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The piezoelectric effect, which was discovered for the first time by the brothers Pierre and Jacques Curie, combines electrical with mechanical quantities and vice versa. If piezoelectric materials (e.g. quartz, turmaline) are subjected to electrical signals along certain crystal orientations, deformations along well-defined crystal orientations appear. Contrary, a mechanical deformation results in a generation of polarization charges. Even if there exist numerous publications on this so-called direct and reciprocal piezoelectric effect, the aim of this paper is to convey a clear and easy understanding of this essential solid body effect in particular for the non-specialist, since a large number of publications is rather superficial and unfortunately sometimes incorrect. A variety of ionic crystals show the direct and reciprocal piezoelectric effect. In this paper, an illustrative representation of both effects is given by the molecular structure of alpha-quartz, a stable modification of the silicon dioxide, the second most common mineral of the earth’s crust. Both effects always involve an important physical quantity, the so-called electrical polarization, which represents an Euclidean vector being defined as the quotient of the total dipole moment resulting from the deformation of the hexagonal unit cell of alpha-quartz and the volume of the unit cell. Based on the physical explanation of the dipole moment, it is shown how the directions of the electrical polarization can be calculated in a simple manner. This finally enables the physical understanding of both effects that are nowadays used in numerous technical applications in the broad field of sensor and actuator technologies.

The design and construction of electromechanical and electroacoustic systems necessitates the knowledge of the dynamic behavior during the design phase, since certain dynamic target parameters must be fulfilled among other requirements. Also the control of an existing system often requires the modeling of the dynamic behavior. This model then allows for simulations. The simulation results are important for further decisions. In order to think purposefully about a task or to discuss with partners, an available model is also useful. Models that focus on the important aspects of the dynamic behavior are especially suitable for this purpose.

Material Characteristics of Crystalline Quartz, Piezoelectric Constants of Sensor Materials, Characteristics of Metallic Structural Materials, Material Characteristics of Silicon and Passivation Layers, Comparison of Main Characteristics of Silicon, Silicon Dioxide and Silicone Nitride Layers

With numerical analyses it is not possible to implement the summation over i from 0 to ∞. However, since the a i and b i converge to zero only for i → ∞, a summation up to i = M ≫ 1 generates only an approximation error that can be estimated with (B.1).

In each case, reciprocity relations represent connections between two transfer factors and transfer impedances or admittances of a linear system, respectively. These relations provide a basis for a series of measuring methods and allow in many cases also for the calculation of relations which would be only achieved with large calculating effort otherwise. In networks of a physical structure they are identical to the symmetry of the ρ- and γ-matrices with respect to the main diagonal represented in Sect. 2.2 and Chap. 4. In this chapter, special conclusions are drawn for two-port networks, i.e. for the interconnection of two pairs of coordinates. By means of the well-known characteristics of tranducer two-port networks, it is particularly demonstrated that also reciprocity relations exist for systems which comprise different physical structures. These relations are of particular practical importance.

The previous network analysis was solely carried out for systems with lumped components. Now an extension to systems with distributed, thus positiondependent parameters is realized. If the wavelength of extensional waves at higher frequencies reaches the order of magnitude of component dimensions, this extension will be inevitable. In the Sects. 6.1 and 6.2, these mechanical and acoustic systems are described as one-dimensional waveguides. The discretized representation in the form of finite network elements takes place in Sect. 6.3. Finally, a method of combined simulation of FEM calculation and network description is presented in Sect. 6.4.

Elektromechanische Systeme aus elektrischen, mechanischen und akustischen Teilsystemen haben im Prazisionsgeratebau, in der Sensorund Aktortechnik, der Elektroakustik sowie in der Medizintechnik eine grose Bedeutung. Die Vermittlung einer anschaulichen, ingenieurmasigen Entwurfsmethode fur diese Systeme auf der Grundlage einer schaltungstechnischen Darstellung ist das Hauptanliegen des Lehrbuchs. Es ermoglicht einen raschen Einstieg in die mechanischen, akustischen, hydraulischen und thermischen Problemstellungen durch die Anwendung des schaltungstechnischen Grundwissens. Die 2. Auflage wurde neu bearbeitet und didaktisch verbessert. Die Netzwerkbeschreibungsmethodik wurde auf finite Netzwerkelemente und die Kombination mit der Finite-Elemente-Beschreibung (FEM) erweitert: aus der Kombination der Vorteile beider Beschreibungsmethoden ergeben sich neuartige Losungsansatze vor allem im hoheren Frequenzbereich. Das Buch bietet zahlreiche aktuelle Beispiele zum Entwurf von Sensoren und Aktoren sowie von direkt gekoppelten Sensor-Aktor-Systemen. Der Anhang enthalt anspruchsvollere Grundlagen zur Signalbeschreibung sowie eine Zusammenstellung wichtiger Materialdaten.