Hans Irschik, Michael Krommer, Alexander Belyaev, Kurt Schlacher,
"Shaping of Piezoelectric Sensors/Actuators for Vibrations of Slender Beams: Coupled Theory and Inappropriate Shape Functions."
, in Journal of Intelligent Material Systems and Structures, Vol. 9, Nummer 7, Seite(n) 546-554, 7-1998, ISSN: 1045-389X

Original Titel:

Shaping of Piezoelectric Sensors/Actuators for Vibrations of Slender Beams: Coupled Theory and Inappropriate Shape Functions.

Sprache des Titels:

Englisch

Original Kurzfassung:

Flexural vibrations of smart slender beams with integrated piezoelectric actuators and sensors are considered. A spatial variation of the sensor/actuator activity is achieved by shaping the surface electrodes and/or varying the polarization profile of the piezoelectric layers, and this variation is characterized by shape functions. Seeking shape functions for a desired purpose is termed a shaping problem. Utilizing the classical lamination theory of slender composite beams, equation for shaped sensors and actuators are derived. The interaction of mechanical, electrical and thermal fields is taken into account in the form of effective stiffness parameters and effective thermal bending moments. Self-sensing actuators are included. From these sensor/actuator equations, shaping problems with a practical relevance are formulated and are cast in the form of integral equations fo the first kind for the shape functions. As a pracitcal interesting aspect of these inverse problems, shape functions which fail to measure or to induce certain structural deformations are investigated in the present paper. Such inappropriate shape functions are termed nilpotent solutions of the shaping problems. In order to derive an easy-to-obtain class of such nilpotent solutions, the homogeneous versions of the integralequations for the shaping problems are compared to orthogonality relations valid for redundant beams. Hence, by analogy, the presented nilpotent solutions are shown to correspond to solutions of the basic theory of thermoelastic structures, namely to thermally induced static bending moment distributions. This result beautifully reflects the close connection between the theory of thermally loaded structures and the theory of smart structures. A particular result for nilpotent shape function previously investigated in the literature is explained in the context of the present theory, and examples of nilpotent shape functions for various strcutural systems are presented.

Sprache der Kurzfassung:

Englisch

Englische Kurzfassung:

Flexural vibrations of smart slender beams with integrated piezoelectric actuators and sensors are considered. A spatial variation of the sensor/actuator activity is achieved by shaping the surface electrodes and/or varying the polarization profile of the piezoelectric layers, and this variation is characterized by shape functions. Seeking shape functions for a desired purpose is termed a shaping problem. Utilizing the classical lamination theory of slender composite beams, equation for shaped sensors and actuators are derived. The interaction of mechanical, electrical and thermal fields is taken into account in the form of effective stiffness parameters and effective thermal bending moments. Self-sensing actuators are included. From these sensor/actuator equations, shaping problems with a practical relevance are formulated and are cast in the form of integral equations fo the first kind for the shape functions. As a pracitcal interesting aspect of these inverse problems, shape functions which fail to measure or to induce certain structural deformations are investigated in the present paper. Such inappropriate shape functions are termed nilpotent solutions of the shaping problems. In order to derive an easy-to-obtain class of such nilpotent solutions, the homogeneous versions of the integralequations for the shaping problems are compared to orthogonality relations valid for redundant beams. Hence, by analogy, the presented nilpotent solutions are shown to correspond to solutions of the basic theory of thermoelastic structures, namely to thermally induced static bending moment distributions. This result beautifully reflects the close connection between the theory of thermally loaded structures and the theory of smart structures. A particular result for nilpotent shape function previously investigated in the literature is explained in the context of the present theory, and examples of nilpotent shape functions for various strcutural systems are presented.

Journal:

Journal of Intelligent Material Systems and Structures

Volume:

9

Number:

7

Seitenreferenz:

546-554

Erscheinungsmonat:

7

Erscheinungsjahr:

1998

ISSN:

1045-389X

Anzahl der Seiten:

9

Notiz zur Publikation:

Irschik H., Krommer M., Belyaev A., Schlacher K.: Shaping of Piezoelectric Sensors/Actuators for Vibrations of Slender Beams: Coupled Theory and Inappropriate Shape Functions, In: Journal of Intelligent Materials Systems and Structures, Vol. 9, No. 7, ISSN: 1045-389X, pp. 546-554, 1998.