Civil Engineering Reference
In-Depth Information
CHAPTER 1
Oscillating systems. Description and analysis
1.1
INTRODUCTION
Sound and vibration are dynamic phenomena, generally referred to as oscillatory motion.
Audible sound is due to oscillations in the air pressure propagating as waves. The term
vibration is used when talking about oscillations in mechanical systems. These may,
depending on the dimensions of the system and the actual frequency, appear as wave
motions of different kinds. It is then time to point out what is meant by the terms
oscillation and wave. Exact definitions may be found in the international standard ISO
2041. To express it in a general way, we may say that an oscillation is the variation with
time of the magnitude of a measurable quantity, the magnitude being alternately greater
and smaller than some mean value. With a wave there is an oscillatory motion
propagating through the actual medium and this motion is wholly dependent on the
physical properties of the medium. There is a transport of energy but not of the medium
itself.
The first step in measurement analysis of oscillations is usually a transformation of
the motion into an electrical oscillation or signal, using some kind of transducer. This
applies to all types of oscillatory motion with which we shall be concerned in building
acoustics, whether we are measuring vibration quantities such as acceleration or velocity,
or sound quantities such as pressure or particle velocity. In the current volume, the notion
signal analysis
is therefore synonymous with the analysis of the actual oscillatory
motion.
In modern stand-alone analysing equipment the signals are digitized and one
normally has at one's disposal a large menu of analysing options. Alternatively, with the
common use of PCs in recent years, signals are input to sound cards in the PC and the
analysing functions are implemented by software. This transforms the PC into a
reasonably prized measuring system taking advantage of already existing resources,
screen etc. No matter how these analysing functions are implemented, there is always a
demand on the user for knowledge of modern signal analysis, in particular, on being
aware of the possibilities and limitations of the actual “instrument” being used.
This chapter is aiming to give an elementary overview of the mathematical basis for
some common types of signal analysis, in particular on the frequency analysis of sound
and vibration quantities where the oscillations are described in the frequency domain.
Some commonly used measurement quantities are introduced when it is natural to do so.
There is a huge literature base on the subject, including textbooks. Some references can
be found at the end of the chapter.
1.2
TYPES OF OSCILLATORY MOTION
Oscillatory motion may, as other kinds of physical phenomena, be characterized as either
deterministic or stochastic (random). A process of some kind is denoted deterministic if it
may be described by an explicit mathematical expression. Using knowledge of the actual
