PrefaceThe focus of this book is concerned with the modeling and precise numerical simulation of mechatronic sensors and actuators. These sensors, actuators, and sensor -actuator systems are based on the mutual interaction of the mechanical field with a magnetic, an electrostatic or an electromagnetic field. In many cases the transducer is immersed in an acoustic fluid and the solid-fluid coupling has to be taken into account. Examples are: piezoelectric stack actuators for common-rail injection systems, micromachined electrostatic gyro sensors used in stabilizing systems of automobiles or ultrasonic imaging systems for medical diagnostics.The modeling of mechatronic sensors and actuators leads to so-called multifield problems, which are described by a system of nonlinear partial differential equations. Such systems can not be solved analytically and, thus a numerical calculation scheme has to be applied. The schemes discussed in this book are based on the finite element (FE) method, which is capable of efficiently solving the partial differential equations. The complexity of the simulation of multifield problems consists in the simultaneous computation of the involved single fields as well as in the coupling terms, which introduce additional nonlinearities. Examples are: moving conductive (electrically charged) body within a magnetic (an electric) field, electromagnetic and/or electrostatic forces.The goal of this book is to present a comprehensive survey of the main physical phenomena of multifield problems and, in addition, to discuss calculation schemes for the efficient solution of coupled partial differential equations applying the FE method. We will concentrate on electromagnetic, mechanical, and acoustic fields with the following mutual interactions: • Coupling Electric Field -Mechanical FieldThis coupling is either based on the piezoelectric effect or results from the force on an electrically charged structure in an electric field (electrostatic force). VI Preface • Coupling Magnetic Field -Mechanical FieldThis coupling is two-fold. First, we have the electromotive force (emf), which describes the generation of an electric field (electric voltage respectively current) when a conductor is moved in a magnetic field, and secondly, the electromagnetic force. • Coupling Mechanical Field -Acoustic FieldVery often a transducer is surrounded by a fluid or a gaseous medium in which an acoustic wave is launched (actuator) or is impinging from an outside source towards the receiving transducer.In Chap. 2, we give an introduction to the finite element (FE) method. Starting from the strong form of a general partial differential equation we describe all the steps concerning spatial as well as time discretization to arrive at an algebraic system of equations. Both nodal and edge finite elements are introduced. Special emphasis is put on an explanation of all the important steps necessary for the computer implementation.A detailed discussion on electromagnetic, mechanical, and acoustic fields including their numerical c...

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SUMMARYFlexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated, focussing on aero-acoustic and elasto-acoustic coupling. In particular, the advantages of using non-matching grids are presented, when one subregion has to be resolved by a substantially finer grid than the other subregion. For the elasto-acoustic coupling, the problem formulation remains essentially the same as for the matching situation, while for the aero-acoustic coupling, the formulation is enhanced with Lagrange multipliers within the framework of mortar finite element methods. Several numerical examples are presented to demonstrate the flexibility and applicability of the approach.

For the investigation of the physical processes of human phonation, inhomogeneous synthetic vocal folds were developed to represent the full fluid-structure-acoustic coupling. They consisted of polyurethane rubber with a stiffness in the range of human vocal folds and were mounted in a channel, shaped like the vocal tract in the supraglottal region. This test facility permitted extensive observations of flow-induced vocal fold vibrations, the periodic flow field, and the acoustic signals in the far field of the channel. Detailed measurements were performed applying particle-image velocimetry, a laser-scanning vibrometer, a microphone, unsteady pressure sensors, and a hot-wire probe, with the aim of identifying the physical mechanisms in human phonation. The results support the existence of the Coanda effect during phonation, with the flow attaching to one vocal fold and separating from the other. This behavior is not linked to one vocal fold and changes stochastically from cycle to cycle. The oscillating flow field generates a tonal sound. The broadband noise is presumed to be caused by the interaction of the asymmetric flow with the downstream-facing surfaces of the vocal folds, analogous to trailing-edge noise.

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