Dynamic Analysis of Structures

John T. Katsikadelis

Preference :

The statement of the laws of motion by Newton 334 years ago (1686)a was a milestone in the evolution of mechanics and modern engineering. The relation between force (cause) and motion (effect) was quantified as a relation between the linear momentum of the body and the force exerted on it. Thus, this relation from a subject of philosophy up to that time turned out to be a valuable tool of science for the study of the natural world. The subsequent developments in the sciences were rapid. Astronomy, mathematics, mechanics of fluid and deformable bodies, and in general, mechanics of continuous media reached their peaks in the centuries that followed, with immense applications to all engineering disciplines. Nevertheless, the laws of motion, which were stated as an axiom (Axiomata sive Leges Motus) by Newton because, apparently, he could not justify their derivation, was a consequence of the discoveries of great scientists who preceded him such as Galileo,b Kepler,c Hook, etc.
The implementation of the laws of motion leads to mathematical models described by differential equations, ordinary or partial, whose solution effort has given a great impetus to the development of mathematics. Unfortunately, analytical solutions are limited to simple problems such as vibrations of discrete systems with a few degrees of freedom; linear vibrations of beams, membranes, plates, and shells with simple geometry; and simple support conditions made from materials, mostly with a linear behavior.