Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 22

So far the frequency response of the oscillator was expressed as the relationship between displacement and force. The ratios u/Fx and D=Fx/u are called mechanical receptance and, respectively. Often used force response relationships are the mechanical impedance impedance ! mechanical (force/velocity=Fx/vx) and the mobility (velocity/force=vx/Fx). The symbols and definitions are:

(1.39)

Considering the solution of the damped oscillator and vx=jωu both quantities become:

(1.40)

The real and imaginary part have specific names resistance reactance

(1.41)

The meaning of this convention becomes clear when inspecting Figure 1.9. When the oscillator is excited in the mass- or stiffness-controlled regime below or above the resonance, the force introduces a reactive movement. The energy can be taken back from the system and it is called reactive. Whether the system response is mass or stiffness controlled can be identified from the slope of the impedance magnitude and the phase. In the resonance regime the system is driven at resonance and the damper dissipates energy. The resistance of the system becomes important and is thus called resistive.

Figure 1.9 Magnitude and phase of oscillator impedance. Source: Alexander Peiffer.