H.-J. Hardtke

Modelling of Components of the Human Middle Ear and Simulation of Their Dynamic Behaviour

In order to get a better insight into the function of the human middle ear it is necessary to simulate its dynamic behaviour by means of the finite-element method. Three-dimensional measurements of the surfaces of the tympanic membrane and of the auditory ossicles malleus, incus and stapes are carried out and geometrical models are created. On the basis of these data, finite-element models are constructed and the dynamic behaviour of the combinations tympanic membrane with malleus in its elastic suspensions and stapes with annular ligament is simulated. Natural frequencies and mode shapes are computed by modal analysis. These investigations showed that the ossicles can be treated as rigid bodies only in a restricted frequency range from 0 to 3.5 kHz.

UNCERTAINTY QUANTIFICATION IN STOCHASTIC SYSTEMS USING POLYNOMIAL CHAOS EXPANSION

In recent years, extensive research has been reported about a method which is called the generalized polynomial chaos expansion. In contrast to the sampling methods, e.g., Monte Carlo simulations, polynomial chaos expansion is a nonsampling method which represents the uncertain quantities as an expansion including the decomposition of deterministic coefficients and random orthogonal bases. The generalized polynomial chaos expansion uses more orthogonal polynomials as the expansion bases in various random spaces which are not necessarily Gaussian. A general review of uncertainty quantification methods, the theory, the construction method, and various convergence criteria of the polynomial chaos expansion are presented. We apply it to identify the uncertain parameters with predefined probability density functions. The new concepts of optimal and nonoptimal expansions are defined and it demonstrated how we can develop these expansions for random variables belonging to the various random spaces. The calculation of the polynomial coefficients for uncertain parameters by using various procedures, e.g., Galerkin projection, collocation method, and moment method is presented. A comprehensive error and accuracy analysis of the polynomial chaos method is discussed for various random variables and random processes and results are compared with the exact solution or/and Monte Carlo simulations. The method is employed for the basic stochastic differential equation and, as practical application, to solve the stochastic modal analysis of the microsensor quartz fork. We emphasize the accuracy in results and time efficiency of this nonsampling procedure for uncertainty quantification of stochastic systems in comparison with sampling techniques, e.g., Monte Carlo simulation.

Shape optimization of a vehicle hat-shelf: Improving acoustic properties for different load cases by maximizing first eigenfrequency

Abstract This paper presents design optimization of the geometry of a vehicle hat-shelf. At first two existing finite element discretizations are investigated for two different element types. The structural model is then parameterized. Only four design variables have been chosen to control the shape modification of the hat-shelf. The aim of this paper is to decrease the vehicle interior noise due to three different excitations for two cases of fluid damping. With respect to the support conditions of the hat-shelf these three load cases and the two cases of different damping are considered simultaneously by maximizing the lowest eigenfrequency of the structural model. Although remarkable differences in the natural frequencies are discovered for the four discretizations, a similar dependence of the objective function in terms of the design variables is observed. Thus, a multigrid strategy can be applied. The coarsest mesh is used to obtain suitable initial sets of optimization variables, one of the finer meshes serves for a pre-optimization and the finest mesh is optimized to find the final set of parameters. While the lowest eigenfrequency of the original model is found at about 31 Hz, the corresponding value in the optimized variant exceeds 100 Hz being the upper bound of the frequency range under consideration. Evaluation of the noise transfer function proves that this strategy decreases its average between 4.4 and 13.9 dB.

Evaluation of implantable actuators by means of a middle ear simulation model.

The extension of indication of implantable hearing aids to cases of conductive hearing loss pushed the development of these devices. There is now a great variety of devices available with different actuator concepts and different attachment points to the middle ear or inner ear fluid. But there is little comparative data available about the devices to provide an insight into advantages and disadvantages of different types of actuators and attachment points at the ossicular chain. This paper investigates two principle (idealized) types of actuators in respect of attachments points at the ossicular chain and direction of excitation. Other parts of implantable hearing aids like microphone, amplifier and signal processing electronics were not incorporated into this study. Investigations were performed by means of a mathematical simulation model of the middle ear (finite element model). Actuator performance and theoretical gain were calculated by harmonic analysis in the frequency range of 100-6000 Hz and were compared for the different situations. The stapes head proofed to be an ideal attachment point for actuators of both types as this position is very insensitive to changes in the direction of excitation. The implantable actuators showed higher ratio of equivalent sound pressure to radiated sound pressure compared to an open hearing aid transducer and should therefore allow for more functional gain.

EXPERIMENTAL VERIFICATION OF STRUCTURAL-ACOUSTIC MODELLING AND DESIGN OPTIMIZATION

A number of papers have been published on the simulation of structural-acoustic design optimization. However, extensive work is required to verify these results in practical applications. Herein, a steel box of 1.0×1.1×1.5 meters with an external beam structure welded on three surface plates was investigated. This investigation included experimental modal analysis and experimental measurements of certain noise transfer functions (sound pressure at points inside the box due to force excitation at beam structure). Using these experimental data, the finite element model of the structure was tuned to provide similar results. With a first structural mode at less than 20 Hertz the reliable frequency range was identified up to about 60 Hertz. Obviously, the finite element model could not be further improved only by mesh refinement. The tuning process will be explained in detail since there was a number of changes that helped to improve the structure. Other changes did not improve the structure. Although this model of the box could be expected as a rather simple structure it can be considered to be a complex structure for simulation purposes. A defined modification of the physical model verified the simulation model. In a final step, the optimal location of stiffening beam structures was predicted by simulation. Their effect on the noise transfer function was experimentally verified. This paper critically discusses modeling techniques that are applied for structural-acoustic simulation of sedan bodies.

Identification of Parameters for the Middle Ear Model

This paper presents a method of parameter identification for a finite-element model of the human middle ear. The parameter values are estimated using a characterization of the difference in natural frequencies and mode shapes of the tympanic membrane between the model and the specimens. Experimental results were obtained from temporal bone specimens under sound excitation (300–3,000 Hz). The first 3 modes of the tympanic membrane could be observed with a laser scanning vibrometer and were used to estimate the stiffness parameters for the orthotropic finite-element model of the eardrum. A further point of discussion is the parameter sensitivity and its implication for the identification process.

Application of the concept of acoustic influence coefficients for the optimization of a vehicle roof

Abstract To improve the acoustic behaviour of vehicles is an increasing challenge for every car manufacturer. The sound pressure at the drivers ear due to an arbitrary excitation of the structure can be calculated by a harmonic analysis first of the structure and then of the fluid. Using the concept of influence coefficients one has to carry out the harmonic analysis of the fluid only once to determine the sound pressure at the drivers ear. If the influence coefficients are available one has to solve an easy algebraic relation instead of a full harmonic analysis. This requires that geometry modifications are small compared with the acoustic wave lengths. So, the computational expenditure is mainly confined to the harmonic analysis of the structure. In this paper, the principal way of carrying out an optimization of a vehicle body is presented for the example of a vehicle roof. The parametric geometry based model of the roof is time harmonically excited. All other parts of the body are considered to remain rigid. Admittance boundary conditions are included. Results are presented for different loads and frequency domains, for limited and for unlimited permissible variations of the geometry and for different modal dampings.

A study on the acoustic boundary admittance. Determination, results and consequences

Abstract The acoustic boundary admittance condition represents the stiffness, the mass and the damping behaviour of the surrounding structure. The harmonic analysis of small interior domains (e.g. vehicle cabin) is often carried out only by applying acoustically rigid boundaries since the admittances are unknown or unreliably determined by commonly applied methods. Determination using an impedance tube (or Kundts tube) does not consider the real sound field; the calculation from the measured reverberation time provides an average admittance (and no phase information) of the whole boundary only. Beginning with the definition of the complex-valued boundary admittance, a brief review of the techniques to determine boundary admittances is followed by a boundary element based method that is suited to calculate the boundary admittances from a known sound pressure field. In addition to known methods, a formulation is found where the nodal admittance is calculated by the quotient of a nodal particle velocity divided by the nodal sound pressure. The nodal particle velocity can be calculated from a known sound pressure field solving a Dirichlet problem. The methods are applied to three simple examples. Finally, other examples are given to demonstrate how the boundary admittance can represent the fluid–structure interaction and phase angle of admittance influences the complex-valued eigenfrequencies.

Estimation of Radiated Sound Power: A Case Study on Common Approximation Methods

The radiated sound power value is often used to evaluate the sound radiation of a machine or a product. Since its estimation requires the sound pressure on a surrounding surface of the radiating object, the sound power value is mostly computed under high numerical costs due to the acoustic field that has to be modeled. Therefore, approximations of the sound pressure are widely popular. In this article three common methods namely the equivalent radiated power, the lumped parameter model and an approximation based on the volume velocity are investigated. It is the goal of this paper to test these methods on realistic examples. The radiated sound power functions of the floor panel of a car and the radiation of a diesel engine under realistic load cases are estimated.

A general concept for design modification of shell meshes in structural-acoustic optimization: part II: Application to a floor panel in sedan interior noise problems

The second part of this paper is dedicated to the application of the new concept that was outlined in the first part. Using this concept, one manipulates the geometry of a finite element shell mesh directly. Part of a sedan floor structure is chosen for this application. A plane rectangular domain of the floor panel is defined as modification domain. The number of 33 design variables consists of nine defining the global modification function and 24 that altogether define four local modification functions, It will be demonstrated in this paper that combination of global and local modification functions allows a great variety of new shapes. In the particular case of design optimization, the root mean square value of the noise transfer function is decreased by about two decibel. Contribution analysis allows to detect reasons for decrease and increase of the optimums noise transfer function at certain frequencies in comparison to the original model. Finally, this result is discussed and compared with other results of structural-acoustic optimization.