Relative sign of electric field strength and polarization

Normal Mode Shear Mode extension torsion bending shear warping warping 

The simultaneous consideration of actuation and sensing, as instituted by the developed theory, becomes interesting as soon as a control unit is incorporated into the simulation. Since this would exceed the scope of the work at hand, we will refrain from such additional complexity within the exemplary calculations. Thus, the consequences for the electrical interconnection of layers read  

Remark 10.1. A single group of electrically paralleled laminae is taken into account for the example configuration. 

Due to the reversibility of the piezoelectric effect and the accomplished homogeneous representation of mechanical and electric measures, it is sufficient to prove the reliability of the method for either actuation or sensing in 

With regard to the above discussions and with the integral blade actuation for the helicopter application in mind, as illustrated in Section 2.5, the example configuration schemes will be focused as follows  

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The change of the relative sign of electric field strength and polarization is associated with the reversal of the deformation direction. To actuate or sense the different beam deformations, the cross-section can be divided into sectors with alternating polarization but with common electric field strength by appropriate interconnection of electrodes. For a clear correlation, these sectors need to be delimited by the relevant principal axes of the cross-section, as shown in Figure 10.1. 

Fig. 10.1. Relative sign of electric field strength and polarization in the cross-sectional sectors.

To achieve actuation or sensing according to schemes I or II of Table 10.2, the relative sign of electric field strength and polarization needs to be constant all over the cross-section ... 

The basis of these examinations are the set-up of walls and the associated actuation schemes as described in Sections 10.1.2 and 10.1.1, respectively. The variables of the optimization problem at hand are the layer orientation angles ol and 02, the relative thickness h of the central, lengthwise oriented fiber layer, and the fiber volume fraction v. The effects of the relative sign of electric field strength and polarization, being allowed to change between layers as well as between sectors, are represented in a discrete manner by the actuation schemes of Table 10.2. 

To be able to model different actuation and sensing schemes, the relative sign of polarization and electric field strength may alternate around the cross-section. It will be summarized in the vector p s) with an entry for every group of electrically paralleled laminae, as exemplarily introduced by Eq. (6.6) ... 

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