When you study a smart system, your first task very often is to evaluate the effective coupling coefficient of this system.
The effective coupling coefficient represents the quality of the system's energy conversion. The greater the effective coupling coefficient, the less electrical energy required by the system to reach a given level of mechanical vibration.
ATILA performs a modal analysis that may include, for each mode, the computation of the resonance and antiresonance frequencies and the effective coupling coefficient.
To illustrate this type of analysis, let's look at the stator of a Traveling Wave Ultrasonic Motor (TWUM), also called a ring-shaped motor (Figure 6).
This type of stator uses a thin ring of piezoelectric material placed on a ring of metal. The piezoelectric ring is divided into sectors which are alternately poled. A real metal ring will have teeth; they are not taken into account in this model.
ATILA computes the resonance frequency, the antiresonance frequency, and the coupling coefficient for each mode. Table I shows part of the computation results in the case of a 45 mm diameter TWUM.
Table 1: Results of the Modal Analysis
These results show that mode number 7 is the most appropriate mode for this stator.