PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Effective modeling of elastic waves for haptic surface interaction
Sebastian Wöckel2, Michael Simon1, Ulrike Steinmann1
1

Otto-von-Guericke Universität Magdeburg, Institut für Automatisierungstechnik, Lehrstuhl Messtechnik,
Universitätsplatz 2, 39106 Magdeburg

2

Institut für Automation und Kommunikation (ifak) e.V. Magdeburg, Department Measurement Technology andPower Electronics, Werner-Heisenberg-Str. 1, 39106 Magdeburg, E-Mail: sebastian.woeckel@ifak.eu

ABSTRACT
Guided acoustic waves can be found in multiple applications as SAW-devices, NDE, hearing aids, fluid
monitoring in tubes or resonance effects in structures. Among those examples, the contribution addresses thesound field design with linear elastic waves on thin display or touchscreen surfaces. Based on the principleof reversibility and the time reversal technique a simulation model was built up to calibrate the refocussingof vibrations on certain area. The main objective (of this work) is the haptic interaction of a finger with virtual
elements modelled by a local vibration. The simulation bases on a finite element model of structural dynamics.
In detail, the influence of elasticity, plate thickness in relation to the wavelength and the transducer positions
on the wave mode selectivity are discussed. Further the numerical calibration is used to define the signals
with respect to the contrast and resolution of tactile sensation in a focal point and the potential to selectively
focus on multiple points at the same time. Finally two demonstrators with different frequency range are used
for evaluation of the consistency of simulated and experimental excitation signals and the respective impacts
on the focal quality.
Keywords: surface wave, haptic

1. INTRODUCTION
Operating a touch-screen is a matter of course in our everyday life. However, it is not taken for
granted for everyone (e.g. in case of individual physical constraints) or in everyday situation (e.g.
unfavorable external conditions). Then, the usability is limited due to an absent haptic feedback as incase of real keys or buttons. This contribution discusses the realization of a transient elastic touch
feedback on panels and planar structures. The key components to realize a transient and local haptic
feedback (pulse or vibration) with a minimum number of actuators are guided elastic waves. Here thereversibility of an acoustic wave can be used to refocus a signal on an arbitrary local position by time
reversal (TR) techniques [1, 2]. Numerous application fields are connected to this technology, such as
medical intervention, non-destructive testing or impact localization on touchscreen systems [3, 4, 5].
Latter technology recently gains increasing attention. Therefore the contribution addresses the local
haptic feedback on panels by using acoustic transducers with randomized patterns. In the current casea limited number of acoustic transducers (Fig. 1) are placed at the edges of the structure only, omitting
the touch sensitive area, since transparent display are addressed. In contrast to known TR -procedures
no use is made of an experimental training stage to set up a database of plate impulse responses.
Instead, the transient signal at the transducer array, that is required to selectively address a point offeedback on the panel, is gained from numerical simulations. Moreover, simulation is used to define
the actuators signals with respect to the contrast and resolution of tactile sensation in a focal point
and the potential to selectively focus on multiple points at the same time. As a main result the studies
illustrate that an arbitrary time and spatial focusing of an elastic impulse can be established in theperceptual haptic frequency range. Due to the wavelength its simple application for larger devices(display) seems to be promising up to now.

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2. METHOD
2.1 Basics: Human perception
The haptic feedback that can be felt by a human fingertip (haptic perceptual detection threshold)depends on the vertical and horizontal displacement of the surface (acoustic energy), the excitation
frequency (wavelength) and the shape of the transient displacement. The lateral spatial resolution of
the perceptual active area mainly depends on the wavelength.
Due to the variety of mechanoreceptors (Fig. 2) that are sensitive to different mechanical stimulus(pressure, strain, vibration, touch) there is a differentiation in static (tactile) and dynamic active(haptic) perception [6]. The tactile perception threshold of a fingertip is in the range of 1 mm. The
maximum of the haptic sensitivity (Vater-Pacini-cell) can be found at a vibration frequency of f = 40
… 300 Hz. The corresponding sensitivity levels (perceptual threshold) of the elongation at thesefrequencies are in the range of'x > 0.2 μm for transversal displacement (Ruffini-cell) and 'z > 5 μm
for displacements vertical to the skin surface. A cumulative movement of the finger over the surface
additionally lowers the threshold (Meissner-cell). Typically, due to the ratio of the propagation
velocity (larger wavelength) to the dimension of the focus point the shear mode is unsuitable despite
the higher sensitivity (0.2 μm). Hence, the presented work concentrates on the basic asymmetricmodes (A0) of guided elastic waves.

Figure 1. Schematic model (3D-simulation example) for local vibro-haptic interaction on a plate(display) by temporal and spatial superposition of elastic waves – with a reduced number of acoustic
transducers.

Figure 2. Classification of most common mechanoreceptors of a human hand corresponding tostatic (tactile) and dynamic (haptic) characteristics of a surface: (left) Vater-Pacini-cell with highest
sensitivity to vibrations perpendicular to the skin in the range of 'z > 5 μm elongation and frequencies
from 40 Hz to 300 Hz; (middle) Meissner-cell for active exploration of elevations of 'z > 1 μm;(right) Ruffini-cell for registration of shear vibrations 'x > 0.2 μm.

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Figure 3. (a) Wavelength of asymmetric lamb-mode A0 for plates with thickness of d = 2 mm anddifferent materials (Tab. 1). (b) Illustration of the transient waveform in relation to the wavelength,
the perceptual threshold (dotted line) and effective (sensible) width of the focus.
2.2 Basics: Dispersive elastic waves
In theory, there are an unlimited number of different modes that can propagate on plate structures [9].
The phase and group velocities of each mode are dispersive and a function of frequency. Hence, it isnecessary to evaluate each mode concerning its cut-off frequency, wavelength and the verticaldisplacement, which is supposed to be the main parameter for haptic interaction. In this case theRayleigh-Lamb-differential equations [7, 8] that describe the elastic transient behaviour depending on
the geometry (plate thickness), the elasticity and the Poisson’s ratio are solved numerically using
Comsol Multiphysics. The derived solution of the phase velocities enables the geometric design ofthe plate and the selection of single wave modes towards an optimized haptic feedback. Norm ally thesolution is depicted within a dispersion diagram. As an example Fig. 3 a represents the dispersive
characteristics of the velocities for different plates with thickness of d = 2 mm. In the range of thehaptic frequency (< 300 Hz) the wavelength on selected display and surface materials varies from 160
mm to 290 mm for the asymmetric mode A0. Concerning transient elastic signals (pulse), the half of
the wavelength can be regarded as the minimal dimension of the vibrating focus. In which the effectiv esensible focus width depends on the perceptual threshold and the energ y of the signal also (Fig. 3 b).
TABLE I.

MATERIAL PARAMETERS

MaterialU[kg/m³]cL [m/s]cT [m/s]

E [GPa]

μ

Acryl

1200

2700

1200

4,76

0,38

Glass

1590

6790

4321

68.9

0.16

Steel

7850

5778

3194

205

0,28

2.3 Time Reversal of elastic waves: Technique, Principle and Challenges
The reversibility of such previous linear elastic waves is used to refocus a sig nal at one calibrated
position to a certain time step by time reversal (TR) techniques [4, 8]. Main challenges or necessary
improvements are the realization of a tempo-spatial localized short pulse on the surface withelongations in the range of the perceptual threshold (z(t,x0) > 5 μm) and the reduction of distributed
signal clutter (z(t,xi) < 5 μm; on the rest of the surface) and audible acoustic noise respectively.
Principle: The ideal replication of the original impulse by time reversal of the diverge nt wave fieldrequires a time reversal mirror, whose unlimited number of excitation points (transducer) forms acurve integral surrounding the original excitation point (focal point) and gathering the total transient
acoustic field crossing that curve [8]. As an alternative in case of a plate (display), an unlimited
number of multiple reflections (without damping) is needed to approximate the same divergent wave
field by virtual sources at the reflecting boundaries and replacing the original mirror. Thereby theaccurate design and selection of the transducers is no crucial precondition: Because of the interaction
at the boundaries of the display different wave mode conversions occur. Due to the TR -technique only
those signal path are counted which lead to a perpendicular surface elongation in the focal point only.
Challenges: The multipath propagation of those elastic waves including reflections is crucial
according to the aims: a) to use as few transducers as possible and b) to place them outside the acti ve995

(transparent) area of the display. Further, because of damping and mode conversion only a limited
number of excitation points and propagation path will be applicable. Hence, mainly the number andpositions of the transducers need to be optimized to approximate the original haptic signal (input).
The remaining challenges in realizing focal spots with guided dispersive elastic waves are:- the providing of selectivity of propagation path and wave mode,- the avoidance of audible acoustic noise,- the increasing of the surface elongation in the range of the perceptual threshold and- the adaption of the wavelength and pulse shape to the desired perceptual focal size.
Typically common touch sensitive displays are made of glass or plastic material with a thickness
in the range of 2 mm to 5 mm [3]. With the restriction of a few transducers only and because of thelarger physical wavelength on such plates neither local steplike thresholds nor multiple arbitrary focus
points in size and spacing of a human fingertip can be realized at the haptic frequencies (< 300 Hz).
Thus, the selective generation of larger feedback spots on comparatively large plate structures seems
to be realistic for now. The least energy and equivalent the smallest number of signal sources is needed
for a stimulus with frequencies in the range of the maximum perceptual threshold (300 Hz). Signals
with higher frequencies (and smaller focal dimensions) will need a higher excitation power due to thelower surface displacement and the decreasing sensitivity of the human finger [3]. Furthermore,
additional acoustic perceptible disturbing signals would occur, which normally are not wanted. In thefollowing example a “low cost” system is described to exemplify the applicability of the virtual
calibration approach to build up a multiple spot transient haptic feedback system on “larger”
transparent display or show window.
Virtual Calibration: Usually the time reversal is done by measuring the impulse response or the
spectral transfer function between two separated single transceivers. This would include all physicaleffects and cross sensitivites within the data. Since the current application does not need an exact
replication and coherence of a given haptic signal, an alternative fully automated virtual calibration
by finite element modelling is used.
Therefore a three dimensional model for plates was created to solve for the stationary eigenmodes
and the transient behavior of short time pulses that are excited from different multiple transducer
locations, including the reflection and mode conversion at the boundaries. The parametric prestudies
covered variations of the number and placement of the source points, the plates ’ material and thickness,
the frequency and fixed and floating bearing of the boundaries. In conclusion the results showed thatthe material parameters don’t need to be exact since the time reversed signal is reduced to the main
propagation path (truncated to 30% of the time window with high signal to noise ratio) and normalized.
The 1-bit-quantization [4] is not applied. In contrast the influence of source patterns (position oftransducers) is more crucial and defines the virtual description of the necessary input data at thetransducers in order to excite a time reversed signal at a desired focus location. Concerning asymmetric placement of the transducer it will force a symmetric (standing) wave pattern on the plate
which could mask a focus displacement. The interference with the predominant symmetric wave (orelongation) pattern leads to an insufficient replication of the focal point. This elongation pattern canbe homogenized by using a stochastic irregular pattern. Based on the wave field snapshots Fig. 4
illustrates the focus quality by time reversal for a regular symmetric transducer pattern and arandomized (not optimized) pattern with 8 source points. In the left figure the interference with thepredominant symmetric wave pattern lead to an insufficient replication of the focal point (white circle).
In contrast the irregular transducer arrangement (right figure) supports the formation of a shifted focal
point.
Hence, to avoid a predominant wave pattern and to support the formation of a shifted focal point,a randomized transducer placement is necessary. For this purpose of adapting the position of anarbitrary number of transducers an optimization algorithm was realized in Matlab – including agraphical output (Fig. 5). As one criterion the variety of distances between each source point was used.
Fig. 6 depicts the steps for designing a local transient haptic feedback on transparent dev ice(surface): Starting information are the geometry, elasticity and poisons ratio of the display. In firststep the demanded basic haptic feedback signal need to be defined (in our case a short pulse withz = +/- 10 μm surface elongation). The second step covers the definition of the haptic focal area on
the display (focal points matrix) and the remaining area used for transducer positioning. Therewith
the optimization algorithm calculates the adapted (optimized) source positions. In the last step the
automated simulation model takes the geometry, the elasticity, the poisson ’s ratio and the defined
haptic signal into account to calculate the transient surface displacement for each transducer (latter996

source) position. Doing this calculation for each focal point the final excitation signal-matrix isformed. In conclusion the time reversed signals of this matrix can be used to reproduce the initialhaptic signal in any calibrated focal point. Further the linear superposition of different excitation
matrix enables multiple vibrating focal points at the same time, whereat the energy spreading needs
to be regarded as well.

Figure 4 (left). Glass-plate (500 x 500 x 2) mm: Time reversal (simulation) with 8 transducers(excitation points) with regular (left) and randomized (right) pattern focusing on the same focal point(white spot) with a spatial offset to the plates center of 'x = 'y = +50 mm (wavelength at 325 Hz:
O A0 = 290 mm, focus timestep)
Figure 5 (right). Graphical output (Matlab) of the optimization algorithm for placing the signal
sources (transducers).

Figure 6. Scheme: Algorithmic positioning of transducers on a display and virtual calibration of
excitation signal-matrix according to the desired focal point grid and haptic surface elongation.
2.4 Results, Verification and Study
As an example the snapshots in Fig. 7 depicts the focus quality on a plastic plate – with nine
calibrated focus points – regarding an optimized position of eight transducers (Fig. 7 a) according to
Fig. 5. Already a number of eight source points is sufficient to reproduce an ideal calibration
displacement (Fig. 7 b) with perceptual adequate quality (Fig. 7 c). With this case studie amongst
others it could be proven, that the forward simulation of haptic impulse are adequate to virtuallycalibrate a data set for time reversal haptic feedback on arbitrary focal points (Fig. 7). Where the sizeof the focus is determined by the physical wavelength (Fig. 3). Regarding the transient behaviour, theelongation in all other focus points, but the desired one, do not cross the perceptual threshold at any
time (Fig. 8). Supplemental to the numerical studies a measurement system was established whichenables the demonstration and investigation of the time reversal on plate s with up to 16 independent997

channels. The elongation of the plate at arbitrary points is captured with a laser triangulation sensor.
During the empirical prestudies a variety of geometric combination, boundary conditions, materials
and mechanic transducers (piezoceramic, vibration motor, structure-borne loudspeaker, voice coilmotor) were tested towards the excitation and time reversal of elastic A0 waves in the haptic frequency
range (40…300) Hz.
Fig. 9 depicts one final optimized demonstrator including a plate according to the same dimensions
as in Fig. 7. The device consists of a plastic plate (70x70 cm², d = 2 mm) clamped in a rigid frame.
Eight exciter (EX60, Visaton) where coupled to the backside of the plate. A simple multichannel soundcard was used as signal generator without any amplification. This robust measurement setup allowed
a reliable study with a number of 70 test persons. Within the study the test persons had to distinguishdifferent focal points (position and size) and to rate their subjective sensation of the focus quality andperception by help of a given decision table (Tab. 2).
The analysis of the study showed that- the concept is well accepted by the majority (84%),- a “blind” recognition of the vibration focus is done by 94% of the persons independent fr om
age and experience with touch displays,- the perceptual intensity shows high diversity and- 50% had a the spatial deviation of the real focus center to the subjective center felt by theindividual of less than 20 mm (which correlates to the wavelength on this plate) (Fig. 10).
In summary the empirical study verified the concept and the functionality of a vibro -acoustic haptic
system for transparent surfaces, which was designed and virtually calibrated with a numerical modeland an algorithm only.

Figure 7. (a) Simulation model of a plastic plate [700 x 700 x 2]mm with 8 randomly distributed
transducers and 9 selected focal points; (b) 2D-distribution of ideal localized displacement and (c)real displacement in focal point.

Displacement
in all focal points

adjusted threshold

0

0.05

0.1

0.15 t [s]Figure 8. comparison: Normalized surface displacements 'z in all nine calibrated focal points –when focusing only one (red curve crosses the perceptual threshold only)

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Figure 9. Demonstrator: plastic plate (700 mm × 700 mm × 2 mm) clamped in an aluminum frame;
source: 8 randomly distributed transducers (Fig. 4) and a 8-channel-audio-device with integrated
storage.

Figure 10. Spatial deviation of the real focus center to the subjective center felt by the individual

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