Modelling and validation of the non-linear elastic stress-strain behaviour of multi-layer silicone composites.

Multi-layer silicone composites are commonly used to mold deformable silicone vocal folds replicas. Nevertheless, so far the stress-strain characterisation of such composite specimens is limited to their effective Young's modulus (up to 40 kPa) characterising the elastic low-strain range, i.e. up to about 0.3. Therefore, in this work, the characterisation is extended to account for the non-linear strain range. Stress-strain curves on 6 single-layer and 34 multi-layer silicone specimens, with different layer stacking (serial, parallel, combined or arbitrary), are measured at room temperature using uni-axial tensile tests for strains up to 1.36, which amounts to about 4.5 times the extent of the linear low-strain range. Cubic polynomial and exponential two-parameter relationships are shown to provide accurate continuous fits (coefficient of determination R2≥99%) of the measured stress-strain data. It is then shown that the parameters can be a priori modelled as a constant or as a linear function of the effective low-strain Young's modulus for strains up to 1.55, i.e. 5 times the low-strain range. These a priori modelled parameter are confirmed by approximations of the best fit parameters for all assessed specimens as a function of the low-strain Young's modulus. Thus, the continuous stress-strain behaviour up to 1.55 can be predicted analytically from the effective low-strain Young's modulus either using the modelled parameters (R2≥85%) or the approximations of the best fit parameter sets (R2≥94%). Accurate stress-strain predictions are particularly useful for the design of composites with different composition and stacking. In addition, analytical expressions of the linear high-strain Young's modulus and the linear high-strain onset, again as a function of the effective low-strain Young's modulus, are formulated as well.

Simulation of vowel-vowel utterances using a 3D biomechanical-acoustic model.

A link is established between biomechanical and acoustic 3D models for the numerical simulation of vowel-vowel utterances. The former rely on the activation and contraction of relevant muscles for voice production, which displace and distort speech organs. However, biomechanical models do not provide a closed computational domain of the 3D vocal tract airway where to simulate sound wave propagation. An algorithm is thus proposed to extract the vocal tract boundary from the surrounding anatomical structures at each time step of the transition between vowels. The resulting 3D geometries are fed into a 3D finite element acoustic model that solves the mixed wave equation for the acoustic pressure and particle velocity. An arbitrary Lagrangian-Eulerian framework is considered to account for the evolving vocal tract. Examples include six static vowels and three dynamic vowel-vowel utterances. Plausible muscle activation patterns are first determined for the static vowel sounds following an inverse method. Dynamic utterances are then generated by linearly interpolating the muscle activation of the static vowels. Results exhibit nonlinear trajectory of the vocal tract geometry, similar to that observed in electromagnetic midsagittal articulography. Clear differences are appreciated when comparing the generated sound with that obtained from direct linear interpolation of the vocal tract geometry. That is, interpolation between the starting and ending vocal tract geometries of an utterance, without resorting to any biomechanical model.

Finite element generation of sibilants /s/ and /z/ using random distributions of Kirchhoff vortices.

The numerical simulation of sibilant sounds in three-dimensional realistic vocal tracts constitutes a challenging problem because it involves a wide range of turbulent flow scales. Rotating eddies generate acoustic waves whose wavelengths are inversely proportional to the flow local Mach number. If that is low, very fine meshes are required to capture the flow dynamics. In standard hybrid computational aeroacoustics (CAA), where the incompressible Navier-Stokes equations are first solved to get a source term that is secondly input into an acoustic wave equation, this implies resorting to supercomputer facilities. As a consequence, only very short time intervals of the sibilant can be produced, which may be enough for its spectral characterization but insufficient to synthesize, for instance, an audio file from it or a syllable sound. In this work, we propose to substitute the aeroacoustic source term obtained from the computational fluid dynamics (CFD) in the first step of hybrid CAA, by a random distribution of Kirchhoff's spinning vortices, located in the region between the upper incisors and the lower lip. In this way, one only needs to solve a linear wave equation to generate a sibilant, and therefore avoids the costly large-scale computations. We show that our proposal can recover the outcomes of hybrid CAA simulations in average, and that it can be applied to generate sibilants /s/ and /z/. Modeling and implementation details of the Kirchhoff vortex distribution in a stabilized finite element code are discussed in the paper, as well as the outcomes of the simulations.

Reconstruction of vocal tract geometries from biomechanical simulations.

Medical imaging techniques are usually utilized to acquire the vocal tract geometry in 3D, which may then be used, eg, for acoustic/fluid simulation. As an alternative, such a geometry may also be acquired from a biomechanical simulation, which allows to alter the anatomy and/or articulation to study a variety of configurations. In a biomechanical model, each physical structure is described by its geometry and its properties (such as mass, stiffness, and muscles). In such a model, the vocal tract itself does not have an explicit representation, since it is a cavity rather than a physical structure. Instead, its geometry is defined implicitly by all the structures surrounding the cavity, and such an implicit representation may not be suitable for visualization or for acoustic/fluid simulation. In this work, we propose a method to reconstruct the vocal tract geometry at each time step during the biomechanical simulation. Complexity of the problem, which arises from model alignment artifacts, is addressed by the proposed method. In addition to the main cavity, other small cavities, including the piriform fossa, the sublingual cavity, and the interdental space, can be reconstructed. These cavities may appear or disappear by the position of the larynx, the mandible, and the tongue. To illustrate our method, various static and temporal geometries of the vocal tract are reconstructed and visualized. As a proof of concept, the reconstructed geometries of three cardinal vowels are further used in an acoustic simulation, and the corresponding transfer functions are derived.

Computational aeroacoustics to identify sound sources in the generation of sibilant /s/.

A sibilant fricative /s/ is generated when the turbulent jet in the narrow channel between the tongue blade and the hard palate is deflected downwards through the space between the upper and lower incisors and then impinges the space between the lower incisors and the lower lip. The flow eddies in that region become a source of direct aerodynamic sound, which is also diffracted by the speech articulators and radiated outwards. The numerical simulation of these phenomena is complex. The spectrum of an /s/ typically peaks between 4 and 10 kHz, which implies that very fine computational meshes are needed to capture the eddies producing such high frequencies. In this work, a large-scale computation of the aeroacoustics of /s/ has been performed for a realistic vocal tract geometry, resorting to two different acoustic analogies. A stabilized finite element method that acts as a large eddy simulation model has been adopted to solve the flow dynamics. Also, a numerical strategy has been implemented that allows the determination, in a single computational run, of the separate contribution of the sound diffracted by the upper incisors from the overall radiated sound. Results are presented for points located close to the lip opening showing the relative influence of the upper teeth depending on frequency.

Construction of an Omnidirectional Parametric Loudspeaker Consisting in a Spherical Distribution of Ultrasound Transducers.

Omnidirectional sound sources are needed to perform a large variety of tests in acoustics. Typically, they consist of conventional speaker drivers arranged in a dodecahedron. However, the directivity of the speaker drivers sharpens with frequency, which induces an intense decrease of the sound pressure levels at the edges of the dodechaedron. In this work, the problem is mitigated by building an Omnidirectional Parametric Loudspeaker (OPL), which contains hundreds of small ultrasound transducers set on a sphere. Each transducer emits an ultrasonic carrier wave modulated by an audible signal. Thanks to nonlinear propagation, the air itself demodulates the signal bringing it back to the audible range. The construction of an OPL prototype is challenging. The structure has been built by 3D-printing a set of pieces that conform to the sphere. Each piece contains the exact location of the transducers, which are aligned in parallels to facilitate the structural assembly and the wiring. The performance of the OPL has been tested in an anechoic chamber. Measurements show that the OPL has a good omnidirectional behavior for most frequencies. It clearly improves the directivity of dodechaedral sources in the high frequency range, but performs worse at low frequencies.

Influence of vocal tract geometry simplifications on the numerical simulation of vowel sounds.

For many years, the vocal tract shape has been approximated by one-dimensional (1D) area functions to study the production of voice. More recently, 3D approaches allow one to deal with the complex 3D vocal tract, although area-based 3D geometries of circular cross-section are still in use. However, little is known about the influence of performing such a simplification, and some alternatives may exist between these two extreme options. To this aim, several vocal tract geometry simplifications for vowels [ɑ], [i], and [u] are investigated in this work. Six cases are considered, consisting of realistic, elliptical, and circular cross-sections interpolated through a bent or straight midline. For frequencies below 4-5 kHz, the influence of bending and cross-sectional shape has been found weak, while above these values simplified bent vocal tracts with realistic cross-sections are necessary to correctly emulate higher-order mode propagation. To perform this study, the finite element method (FEM) has been used. FEM results have also been compared to a 3D multimodal method and to a classical 1D frequency domain model.

Influence of lips on the production of vowels based on finite element simulations and experiments.

Three-dimensional (3-D) numerical approaches for voice production are currently being investigated and developed. Radiation losses produced when sound waves emanate from the mouth aperture are one of the key aspects to be modeled. When doing so, the lips are usually removed from the vocal tract geometry in order to impose a radiation impedance on a closed cross-section, which speeds up the numerical simulations compared to free-field radiation solutions. However, lips may play a significant role. In this work, the lips' effects on vowel sounds are investigated by using 3-D vocal tract geometries generated from magnetic resonance imaging. To this aim, two configurations for the vocal tract exit are considered: with lips and without lips. The acoustic behavior of each is analyzed and compared by means of time-domain finite element simulations that allow free-field wave propagation and experiments performed using 3-D-printed mechanical replicas. The results show that the lips should be included in order to correctly model vocal tract acoustics not only at high frequencies, as commonly accepted, but also in the low frequency range below 4 kHz, where plane wave propagation occurs.

Effects of higher order propagation modes in vocal tract like geometries.

In this paper, a multimodal theory accounting for higher order acoustical propagation modes is presented as an extension to the classical plane wave theory. This theoretical development is validated against experiments on vocal tract replicas, obtained using a 3D printer and finite element simulations. Simplified vocal tract geometries of increasing complexity are used to investigate the influence of some geometrical parameters on the acoustical properties of the vocal tract. It is shown that the higher order modes can produce additional resonances and anti-resonances and can also strongly affect the radiated sound. These effects appear to be dependent on the eccentricity and the cross-sectional shape of the geometries. Finally, the comparison between the simulations and the experiments points out the importance of taking visco-thermal losses into account to increase the accuracy of the resonance bandwidths prediction.

Two-dimensional vocal tracts with three-dimensional behavior in the numerical generation of vowels.

Two-dimensional (2D) numerical simulations of vocal tract acoustics may provide a good balance between the high quality of three-dimensional (3D) finite element approaches and the low computational cost of one-dimensional (1D) techniques. However, 2D models are usually generated by considering the 2D vocal tract as a midsagittal cut of a 3D version, i.e., using the same radius function, wall impedance, glottal flow, and radiation losses as in 3D, which leads to strong discrepancies in the resulting vocal tract transfer functions. In this work, a four step methodology is proposed to match the behavior of 2D simulations with that of 3D vocal tracts with circular cross-sections. First, the 2D vocal tract profile becomes modified to tune the formant locations. Second, the 2D wall impedance is adjusted to fit the formant bandwidths. Third, the 2D glottal flow gets scaled to recover 3D pressure levels. Fourth and last, the 2D radiation model is tuned to match the 3D model following an optimization process. The procedure is tested for vowels /a/, /i/, and /u/ and the obtained results are compared with those of a full 3D simulation, a conventional 2D approach, and a 1D chain matrix model.

Effects of head geometry simplifications on acoustic radiation of vowel sounds based on time-domain finite-element simulations.

One of the key effects to model in voice production is that of acoustic radiation of sound waves emanating from the mouth. The use of three-dimensional numerical simulations allows to naturally account for it, as well as to consider all geometrical head details, by extending the computational domain out of the vocal tract. Despite this advantage, many approximations to the head geometry are often performed for simplicity and impedance load models are still used as well to reduce the computational cost. In this work, the impact of some of these simplifications on radiation effects is examined for vowel production in the frequency range 0-10 kHz, by means of comparison with radiation from a realistic head. As a result, recommendations are given on their validity depending on whether high frequency energy (above 5 kHz) should be taken into account or not.

Directivity control and efficiency of parametric loudspeakers with horns.

This manuscript presents some recent results on directivity control and efficiency of parametric loudspeakers utilizing horns. Horns act both like an acoustic transformer and a directivity control method. An experimental device has been built and measurements have revealed that the horn has a clear influence on the audible sound levels and directivity of the parametric loudspeakers. When compared with a conventional megaphone, a much more flat frequency response is obtained and the resulting directivity is shown to be almost frequency independent.

Realization of an omnidirectional source of sound using parametric loudspeakers.

Parametric loudspeakers are often used in beam forming applications where a high directivity is required. Withal, in this paper it is proposed to use such devices to build an omnidirectional source of sound. An initial prototype, the omnidirectional parametric loudspeaker (OPL), consisting of a sphere with hundreds of ultrasonic transducers placed on it has been constructed. The OPL emits audible sound thanks to the parametric acoustic array phenomenon, and the close proximity and the large number of transducers results in the generation of a highly omnidirectional sound field. Comparisons with conventional dodecahedron loudspeakers have been made in terms of directivity, frequency response, and in applications such as the generation of diffuse acoustic fields in reverberant chambers. The OPL prototype has performed better than the conventional loudspeaker especially for frequencies higher than 500 Hz, its main drawback being the difficulty to generate intense pressure levels at low frequencies.

Finite element computation of elliptical vocal tract impedances using the two-microphone transfer function method.

A two-microphone transfer function (TMTF) method is adapted to a numerical framework to compute the radiation and input impedances of three-dimensional vocal tracts of elliptical cross-section. In its simplest version, the TMTF method only requires measuring the acoustic pressure at two points in an impedance duct and the postprocessing of the corresponding transfer function. However, some considerations are to be taken into account when using the TMTF method in the numerical context, which constitute the main objective of this paper. In particular, the importance of including absorption at the impedance duct walls to avoid lengthy numerical simulations is discussed and analytical complex axial wave numbers for elliptical ducts are derived for this purpose. It is also shown how the direct impedance of plane wave propagation can be computed beyond the TMTF maximum threshold frequency by appropriate location of the virtual microphones. Virtual microphone spacing is also discussed on the basis of the so-called singularity factor. Numerical examples include the computation of the radiation impedance of vowels /a/, /i/, and /u/ and the input impedance of vowel /a/, for simplified vocal tracts of circular and elliptical cross-sections.

Graph theory applied to noise and vibration control in statistical energy analysis models.

A fundamental aspect of noise and vibration control in statistical energy analysis (SEA) models consists in first identifying and then reducing the energy flow paths between subsystems. In this work, it is proposed to make use of some results from graph theory to address both issues. On the one hand, linear and path algebras applied to adjacency matrices of SEA graphs are used to determine the existence of any order paths between subsystems, counting and labeling them, finding extremal paths, or determining the power flow contributions from groups of paths. On the other hand, a strategy is presented that makes use of graph cut algorithms to reduce the energy flow from a source subsystem to a receiver one, modifying as few internal and coupling loss factors as possible.