9780203014554.pt1

9780203014554.pt1 - Part I Theory and methods Paolo L.Gatti...

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Part I Theory and methods Paolo L.Gatti Copyright © 2003 Taylor & Francis Group LLC
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1 Review of some fundamentals 1.1 Introduction It is now known from basic physics that force and motion are strictly connected and are, by nature, inseparable. This is not an obvious fact; it has taken almost two millennia of civilized human history and the effort of many great minds to understand. At present, it is the starting point of almost every branch of known physics and engineering. One of these branches is dynamics: the study that relates the motion of physical bodies to the forces acting on them. Within certain limitations, this is the realm of Newton’s laws, in the framework of the theory that is generally referred to as classical physics . Mathematically, the fact that force causes a change in the motion of a body is written (1.1) This is Newton’s second law which defines the unit of force once the fundamental units of mass and distance are given. An important part of dynamics is the analysis and prediction of vibratory motion of physical systems, in which the system under study oscillates about a stable equilibrium position as a consequence of a perturbing disturbance which, in turn, starts the motion by displacing the system from such a position. This type of behaviour and many of its aspects—wanted or unwanted— is common everyday experience for all of us and is the subject of this book. However, it must be clear from the outset that we will only restrict our attention to ‘linear vibrations’ or, more precisely, to situations in which vibrating systems can be modelled as ‘linear’ so that the principle of superposition applies. Future sections of this chapter and future chapters will clarify this point in stricter detail. Copyright © 2003 Taylor & Francis Group LLC
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1.2 The role of modelling (linear and nonlinear, discrete and continuous systems, deterministic and random data) In order to achieve useful results, one must resort to models. This is true in general and applies also to all the cases of our concern. Whether these models be mathematical or nonmathematical in nature, they always represent an idealization of the actual physical system, since they are based on a set of assumptions and have limits of validity that must be specified at some point of the investigation. So, for the same system it is possible to construct a number of models, the ‘best’ being the simplest one that retains all the essential features of the actual system under study. Generally speaking, the modelling process can be viewed as the first step involved in the analysis of problems in science and engineering: the so-called ‘posing of the problem’. Many times this first step presents considerable difficulties and plays a key role to the success or failure of all subsequent procedures of symbolic calculations and statement of the answer. With this in mind, we can classify oscillatory systems according to a few basic criteria. They are not absolute but turn out to be useful in different situations and
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This note was uploaded on 05/18/2011 for the course MAE 269A taught by Professor Ju during the Spring '11 term at UCLA.

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9780203014554.pt1 - Part I Theory and methods Paolo L.Gatti...

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