Manfred Kaltenbacher

Numerical Simulation of Mechatronic Sensors and Actuators

Introduction.- The Finite Element Method (FEM).- Mechanical Field - Electromagnetic Field.- Acoustic Field.- Coupled Electrostatic-Mechanical Systems.- Coupled Magnetomechanical Systems.- Coupled Mechanical-Acoustic Systems.- Piezoelectric Systems.- Multigrid Solvers.- Industrial Applications.- Summery and Outlook.- References.- Index.

Flow-structure-acoustic interaction in a human voice model

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.

Nested multigrid methods for the fast numerical computation of 3D magnetic fields

This paper deals with the numerical solution of static as well as transient 3D magnetic field problems. A finite element method (FEM) with the magnetic vector potential as field variable and a discretization with edge elements is used. For the efficient solution of the obtained matrix equation system a nested geometrical multigrid solver (MG) is presented, which reduces the solution time considerably. Numerical simulations demonstrate the superiority of the proposed method versus conventional solving strategies.

FEM-Based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials

We propose an enhanced iterative scheme for the precise reconstruction of piezoelectric material parameters from electric impedance and mechanical displacement measurements. It is based on finite-element simulations of the full three-dimensional piezoelectric equations, combined with an inexact Newton or nonlinear Landweber iterative inversion scheme. We apply our method to two piezoelectric materials and test its performance. For the first material, the manufacturer provides a full data set; for the second one, no material data set is available. For both cases, our inverse scheme, using electric impedance measurements as input data, performs well.

Efficient Modeling of Ferroelectric Behavior for the Analysis of Piezoceramic Actuators

This work proposes a method of efficiently modeling the hysteresis of ferroelectric materials. Our approach includes the additive combination of a reversible and an irreversible portion of the polarization and strain, respectively. Whereas the reversible parts correspond to the common piezoelectric linear equations, the irreversible parts are modeled by hysteresis operators. These operators are based on Preisach and Jiles-Atherton hysteresis models which are well-established tools in ferromagnetic modeling. In contrast to micromechanical approaches, a Preisach or a Jiles-Atherton hysteresis operator can be efficiently numerically evaluated. A comparison of the resulting simulations to measured data concludes the article.

Finite element simulation of nonlinear wave propagation in thermoviscous fluids including dissipation

A recently developed finite element method (FEM) for the numerical simulation of nonlinear sound wave propagation in thermoviscous fluids is presented. Based on the nonlinear wave equation as derived by Kuznetsov, typical effects associated with nonlinear acoustics, such as generation of higher harmonics and dissipation resulting from the propagation of a finite amplitude wave through a thermoviscous medium, are covered. An efficient time-stepping algorithm based on a modification of the standard Newmark method is used for solving the nonlinear semidiscrete equation system. The method is verified by comparison with the well-known Fubini and Fay solutions for plane wave problems, where good agreement is found. As a practical application, a high intensity focused ultrasound (HIFU) source is considered. Impedance simulations of the piezoelectric transducer and the complete HIFU source loaded with air and water are performed and compared with measured data. Measurements of radiated low and high amplitude pressure pulses are compared with corresponding simulation results. The obtained good agreement demonstrates validity and applicability of the nonlinear FEM.

An efficient calculation scheme for the numerical simulation of coupled magnetomechanical systems

A recently developed modeling scheme for the numerical simulation of coupled magnetomechanical systems immersed in an acoustic fluid is presented. The scheme allows the calculation of dynamic rigid motions as well as deformations of magnetic and anti-magnetic materials in a magnetic field. The equations governing the magnetic, mechanical and acoustic field quantities are solved using a combined finite-element-boundary-element-method (FEM-BEM), resulting in a separation of the stationary and the moving parts of the structure. Therewith, the well known problem of mesh distortion in finite element techniques due to moving parts can be avoided. A computer simulation of a magnetomechanical transducer immersed in an acoustic fluid (acoustic power source) is presented demonstrating the efficiency of the developed algorithm.

A modified and stable version of a perfectly matched layer technique for the 3-d second order wave equation in time domain with an application to aeroacoustics

We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems.

Mathematical Models and Numerical Schemes for the Simulation of Human Phonation

Acoustic data has long been harvested in fundamental voice investigations since it is easily obtained using a microphone. However, acoustic signals alone do not reveal much about the complex interplay between sound waves, structural surface waves, mechanical vibrations, and fluid flow involved in phonation. Available high speed imaging techniques have over the past ten years provided a wealth of information about the mechanical deformation of the superior surface of the larynx during phonation. Time-resolved images of the inner structure of the deformable soft tissues are not yet feasible because of low temporal resolution (MRI and ultrasound) and x-ray dose-related hazards (CT and standard x- ray). One possible approach to circumvent these challenges is to use mathematical models that reproduce observable behavior such as phonation frequency, closed quotient, onset pressure, jitter, shimmer, radiated sound pressure, and airflow. Mathematical models of phonation range in complexity from systems with relatively small degrees of freedom (multi-mass models) to models based on partial differential equations (PDEs) mostly solved by finite element (FE) methods resulting in millions of degrees-of-freedom. We will provide an overview about the current state of mathematical models for the human phonation process, since they have served as valuable tools for providing insight into the basic mechanisms of phonation and may eventually be of sufficient detail and accuracy to allow surgical planning, diagnostics, and rehabilitation evaluations on an individual basis. Furthermore, we will also critically discuss these models w.r.t. the used geometry, boundary conditions, material properties, their verification, and reproducibility.

Finite element analysis of coupled electromagnetic acoustic systems

Electromagnetic acoustic transducers (EMATs) are used for nondestructive testing of electric conductive materials. In this paper, the authors introduce an efficient numerical calculation scheme, based on the finite element method, which is capable of simulating both the transmission and detection of ultrasonic waves by EMATs. Therefore, the generation of waves by electromagnetic forces (transmitting case), as well as the induced voltage resulting from the magnetic field of eddy currents, which are generated by the waves in a constant magnetic field, can be calculated. 2D computer simulations and measured data obtained with a pair of matched plate wave EMATs are presented to show the applicability of the developed calculation scheme.