By Paolo L. Gatti
The elemental techniques, principles and techniques underlying all vibration phenomena are defined and illustrated during this booklet. the rules of classical linear vibration idea are introduced including vibration dimension, sign processing and random vibration for program to vibration difficulties in all components of engineering. The e-book will pay specific recognition to the dynamics of buildings, however the tools of study awarded right here follow comfortably to many different fields.
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Extra info for Applied structural and mechanical vibrations: theory, methods, and measuring instrumentation
13) and the coefficients of its Fourier series. The result we will obtain is called Parseval’s theorem and is very important in many practical applications where energy and/or power are involved. 14a) Copyright © 2003 Taylor & Francis Group LLC which shows that each Fourier component of x(t), independently of the other Fourier components, makes its own separate contribution to the mean squared value. In other words, no cross (or ‘interference’) terms of the form appear in the expression of the mean squared value of x(t).
1 Mathematical preliminaries Introduction The purpose of this chapter is twofold: (1) to introduce and discuss a number of concepts and fundamental results of a mathematical nature which will be used whenever necessary in the course of our analysis of linear vibrations, and (2) to provide the reader with some notions which are important for a more advanced and more mathematically oriented approach to the subject matter of this text. In this light, some sections of this chapter can be skipped in a first reading and considered only after having read the chapters that follow, in particular Chapters 6–9.
A second important property has to do with the Fourier transform of the function df(t)/dt. 26b) is true only if is a Fourier-transformable function in its own right. By similar arguments, if f(t) is absolutely integrable then the Copyright © 2003 Taylor & Francis Group LLC function then is continuous. 27) Consider now two Fourier-transformable functions f(t) and g(t) with Fourier transforms F(ω) and G(ω), respectively. 28) is called the convolution of f(t) and g(t) and it has considerable importance when calculating the time response of linear systems.
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