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= A fluid-structure interaction benchmark in turbulent flow (FSI-PfS-1a) =
=Fluid-structure interaction in turbulent flow past cylinder/plate configuration  I (First swiveling mode)=
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=  Introduction =
 
== Flows around bodies ==
=== Underlying Flow Regime 2-13 ===
 
= Description =
 
==  Introduction ==


A flexible structure exposed to a fluid flow is deformed and deflected
A flexible structure exposed to a fluid flow is deformed and deflected
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simulation tools are required.  
simulation tools are required.  


The long-term objective of the present research project is the coupled
The long-term objective of the research reported here is the coupled
simulation of big lightweight structures such as thin membranes
simulation of big lightweight structures such as thin membranes
exposed to turbulent flows (outdoor tents, awnings...). To study these
exposed to turbulent flows (outdoor tents, awnings...). To study these
complex FSI problems, a multi-physics code framework was recently
complex FSI problems, a multi-physics code framework was recently
developed~\citep{fsi-les-2012}. In order to assure reliable numerical
developed (Breuer et al., 2012) combining Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) solvers . In order to assure reliable numerical
simulations of complex configurations, the whole FSI code needs to be
simulations of complex configurations, the whole FSI code needs to be
validated at first on simpler test cases with trusted reference
validated at first on simpler test cases with trusted reference
data. In~\cite{fsi-les-2012} the verification process of the code
data. In Breuer et al. (2012) the verification process of the code
developed is detailed. The CFD and CSD solvers were at first checked
developed is detailed. The CFD and CSD solvers were at first checked
separately and then, the coupling algorithm was considered in detail
separately and then, the coupling algorithm was considered in detail
based on a laminar benchmark. A 3D turbulent test case was also taken
based on a laminar benchmark. A 3D turbulent test case was also calculated to prove the applicability of the newly developed
into account to prove the applicability of the newly developed
coupling scheme in the context of large-eddy simulations
coupling scheme in the context of large-eddy simulations
(LES). However, owing to missing reference data a full validation was
(LES). However, owing to missing reference data a full validation was
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interacting with flexible structures.
interacting with flexible structures.


The present study is mainly related to two former investigation of Turek and Hron (2006,2010) and Gomes and Lienhart (2006, 2012) on vortex-induced fluid-structure interactions.
==  Review of previous work ==
The well-known 2D purely numerical laminar benchmarks of Turek and Hron (2006,2010) developed in a collaborative research effort on  
 
The present study is mainly related to two former investigations
of Turek and Hron (2006, 2010) and Gomes et al. (2006, 2012) on vortex-induced fluid-structure interactions.
The well-known 2D purely numerical laminar benchmarks of Turek and Hron (2006, 2010) developed in a collaborative research effort on  
FSI (DFG Forschergruppe 493) consists of an elastic cantilever
FSI (DFG Forschergruppe 493) consists of an elastic cantilever
plate which is clamped behind a rigid circular cylinder. Three different
plate which is clamped behind a rigid circular cylinder. Three different
Line 55: Line 65:
additional self-contained CFD and CSD test cases to check both solvers
additional self-contained CFD and CSD test cases to check both solvers
independently. These test cases were also used to validate the solvers
independently. These test cases were also used to validate the solvers
applied in the present study (Breuer et al, 2012).  
applied in the present study (Breuer et al., 2012).  
In order to close the gap of complementary experimantel and numerical data, a nominally 2D laminar experimental case
In order to close the gap of complementary experimantel and numerical data, a nominally 2D laminar experimental case
was provided by~\cite{gomes2006,gomes2013} and \cite{gomes2011b}. Here, a
was provided by Gomes et al. (2006, 2013) and Gomes (2011). Here, a
very thin metal sheet with an additional weight at the end is attached
very thin metal sheet with an additional weight at the end is attached
behind a rotating circular cylinder and mounted inside a channel
behind a rotating circular cylinder and mounted inside a channel
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demanding.
demanding.
There are also turbulent FSI benchmarks involving 2D structures:
There are also turbulent FSI benchmarks involving 2D structures:
in~\cite{stab-fsi-2008} a rigid plate with a single rotational degree
in Gomes et al. (2010) a rigid plate with a single rotational degree
of freedom was mounted into a water channel and experimentally studied
of freedom was mounted into a water channel and experimentally studied
by particle-image velocimetry (PIV). This study also presents the
by particle-image velocimetry (PIV). This study also presents the
Line 73: Line 83:
achieved by the present code for a turbulent FSI problem. As another
achieved by the present code for a turbulent FSI problem. As another
turbulent experimental benchmark, the investigations
turbulent experimental benchmark, the investigations
of~\cite{gomes2010,gomes2013} and \cite{gomes2011b} have to be
of Gomes et al. (2010, 2013) and Gomes (2010) have to be
cited: the same geometry as in~\cite{gomes2006} was used, but this
cited: the same geometry as in Gomes et al. (2006) was used, but this
time with water as the working fluid leading to much higher Reynolds
time with water as the working fluid leading to much higher Reynolds
numbers within the turbulent regime. The resulting FSI test case was
numbers within the turbulent regime. The resulting FSI test case was
Line 87: Line 97:
structural simulation and the grid adaptation of the flow
structural simulation and the grid adaptation of the flow
prediction.
prediction.
==  Choice of test case ==


Thus, in the present study a slightly different configuration is
Thus, in the present study a slightly different configuration is
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for the coupled problem) and the processing of the respective data to
for the coupled problem) and the processing of the respective data to
guarantee a reliable reproduction of the proposed test case with
guarantee a reliable reproduction of the proposed test case with
various suitable methods.
various suitable methods. A detailed description of the present test case is published in De Nayer et al. (2014).
 
= Test case description =
== Description of the geometrical model and the test section ==
 
FSI-PfS-1a consists of a flexible thin structure with a distinct
thickness clamped behind a fixed rigid non-rotating cylinder installed
in a water channel (see Fig.~\ref{fig:rubber_plate_geom}). The
cylinder has a diameter <math>D \operatorname{=} 0.022m</math>. It is positioned in the
middle of the experimental test section with <math>H_c = H/2 \operatorname{=} 0.120m</math> <math>H_c/D \approx 5.45</math>, whereas the test section denotes a
central part of the entire water channel (see
Fig.~\ref{fig:water_channel}). Its center is located at <math>L_c \operatorname{=}
  0.077m</math> <math>(L_c/D \operatorname{=} 3.5)</math> downstream of the inflow
section. The test section has a length of <math>L \operatorname{=}  0.338m</math>
<math>(L/D \approx 15.36)</math>, a height of <math>H \operatorname{=}  0.240m</math>
<math>(H/D \approx 10.91)</math> and a width <math>W \operatorname{=}  0.180m</math>
<math>(W/D \approx 8.18)</math>. The blocking ratio of the channel is
about <math>9.2\%</math>. The gravitational acceleration <math>g</math> points in
x-direction (see Fig.~\ref{fig:rubber_plate_geom}), i.e. in the
experimental setup this section of the water channel is turned 90
degrees. The deformable structure used in the experiment behind the
cylinder has a length <math>l \operatorname{=}  0.060m</math> <math>(l/D \approx 2.72)</math>
and a width <math>w \operatorname{=}  0.177m</math> <math>(w/D \approx 8.05)</math>.
Therefore, in the experiment there is a small gap of about <math>1.5
  \times 10^{-3}m</math> between the side of the deformable structure and
both lateral channel walls.
The thickness of the plate is <math>h \operatorname{=}  0.0021m</math> <math>(h/D
  \approx 0.09)</math>. This thickness is an averaged value. The material
is natural rubber and thus it is difficult to produce a perfectly
homogeneous 2 mm plate. The measurements show that the thickness of
the plate is between 0.002 and 0.0022 m. All parameters of the
geometrical configuration of the FSI-PfS-1a benchmark are summarized
in Table~\ref{tab:geom_conf_bench}.
 
[[File:FSI-PfS-1a_Benchmark_Rubberplate_geometry0001.jpg]]
 
== Description of the water channel ==
 
 
In order to validate numerical FSI simulations based on reliable
experimental data, the special research unit on FSI~\citep{for493}
designed and constructed a water channel (G\"ottingen type, see
Fig.~\ref{fig:water_channel}) for corresponding experiments with a
special concern regarding controllable and precise boundary and
working conditions \citep{gomes2006, gomes2010, gomes2011b}. The
channel (\mbox{$2.8~$m$~ \times~1.3~$m$~\times~0.5~$m}, fluid volume
of $0.9~$m$^3$) has a rectangular flow path and includes several
rectifiers and straighteners to guarantee a uniform inflow into the
test section. To allow optical flow measurement systems like
Particle-Image Velocimetry, the test section is optically accessible
on three sides. It possesses the same geometry as the test section
described in Section~\ref{sec:Description_model}. The structure is
fixed on the backplate of the test section and additionally fixed in
the front glass plate. With a 24~kW axial pump a water inflow of up to
\mbox{$u_{\text{max}}=6$ m/s} is possible. To prevent asymmetries the
gravity force is aligned with the x-axis in main flow direction.
 
[[File:waterchannel.png]]
 
 
== Flow parameters ==
 
Several preliminary tests were performed to find the best working
conditions in terms of maximum structure displacement, good
reproducibility and measurable structure frequencies within the
turbulent flow regime. Figure~\ref{fig:structure_lastpoint_peaks_ramp}
depicts the measured extrema of the structure displacement versus the
inlet velocity and
Figure~\ref{fig:structure_lastpoint_frequency_St_ramp} gives the
frequency and Strouhal number as a function of the inlet
velocity. These data were achieved by measurements with the laser
distance sensor explained in Section~\ref{sec:Laser_Sensor}. The
entire diagrams are the result of a measurement campaign in which the
inflow velocity was consecutively increased from 0 to <math>2.2 m/s</math>. At an inflow velocity of  <math>u_{\text{inflow}}=1.385 m/s </math>
the displacement are symmetrical, reasonably large and well
reproducible. Based on the inflow velocity chosen and the cylinder
diameter the Reynolds number of the experiment is equal to
<math>\text{Re}=30,470</math>. Regarding the flow around the front
cylinder, at this inflow velocity the flow is in the sub-critical
regime. That means the boundary layers are still laminar, but
transition to turbulence takes place in the free shear layers evolving
from the separated boundary layers behind the apex of the
cylinder. Except the boundary layers at the section walls the inflow
was found to be nearly uniform (see
Fig.~\ref{fig:water_channel_inflow}). The velocity components
<math>\overline{u} </math> and  <math>\overline{v}</math> are measured with two-component
laser-Doppler velocimetry (LDV) along the y-axis in the middle of the
measuring section at  <math>x/D=4.18 </math> and  <math>z/D=0 </math>. It can be assumed that
the velocity component $\overline{w}$ shows a similar velocity profile
as <math>\overline{v} </math>. Furthermore, a low inflow turbulence level of
<math>\text{Tu}_{\text{inflow}}=\sqrt{0.5~\left(\overline{u'^2}+\overline{v'^2} \right)}/u_{\text{inflow}}=0.02 </math> is measured. All
experiments were performed with water under standard conditions at
<math>T=20^\circ~C </math>. The flow parameters are summarized to
  Inflow velocity <math>u_{\text{inflow}}=1.385 m/s </math>
  Flow density <math> \rho_f=1000 kg/m^3</math>
  Flow dynamic viscosity <math> \mu_f=1.0 \times 10^{-3}Pa s </math>
 
[[File:channel_inflow_profile.jpg]]
 
== Material Parameters ==
 
Although the material shows a strong non-linear elastic behavior for
large strains, the application of a linear elastic constitutive law
would be favored, to enable the reproduction of this FSI benchmark by
a variety of different computational analysis codes without the need
of complex material laws. This assumption can be justified by the
observation that in the FSI test case, a formulation for large
deformations but small strains is applicable. Hence, the
identification of the material parameters is done on the basis of the
moderate strain expected and the St. Venant-Kirchhoff constitutive law
is chosen as the simplest hyper-elastic material.
 
The density of the rubber material can be determined to be
<math>\rho_{\text{rubber plate}}</math>=1360 kg/m<math>^3</math> for a thickness
of the plate h = 0.0021 m. This permits the accurate modeling
of inertia effects of the structure and thus dynamic test cases can be
used to calibrate the material constants. For the chosen material
model, there are only two parameters to be defined: the Young's
modulus E and the Poisson's ratio <math>\nu</math>. In order to avoid
complications in the needed element technology due to
incompressibility, the material was realized to have a Poisson's ratio
which reasonably differs from <math>0.5</math>. Material tests of the
manufacturer indicate that the Young's modulus is E=16 MPa and
the Poisson's ratio is <math>\nu</math>=0.48.
 
density <math>\rho_{\text{rubber plate}}</math>=1360 kg/m<math>^3</math>, Young's modulus E=16 MPa, Poisson's ratio <math>\nu</math>=0.48


== Measuring Techniques ==
The described test case FSI-PfS-1a is a part of a series of reference
 
test cases designed to improve numerical FSI codes. A second test case
Experimental FSI investigations need to contain fluid and structure
FSI-PfS-2a is described in Kalmbach and Breuer (2013). The geometry is
measurements for a full description of the coupling process. Under
similar to the first one: A fixed rigid cylinder with a plate clamped
certain conditions, the same technique for both disciplines can be
behind it. However, this time a rear mass is added at the extremity of
used. The measurements performed by
the flexible structure and the material (para-rubber) is less
\cite{gomes2006,gomes2010,gomes2013} used the same camera system for
stiff. The flexible structure deforms in the second swiveling mode and
the simultaneous acquisition of the velocity fields and the structural
the structure deflections are completely two-dimensional and
deflections. This procedure works well for FSI cases involving laminar
larger.
flows and 2D structure deflections. In the present case the structure
deforms slightly three-dimensional with increased cycle-to-cycle
----
variations caused by turbulent variations in the flow. The applied
measuring techniques, especially the structural side, have to deal
with those changed conditions especially the formation of
shades. Furthermore, certain spatial and temporal resolutions as well
as low measurement errors are requested. Due to the different
deformation behavior a single camera setup for the structural
measurements like in \cite{gomes2006,gomes2010,gomes2013} used was not
practicable. Therefore, the velocity fields were captured by a 2D
Particle-Image Velocimetry (PIV) setup and the structural deflections
were measured with a laser triangulation technique. Both devices are
presented in the next sections.
 
=== Particle-image velocimetry ===
 
A classic Particle-Image Velocimetry~\citep{adrian1991} setup depicted
in Fig.~\ref{fig:piv} consists of a single camera obtaining two
components of the fluid velocity on a planar surface illuminated by a
laser light sheet. Particles introduced into the fluid are following the
flow and reflecting the light during the passage of the light sheet.
By taking two reflection fields in a short time interval <math>\Delta</math>t, the most-likely displacements of several particle groups on an
equidistant grid are estimated by a cross-correlation technique or a
particle-tracking algorithm. Based on a precise preliminary
calibration, the displacements obtained and the time interval
<math>\Delta</math>t chosen the velocity field can be calculated. To prevent
shadows behind the flexible structure a second light sheet was used to
illuminate the opposite side of the test section.
 
The phased-resolved PIV-measurements (PR-PIV) were carried out with a
4 Mega-pixel camera (TSI Powerview 4MP, charge-coupled device (CCD)
chip) and a pulsed dual-head Neodym:YAG laser (Litron NanoPIV 200)
with an energy of 200 mJ per laser pulse. The high energy of
the laser allowed to use silver-coated hollow glass spheres (SHGS)
with an average diameter of <math>d_{\text{avg,SHGS}}</math>=10~µm and
a density of <math>\rho_{SHGS}</math> = 1400 kg m<math>^{-3}</math> as tracer
particles. To prove the following behavior of these particles a
Stokes number Sk=1.08 and a particle sedimentation velocity
<math>u_{\text{SHGS}}=2.18 \times 10^{-5}~\text{m/s}</math> is calculated
With this Stokes number and a particle sedimentation velocity which is
much lower than the expected velocities in the experiments, an eminent
following behavior is approved. The camera takes 12 bit pictures with
a frequency of about 7.0 Hz and a resolution of 1695 x 1211 px with respect to the rectangular size of the test
section. For one phase-resolved position (described in
Section~\ref{sec:Generation_of_phase-resolved_data}) 60 to 80
measurements are taken. Preliminary studies with more and fewer
measurements showed that this number of measurements represent a good
compromise between accuracy and effort. The grid has a size of 150 x 138 cells and was calibrated with an average
factor of 126 <math>\mu</math> m/px}, covering a planar flow field of
x/D = -2.36 to 7.26 and y/D = -3.47 to ~3.47 in the middle of the test section at
z/D = 0. The time between the frame-straddled laser
pulses was set to <math>\Delta</math> t=200 <math>\mu</math>s. Laser and camera were
controlled by a TSI synchronizer (TSI 610035) with 1 ns
resolution. The processing of the phase-resolved fluid velocity fields
involving the structure deflections is described in
Section~\ref{sec:Generation_of_phase-resolved_data}.
 
=== Laser distance sensor ===
 
Non-contact structural measurements are often based on laser distance
techniques. In the present benchmark case the flexible structure shows
an oscillating frequency of about 7.1 Hz. With the
requirement to perform more than 100 measurements per period, a
time-resolved system was needed. Therefore, a laser triangulation was
chosen because of the known geometric dependencies, the high data
rates, the small measurement range and the resulting higher accuracy
in comparison with other techniques such as laser phase-shifting or
laser interferometry. The laser triangulation uses a laser beam which
is focused onto the object. A CCD-chip located near the laser output
detects the reflected light on the object surface. If the distance of
the object from the sensor changes, also the angle changes and thus
the position of its image on the CCD-chip. From this change in
position the distance to the object is calculated by simple
trigonometric functions and an internal length calibration adjusted to
the applied measurement range. To study simultaneously more than one
point on the structure, a multiple-point triangulation sensor was
applied (Micro-Epsilon scanControl 2750, see
Fig.~\ref{fig:sensor_alignment}). This sensor uses a matrix of CCD
chips to detect the displacements on up to 640 points along a laser
line reflected on the surface of the structure with a data rate of
\mbox 800 profiles per second. The laser line was positioned in a
horizontal (x/D = 3.2, see
Fig.~\ref{fig:sensor_alignment}(a)) and in a vertical
alignment(z/D = 0, see
Fig.~\ref{fig:sensor_alignment}(b)) and has an accuracy of
40 µm}. Due to the different refraction indices of air,
glass and water a custom calibration was performed to take the
modified optical behavior of the emitted laser beams into account.
 
[[File:structure_sensors_scancontrolonly0001.jpg]]


{{ACContribs
{{ACContribs
| authors=Michael Breuer
|authors=G. De Nayer, A. Kalmbach, M. Breuer
| organisation=Helmut-Schmidt Universität Hamburg
|organisation= Helmut-Schmidt Universität Hamburg (with support by S. Sicklinger and R. Wüchner from Technische Universität München)
}}
}}
{{UFRHeader
{{UFRHeader
|area=2
|area=2

Latest revision as of 12:10, 12 February 2017

Fluid-structure interaction in turbulent flow past cylinder/plate configuration I (First swiveling mode)

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References


Flows around bodies

Underlying Flow Regime 2-13

Description

Introduction

A flexible structure exposed to a fluid flow is deformed and deflected owing to the fluid forces acting on its surface. These displacements influence the flow field resulting in a coupling process between the fluid and the structure shortly denoted fluid-structure interaction (FSI). Due to its manifold forms of appearance it is a topic of major interest in many fields of engineering. Based on enhanced numerical algorithms and increased computational resources numerical simulations have become an important and valuable tool for solving this kind of problem within the last decade. Today FSI simulations complement additional experimental investigations. A long-lasting vision of the computational engineer is to completely replace or at least strongly reduce expensive experimental investigations in the foreseeable future. However, to attain this goal validated and thus reliable simulation tools are required.

The long-term objective of the research reported here is the coupled simulation of big lightweight structures such as thin membranes exposed to turbulent flows (outdoor tents, awnings...). To study these complex FSI problems, a multi-physics code framework was recently developed (Breuer et al., 2012) combining Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) solvers . In order to assure reliable numerical simulations of complex configurations, the whole FSI code needs to be validated at first on simpler test cases with trusted reference data. In Breuer et al. (2012) the verification process of the code developed is detailed. The CFD and CSD solvers were at first checked separately and then, the coupling algorithm was considered in detail based on a laminar benchmark. A 3D turbulent test case was also calculated to prove the applicability of the newly developed coupling scheme in the context of large-eddy simulations (LES). However, owing to missing reference data a full validation was not possible. The overall goal of the present paper is to present a turbulent FSI test case supported by experimental data and numerical predictions based on the multi-physics code developed. Thus, on the one hand the current FSI methodology involving LES and shell structures undergoing large deformations is validated. On the other hand, a new turbulent FSI benchmark configuration is defined, based on the specific insights into numerical flow simulation, computational structural analysis as well as coupling issues. Hence, the present study should provide a precisely described test case to the FSI community for the technically relevant case of turbulent flows interacting with flexible structures.

Review of previous work

The present study is mainly related to two former investigations of Turek and Hron (2006, 2010) and Gomes et al. (2006, 2012) on vortex-induced fluid-structure interactions. The well-known 2D purely numerical laminar benchmarks of Turek and Hron (2006, 2010) developed in a collaborative research effort on FSI (DFG Forschergruppe 493) consists of an elastic cantilever plate which is clamped behind a rigid circular cylinder. Three different test cases, named FSI1, FSI2 and FSI3 are provided, complemented by additional self-contained CFD and CSD test cases to check both solvers independently. These test cases were also used to validate the solvers applied in the present study (Breuer et al., 2012). In order to close the gap of complementary experimantel and numerical data, a nominally 2D laminar experimental case was provided by Gomes et al. (2006, 2013) and Gomes (2011). Here, a very thin metal sheet with an additional weight at the end is attached behind a rotating circular cylinder and mounted inside a channel filled with a mixture of polyglycol and water to reach a low Reynolds number in the laminar regime. Experimental data are provided for several inflow velocities and two different swiveling motions could be identified depending on the inflow velocity. Owing to the thin metal sheet and the rear mass the accurate prediction of this case is demanding. There are also turbulent FSI benchmarks involving 2D structures: in Gomes et al. (2010) a rigid plate with a single rotational degree of freedom was mounted into a water channel and experimentally studied by particle-image velocimetry (PIV). This study also presents the first comparison between experimental data and predicted results achieved by the present code for a turbulent FSI problem. As another turbulent experimental benchmark, the investigations of Gomes et al. (2010, 2013) and Gomes (2010) have to be cited: the same geometry as in Gomes et al. (2006) was used, but this time with water as the working fluid leading to much higher Reynolds numbers within the turbulent regime. The resulting FSI test case was found to be very challenging from the numerical point of view. Indeed, the prediction of the deformation and motion of the very thin flexible structure requires two-dimensional finite-elements. On the other hand the discretization of the extra weight mounted at the end of the thin metal sheet calls for three-dimensional volume elements. Thus for a reasonable prediction of this test case both element types have to be used concurrently and have to be coupled adequately. Additionally, the rotational degree of freedom of the front cylinder complicates the structural simulation and the grid adaptation of the flow prediction.

Choice of test case

Thus, in the present study a slightly different configuration is considered to provide in a first step a less ambitious test case for the comparison between predictions and measurements focusing the investigations more to the turbulent flow regime and its coupling to a less problematic structural model. For this purpose, a fixed cylinder with a thicker rubber tail and without a rear mass is used. This should open the computation of the proposed benchmark case to a broader spectrum of codes and facilitates its adoption in the community. Strong emphasis is put on a precise description of the experimental measurements, a comprehensive discussion of the modeling in the numerical simulation (for the single field solutions as well as for the coupled problem) and the processing of the respective data to guarantee a reliable reproduction of the proposed test case with various suitable methods. A detailed description of the present test case is published in De Nayer et al. (2014).

The described test case FSI-PfS-1a is a part of a series of reference test cases designed to improve numerical FSI codes. A second test case FSI-PfS-2a is described in Kalmbach and Breuer (2013). The geometry is similar to the first one: A fixed rigid cylinder with a plate clamped behind it. However, this time a rear mass is added at the extremity of the flexible structure and the material (para-rubber) is less stiff. The flexible structure deforms in the second swiveling mode and the structure deflections are completely two-dimensional and larger.


Contributed by: G. De Nayer, A. Kalmbach, M. Breuer — Helmut-Schmidt Universität Hamburg (with support by S. Sicklinger and R. Wüchner from Technische Universität München)


Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References


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