). Similarly, analytical results

may appear unnecessary at a time where extensive parametric studies may be

performed numerically very quickly, but knowledge of the parametric dependence

of critical properties such as natural frequency on design parameters (dimensions,

material properties,…) is invaluable in design, especially when scale effects are

involved.


This book is based on the vibration course that I teach in the joint masters

program ULB/VUB at the university of Brussels, and the random vibration course

that I taught for a decade at the university of Liege. It has also been strongly

influenced by my research work in the active control of structures, where we

usually work with models of moderate size, but which accounts for all the relevant

features of the system dynamics. The book is focused on modeling, with very little,

if any, attention paid to the numerical methods that I consider as mature and well

established, and which are well covered in the excellent books written by those

more qualified than me (e.g., Geradin and Rixen).


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