Particle Damping in Vibrating Cantilever Beams Team: Shaken Not Stirred Department of Aerospace Engineering The University of Texas at Austin 210 E. 24 th St, W.R. Woolrich Laboratories 1 University Station C0600 Austin, TX 78712-1085 Faculty Supervisor: Stearman, Ronald; [email protected]; 512-471-4169 Tandy, William: Flyer, Team Leader, [email protected]Ross, Robert: Flyer, [email protected]Allison, Tim: Flyer, [email protected]Hatlelid, John: Flyer, [email protected]Hoang, Ann: Alternate Flyer, [email protected]* All Participants are Seniors in the Aerospace Engineering Department Faculty Adviser’s Signature: ____________________________________________
Transcript
Particle Damping in Vibrating Cantilever Beams
Team: Shaken Not Stirred
Department of Aerospace Engineering The University of Texas at Austin
210 E. 24th St, W.R. Woolrich Laboratories 1 University Station C0600
Austin, TX 78712-1085 Faculty Supervisor: Stearman, Ronald; [email protected]; 512-471-4169 Tandy, William: Flyer, Team Leader, [email protected] Ross, Robert: Flyer, [email protected] Allison, Tim: Flyer, [email protected] Hatlelid, John: Flyer, [email protected] Hoang, Ann: Alternate Flyer, [email protected] * All Participants are Seniors in the Aerospace Engineering Department Faculty Adviser’s Signature: ____________________________________________
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Table of Contents 1.0 Preferred Flight Week ................................................................................................ 1
10.1 Appendix A – Figures ......................................................................................... 20
10.2 Appendix B – Letters .......................................................................................... 22
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1.0 Preferred Flight Week
Due to team member graduation concerns, our top three choices for flight week are, in
order of most desirable:
(1) April 1-10, 2004
(2) March 18-27, 2004
(3) March 4-13, 2004
2.0 Advisor/Mentor Request
Our team does not need the assistance of a JSC scientist or engineer.
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3.0 Abstract Particle damping is theoretically a sound approach to reducing the effect of vibration within a structure. In particular, the hollow rod used to hold the particles reduces the thermal path when compared to a solid beam, thus providing an important benefit in areas of a satellite where both vibration and thermal load concerns exist. Previous research has been dedicated to determining the effect of particles of varying properties within specific structures with positive results. However, its application in space oriented vehicles has seen limited use, partly due to continuing concerns of unpredictability. Therefore, the goal of the team is to investigate the effect of particle damping on the response of a beam subjected to vibrations of varying frequency. It is anticipated that the reduction of acceleration due to gravity will have an impact which mathematical theory cannot predict. Specifically, the particles will not be predisposed to settle in the direction of the gravity vector (thus allowing the initial dissipation of particles) as well as allowing an increased period of movement after excitation. Points of interest that the team will research include the transient response, the response of the structure near the natural frequency, the steady-state response across a range of frequencies and the residual vibration after excitation due to the continuing motion of the free floating particles. To investigate this phenomena a cantilever beam will be filled with particles of varying material properties and then subjected to base excitation via a function generator and single axis vibrator. A point mass will be installed on the free end of the hollow rod. To measure the data an accelerometer, from which the data will be recorded, will be attached to the point mass. The data will be captured in Lab View and analyzed with Matlab and Microsoft Excel.
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4.0 Test Objectives The objective of the team is to determine the effect of particles within a cantilever beam
on the response of a point mass subjected to base excitation. Specifically, the interest is
to make correlations between the response of the system in varying gravitational
environments and particle properties such as mass and diameter. The aim of the
experiment being flown is to confirm the hypothesis that further reductions in the
amplitude of the response of the point mass to excitation can be achieved in a reduced
gravitational environment. The improvements in the response of the system in reduced
gravity will be in addition to those seen by the effect of using particles to transfer energy
within the system. It is believed that advantages to sensitive spacecraft components,
which could benefit from increased vibration damping, as well as a lower thermal path,
will be seen. To the best of the team’s knowledge this area of study has never been
conducted on a RGSFOP flight by the University of Texas, or any previous team from
other institutions.
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5.0 Test Description The test description is as follows.
5.1 Description of the Test
The purpose of the test is to measure the transient response, the response of the structure
near the natural frequency, the steady-state response across a range of input frequencies
and the residual vibration after excitation (due to the continuing motion of the free
floating particles) of particle filled rods to determine the correlation between particle
properties and the response of the rod to a range of vibrations. A visualization of this rod
can be seen in Figure 1. The tests will first be conducted at the nominal value of ground
level gravity, and then performed at a reduced acceleration due to gravity aboard the KC-
135. The experiment will be conducted using multiple sets of pre-fabricated hollow rods,
filled with varying types of particles. For instance, the first rod will be filled with a
particle of a certain mass and diameter. A second rod will be filled with a particle of the
same mass, but different diameter. A third rod will be filled with the same diameter
particle as the first, but with a different mass. In this way a correlation can be made with
respect to size and mass. Additional rods, designed by similar logic, will be tested to
further explore the relationship between the volume of particles within the rod and the
response of the rod.
Each rod will be tested using a varying input frequency function generator and vibrator
combination to determine the response of the point mass to vibration. On the ground the
resulting data will be plotted to give the natural frequency of each rod under 1g
conditions and the values of the acceleration of the point mass. The accelerations at the
point mass will be measured with an accelerometer. In flight, the same setup will be used
to determine the effect of reduced gravity on the response of the point mass. Each
experiment should take less than twenty seconds to complete, or specifically, enough
time to transition from the transient response to the steady state response and then to
measure the response after the termination of the excitation.
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The electronic equipment used in the experiment will include a laptop for use in
recording data and running the function generator, a function generator, a single axis
vibration shaker, and an accelerometer. Backup equipment will be available if needed.
The hardware used in the experiment will consist of the point mass, the test bed to which
the experiment will be bolted and strapped to, and a number of particle filled aluminum
rods. A surge protector will be used to protect all equipment and hardware. Finally, the
entire experiment will be enclosed within a cabinet for further safety. It is expected that
the entire setup should fit within a volume of 24x48x40 in3. See Figure 2 for a visual
layout.
5.2 Expected results for accompanying ground based experiments
By performing ground experiments a base line for the response of the point mass will be
determined. The results will be used in comparison against the results from the reduced
gravity flights. It is expected that the particle filled rods will effectively reduce the
amplitude of the response of the point mass to the base excitation. The percentage
improvement is still to be determined, but from previous it has been seen that the benefits
can be large [Chen, T.], [Olson, S.].
In addition, experiments will be carried out to determine the differences in response of
the solid rod, hollow rod, and particle filled rod. It is anticipated that the solid rod will
perform better than the hollow rod, but that the hollow rod filled with particles will
perform the best.
To create a second baseline, a theoretical approach will be used to predict the response of
each test subject. The underlying equations are based on energy and acceleration
principles, and are drawn from previous work in published papers. Section 5.3 is a
summary of this theory.
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5.3 Theory
The theory is as follows:
5.3.1 Viscoelastic Damping
A particle damper consists of many particles placed in a cavity attached to or inside the
vibrating structure. As the structure vibrates, the particles collide with other particles as
well as the cavity walls. The energy transfer during a collision between two particles
may be modeled by the following two equations [Olson, S.]:
aabb vmvmvmvm 22112211 +=+ (1)
bb
aa
vvvv
e12
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−−
= (2)
The subscripts “a” and “b” denote after and before the impact, respectively, v is the
velocity of each particle, and e is the coefficient of restitution between the two particles
(or between the particles and the cavity wall). The particles may then be represented by
Maxwell models and the energy loss due to particle deformation may be calculated
[Olson, S.].
5.3.2 Friction Damping
Friction also dissipates energy as particles slide against each other and the cavity
walls. The shear acting on each particle due to oblique impacts is given by [CSA 2000]
( ) NtS FvF µsgn−= (3)
where vt is the relative tangential velocity, µ is the coefficient of friction, and FN is the
normal force acting on the particles.
In order to simulate the friction between the particles and the cavity, it has been
shown that the particles may be accurately modeled by a single mass [CSA 2000]. The
particle damper may then be treated as a single particle impact damper (Figure 3), and the
equations of motion for the system become [CSA 1999]
( )yxgmFkxxcxm part &&&&& −−=++ sgnµ (4)
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( )yxgmym partpart &&&& −= sgnµ (5)
where mpart is the combined mass of the particles and F is the excitation force. These
equations, however, only predict the friction between the particles and cavity walls in a
gravitational field; a reduced-gravity environment will not follow this model.
5.4 What does the team expect to learn as a result of the experiment?
The particle filled rod will be lighter than the solid rod, therefore leading to a lower first
modal frequency. However, under vibration it is expected that the energy dissipated by
exciting the particles will reduce the accelerations of the point mass. It is expected that a
correlation will be made between the particle properties (mass, diameter, and fill volume)
and the response of the mass to vibration. It is also expected that comparisons between
nominal ground level values of gravity and reduced levels of gravitational acceleration
will show an improvement in desired response as the effects of gravity are reduced.
The transient response will be of interest due to the nature of vibrations in a satellite.
Short vibration inputs are common in the case of unwinding a solar array or undergoing
vibrations due to heat transfer from moving between the dark side to the light side of the
earth. It is expected that reduced gravity will improve the transient response by reducing
the amplitude of the peak response through increased initial energy transfer between the
rod and particles.
5.5 Exactly how will the test be conducted?
Each test will be conducted by attaching a pre-filled rod to the fixed vibrator. Data
recording will begin on a laptop with LabView software installed. A pre-compiled
program, which will control the input frequencies and amplitudes, will begin and run for
the allotted time. When the vibration ends the data recording will continue for a short
time to record the continuation of movement of the particles. At the pre-determined time
the data collection will end. In between periods of reduced gravity a new rod will replace
the previous. At the onset of reduced gravity the experiment will continue with the new
rod. This process will repeat as many times as allowed within the reduced flight
environment. Figure 4 shows the interconnection of the testing systems.
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5.6 Data Acquisition and Analysis
The accelerometer at the point mass will record data for future analysis. The data from
the accelerometer will be analyzed and saved within National Instrument’s LabView
program. The input vibration will be controlled via a pre-compiled routine and will be
used to format the data into Response vs. Input plots. With the collection of all data,
overlay plots of each result will be created to visually determine the relationships
between particle properties and the resultant responses. In addition, mathematical
relationships such as percentage decrease in response for a given experiment in the two
gravitational environments will be calculated. Finally, the theoretical results will be
compared with experimental results.
5.7 Effects of Reduced Gravity on the Experiment
A reduced gravity environment will change the transient response of the structure by first
changing the initial state of the particles. A 1g environment will cause the particles to
settle towards the bottom of the beam, while in a reduced gravitational environment the
particles will be free to disperse. In addition, the point mass will be free to vibrate under
less than 1g conditions. Although this will add to the amplitude of the response, the mass
will be more responsive to the state of the supporting rod. Also, the reduction of
acceleration due to gravity will allow the particles to bounce around more after
excitation. It is predicted that the reduction of ‘g’ in the theoretical equations will not
take into account the initial dispersion of the particles, the migration of particles in the
direction of the gravity vector, or the response decay after the excitation has ended.
Because of the number of factors that change in a reduced gravity environment it is
believed that the only method of correctly determining the response of the system is to
test it under the appropriate conditions.
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6.0 References Olson, S., Drake, M., Flint, E., Fowler, B. Development of Analytical Methods for Particle Damping, University of Dayton Research Institute in Conjunction with CSA Engineering, inc., 1999 Olson, S., Flint, E., Fowler, B., Effectiveness and Predictability of Particle Damping, University of Dayton Research Institute in Conjunction with CSA Engineering, inc., 2000 Chen T., Mao K., Huang X., Wang, M., Dissipation mechanisms of non-obstructive particle damping using discrete element method, Xi'an Jiaotong University, China; Huazhong University of Science and Technology, China; and The Chinese University of Hong Kong, Hong Kong, 2001
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7.0 Safety Evaluation
7.1 What are you bringing to Houston?
The necessary equipment will include a function generator, vibrator, a backup power
source, a laptop for controlling the experiment and recording the results, the pre-
manufactured rods, the point mass, and an accelerometer. The setup will be mounted to a
24 inch by 48 inch platform using bolts and/or straps as appropriate.
7.2 What do you need on the ground?
Ground equipment will include a backup of all hardware and electronic flight equipment.
A second computer will be used to transfer data to a second source in order to protect
accidental loss of the data.
7.3 What are you doing in the aircraft?
Everything except the installation of the rods will be set before flight. The rods will be
stored until needed. They will be stored within a container, which itself is mounted to the
platform, allowing easy access to each labeled rod, while holding them secure until
needed. After each experiment the previously tested rod will be marked and stored, after
which the next rod will be pulled from the case and inserted into the socket on the
vibrator. The point mass with pre-attached accelerometer will be transferred between
rods by screwing it on to the end of the rod. The entire process of switching rods should
take about forty five seconds and will follow a set routine to maximize efficiency and
reduce the time needed between experiments.
The computer programs will be checked before flight and automated to the point of single
click use during the flight. Data will be recorded and saved for future use, but briefly
analyzed in flight to validate the current experiment setup.
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7.4 Flight Manifest
None of the proposed flyers have any hands on experience with the RGSFOP. The only
experience, which is shared by all five participants, is second hand accounts from fellow
students. The proposed flyers are as follows:
Proposed Flyers
Bill Tandy
John Hatlelid
Robert Ross
Tim Allison
Alternate Flyer
Ann Hoang
7.5 Experiment Description / Background
Team “Shaken not Stirred” is researching particle damping as it would apply for use in
satellites and other space vehicles. Our intentions include showing the difference zero ‘g’
and one ‘g’ environments have on the transient, steady-state and decay response of a
particle damped system, and to show a correlation between particle mass, diameter and
volume ratio that may be able to be used to optimize a particle damping system to a
specific design requirement. We intend to accomplish this objective by measuring the
response to 24 various practically damped systems in a zero and one g environment.
Results will be formatted and plotted so that visual and mathematical conclusions can be
made.
7.6 Equipment Description
Ground operation time will be used to setup each specimen and prepare Lab View, our
data acquisition software. A programmable function generator will be used so that each
specimen will undergo the same range and amplitudes. The function generator has not
been selected as of the writing of this report, but the University of Texas has offered
several solutions which all share small volume and programmability properties. Each rod
specimen will consist of a one inch diameter aluminum tube that will be filled with the
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appropriate type and amount of particle and permanently sealed to increase safety by
reducing the chance of accidental particle dispersion under the testing conditions. The
point mass will consist of an aluminum block with a threaded hole for attachment to each
rod. An accelerometer will be permanently attached to the point mass. The frequency
input will be provided by a small, single axis vibrator which derives its input amplitude
from the input voltage. Figure 2 provides a visual description of the equipment used by
the team.
7.7 Structural Design
Our experiment will be completely enclosed within a cabinet structure which consists of
a two inch wooden base, two ¾ inch wooden shelves, aluminum backing, and ½ inch
Plexiglas sides, top and doors. Bolts will be used to mount the vibrator to the base level
and the function generator and surge protector to the 2nd shelf. A series of clamps will be
used to attach the extra rod specimens securely to the mid-shelf. Each component’s
location has been carefully considered weighing safety concerns and ergonomics. The
two inch thick base to which the vibrator is attached will provide increased stiffness
which will minimize residual vibration input into the cabinet by the environment of the
KC-135. By placing the surge protector on the second shelf, the length of wiring
between components will be minimized.
7.8 Electrical System
Our experiment will require electricity for the computer, function generator, and vibrator.
These three components will be connected to a surge protector, which in turn will be
connected to the KC-135 power source. The wiring connecting these components will
be secured and confined in a wire housing that runs along the backside of the cabinet
from bottom to top. The components will run on 120 V and 60 Hz. The currents drawn
by each component are as follows:
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Component Current
Computer 3.5 amps
Function Generator --
Vibrator --
The specific function generator and vibrator have not been selected yet, but the current
draw of these components will be provided with the formal TEDP after the proposal has
been accepted. Figure 4 is a schematic of the proposed electrical system.
7.9 Pressure / Vacuum System
There will be no pressure or vacuum system required.
7.10 Laser System
No laser system will be required.
7.11 Crew Assistance Requirements
Our experiment will be completely self-contained. Therefore we will require minimum
crew assistance. However, to ensure safety, we ask that crew be available to assure that
our experiment bay is properly secured to the KC-135.
7.12 Institutional Review Board (IRB)
Our experiment will not require approval from the IRB.
7.13 Hazard Analysis
While it would be impossible to predict all possible hazards, we will be taking significant
precautions for what we think could be the most obvious hazards during flight. To begin,
the presence of any electrical system creates the possibility for electrical fire. For this
reason, our test bay will be constructed with inflammable and flame resistant materials.
The thick wooden ¾ inch shelves and 2 inch base will have no paint or any other
flammable substance on them. Another hazard involves the structural integrity of our test
bay. Structural integrity will be insured by constructing a test bay that would be able to
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withstand loads that far exceed those that it will be exposed to it during flight. So that the
flyers can continually observe the experiment, the cabinet will have an aluminum backing
and Plexiglas sides, top and doors. To gain access to the experiment a swinging door will
be used. To prevent unintentional opening of the doors a duel latch system will be used
to insure that the bay doors stay closed during flight. The ½ inch Plexiglas sides will
provide more than enough strength to warrant against any cracking or breaking due to
adverse impact of equipment. However, to curb hazards, each component will have two
systems in place to ensure that they are securely attached to the test bay. First, each
component will be bolted in its perspective position, and accompanying this set up will
be a short safety cable to protect against the possibility of a component breaking and
flying loose. Clamps will secure the rod specimens to the first shelf of the cabinet, and
they will also be enclosed within the cabinet and separated from the other components of
the experiment. Precautions will also be taken to prevent against the rod specimens
breaking loose during testing. To ensure that each specimen stays attached during
testing, specimens will have threaded ends that will be screwed into the base and point
masses. It is anticipated that the cabinet should be a more than adequate confinement
center, in the event that a test specimen does break loose. Finally, in case of problems
with the vibrator during the experiment a simple external kill switch will be used to
ensure that the vibrator can be cut off at any time.
7.14 Tool Requirements
The experiment will require the following tools: Tools Inventory
Computer 2
Vibrator 2
Function Generator 1
Surge Protector 1
Digital Video Camera 1
Since construction of the actual cabinet has not begun yet it is difficult to predict every
tool needed for the experiment. A complete tool list will be provided with the formal
TEDP after the proposal has been accepted.
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7.15 Ground Support Requirements
No ground support services will be required
7.16 Hazardous Materials
There will be no hazardous materials used.
7.17 Procedures
The ground operation will consist of setting up Lab View and ensuring that all electrical
and data collection wires are properly connected. Functionality of each component will
be checked, and a general pre-flight inspection of the test bay’s structure will be
conducted. The first test specimen will also be attached to the vibrator and point mass in
the test bay during the ground operations. We have also asked for crew assistance to
ensure proper test bay security in the KC-135. Just prior to flight, we will conduct
another general pre-flight inspection of the test bay’s security to the KC-135, and we will
insure that all components are still in their correct operation modes. On the ground, Lab
View will be set up so that only one button will need to be pushed during the tests.
Therefore, the in-flight one-g phase will only consist of switching out test specimens,
which should take about 45 seconds, and the zero-g phase will consist of activating Lab
View at the onset of the zero-g phase. It is estimated that each test will run for 15 to 20
seconds, which will be will well within the 30 second zero-g time span. In this time, Lab
View will also automatically retrieve and record all data. After the flight, data will be
backed up onto a second computer. Before the second flight the ground operations will
be repeated to ensure that all components are in flight condition.
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8.0 Outreach Plan Our outreach objective is to promote interest in the study of aerospace engineering. To
encourage development in the Aerospace field, incoming freshman and K-12 students
must be informed of the benefits of an aerospace degree. To accomplish this goal, the
team “Shaken Not Stirred” plans on targeting several campus and community
organizations.
“Shaken Not Stirred” has started developing a website to inform the public of our project
and its objectives. The site is temporarily available at www.ae.utexas.edu/~risus, but will
be changed to a permanent address in the near future. Currently this webpage is in the
developmental stage and only has a general outline of the project, but as the project is
developed further, the webpage will be updated to keep the public informed of
developments in the project.
Also, to inform the local media of our project, “Shaken Not Stirred” will contact several
newspapers and TV stations. Media outlets include: The Daily Texan (the UT Austin
student newspaper), The Austin American Statesman (an Austin area newspaper), and
Channel Eight News (an Austin area local news station).
8.1 Confirmed Outreach Audiences
University of Texas at Austin Freshman Interest Groups (FIGs) – these are groups of
incoming freshman that are given the same class schedule. Weekly meetings encourage
active participation in the department and extra curricular projects.
The Women in Engineering Program (WEP) – an organization committed to recruiting
and retaining female engineering students. Recent activities include speaking with high
school seniors about the department and the project.
Parker Lane United Methodist Church – A local church. This church has a predominance
of underprivileged children who might otherwise not be exposed to the aerospace field.
One of the team members is a Youth Sponsor at the church and has been able to
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coordinate events for the K-12 students. Appendix B includes a letter from the Parker
Lane United Methodist Church Youth Director confirming our intentions.
University of Texas AIAA Student Chapter – this is a student run chapter of the
American Institute of Aeronautics and Astronautics. Bi-weekly meetings encourage
intra-departmental participation as well as providing a forum for speakers and planned
activities.
8.2 Potential Outreach Activities
The outreach activities will vary depending on the target audience. Obviously the K-12
students will require a program significantly different from that of college age students.
The presentation to the FIG’s, WEP, and AIAA student chapter will be largely the same.
These presentations will consist of an overview of the courses and projects completed
while earning an undergraduate degree in aerospace engineering at the University of
Texas at Austin. The presentation will also include a brief overview of the RGSFOP and
our project. The purpose of this activity will be largely to inform the students of the
benefits of a degree in aerospace engineering and to encourage participation.
For presentations to the K-12 students we envision a very short and rudimentary
overview of a degree in aerospace engineering followed by a paper airplane building
contest. Even if the age range of the students is broad, the students can be divided into
categories based on age. The purpose of this activity is to expose the students to the field
of aerospace engineering.
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9.0 Administrative Requirements The administrative requirements are as follows.
9.1 Institution’s Letter of Endorsement
This section is included in Appendix B of the hard copy only.
9.2 Statement of Supervising Faculty
This section is included in Appendix B of the hard copy only.
9.3 Funding/Budget Statements
Particle Damping Costs Item Quantity Cost Per Item Total Cost Materials Cost Rods 24 $ 15.00 $ 360.00 Cabinet Materials 1 $ 240.00 $ 240.00 Damping Particles 1 $ 100.00 $ 100.00 Attachments for Rods 60 $ 1.00 $ 60.00 Point Mass 1 $ 5.00 $ 5.00 Wiring 1 $ 25.00 $ 25.00 General Construction Materials 1 $ 50.00 $ 50.00 Tie Downs to Secure Cabinet 4 $ 10.00 $ 40.00 Room and Board During Trip Travel to/from Houston 1 $ 200.00 $ 200.00 Seven nights staying in Houston 5 $ 350.00 $1,750.00 Meals during stay 100 $ 7.00 $ 700.00 Total Cost $3,440.00 Equipment Provided By University of Texas Laptop and needed software Function Generator Mechanical Vibrator Camera Possible Sources of Funding University of Texas at Austin
$2,000.00
Texas Space Grant Consortium $2,000.00
9.4 Institutional Animal Care and Use Committee
This section does not apply to the proposed experiment.
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9.5 Parental Consent Forms
This section does not apply to the proposed experiment.
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10.0 Appendices 10.1 Appendix A – Figures
Figure 1: Specimen Cross Section
Figure 2: Test Cabinet
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Figure 3: Single Particle Impact Damper [Olson, S]
Figure 4: Electrical Schematic
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10.2 Appendix B – Letters
The following letters are attached to the hard copy of this proposal.
