Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 24

In many practical applications ζ is small and the amplitude can be estimated by linear expansion from (1.34)

(1.50)

with the corresponding phase angle

(1.51)

The amplitude- and phase resonances are assumed to be equal for systems with small damping. The magnification is thus 1/2ζ, and it is called the quality factor:

(1.52)

Figure 1.10 Half power bandwidth for harmonic oscillator. Source: Alexander Peiffer.

This factor is a measure for the sharpness of the resonance peak or the quality of the resonator. In response diagrams when the shape of the amplitude over frequency is measured the half power bandwidth is used. This is the distance of the points where the amplitude is 1/2 of the peak value u^r. Solving Equation (1.31) for u^r/u^0=1/2 the frequencies of half power can be found:

(1.53)

and therefore

(1.54)

Obviously the decay time is also related to damping. If Equation (1.22) is considered we get

(1.55)

We have presented several expressions that describe damping. Nevertheless, even more quantities for damping are used depending on the engineering discipline and will be shown in Section 1.2.5. Section 1.2.5.1 aims at sorting all those expressions and their relationships among each other.