User`s guide
101
The critical damping factor of a cantilever beam is
=
2.3 Measurement Methods of Dynamic Characteristics
The dynamic characteristics of a vibrating object, including vibrating frequency and
damping factor extracted from strain and acceleration data acquired during the vibration .
2.3.1 Measurement of Vibration Frequency: Fourier Transformation
Fourier series decomposes periodic signals into the sum of an infinite series of simple
oscillating functions, namely sines and cosines, or complex exponentials. The technique can be
applied to mathematical and physical problems, especially electrical engineering, vibration
analysis, acoustics, optics, signal processing, image processing, quantum mechanics,
econometrics, etc.
2.3.1.1 Fourier Series
The Fourier series of a periodic function consists of an offset value, an even (cosine)
component, and an odd (sine) component. The offset value
of a periodic function with
period T is defined as the average value of the periodic function over a period. The even
component relates to the portion of the periodic function behaving as
, which is a
property of the cosine function. The odd component relates to the portion of the periodic function
behaving as
, which is a property of the sine function.
The components
,
, and
are given by the relationships
Eq.40
Eq.41
Eq.39