Varying the Constituents of Meta-materials to Improve Efficiency

Chan Hyuck BangDecember, 2013

Rockdale Magnet School for Science and Technology930 Rowland Road Conyers, GA 30012

Varying the Constituents of Meta-materials to Improve Efficiency

Jeff Bang

Earthquakes are catastrophic geological disasters that are a major cause of destruction and death.

It reduced the number of lives and causes countless amounts of property damage. If the effects of

earthquakes could be lessened, it would save innumerous lives and money. The purpose of this

project is to test different materials to determine its effects on the meta-material’s efficiency. The

research hypothesis for this project states that if different materials are used to construct meta-

materials, then it will have a significant effect on the meta-material’s efficiency. Meta-materials

are constructed structure used to dissipate seismic energy to reduce the force that hits buildings.

The procedure involved constructing meta-materials from PVC pipes, wood, and concrete by

measuring the dimensions of the meta-materials and drilling holes in the correct positions and

constructing model building from wood. The experiment was then conducted with and without

the treatment. Three trials were tested for each building, with 8 different frequencies per trial.

The data was analyzed using ANOVA. From the data obtained, it was concluded that the

research hypothesis was accepted due to the fact that the data of one material’s meta-material

deviated from the data of another materials meta-materials (Materials DF: 2; F: 805.17; P<0.05)

(Frequency DF: 7; F: 109.91; P<0.05). This showed that the different materials had significant

effect on the meta-material’s efficiency. Research supported by David Bonar, Sang-Hoon Kim,

Mukunda P. Das, and Jesse Smith.

Table of Contents

Introduction...............................................................................Pg. 1

Literature Review......................................................................Pg. 3

Methodology.............................................................................Pg. 6

Data Analysis............................................................................Pg. 8

Discussion & Conclusion..........................................................Pg. 11

Acknowledgements...................................................................Pg. 12

Bibliography.............................................................................Pg. 13

Appendix A...............................................................................Pg. 14

(Experimental Design Diagram)

Appendix B...............................................................................Pg. 15

(Materials)

Appendix C...............................................................................Pg. 16

(Procedures)

Introduction:

Is it possible to stop an earthquake? Several million earthquakes occur in the world each

year. Out of those, only about 20,000 earthquakes are identified. Last year, there have been 4086

earthquakes worldwide causing 113 deaths (USGS, 2012). Research on how to prevent

earthquakes from causing death and destruction is a main focus in society today.

Maintaining the safety of lives is critical since earthquakes are one of the most

devastating natural disasters; prevention of deaths would save many lives. The purpose of this

project is to test different materials to determine its effects on the meta-material’s efficiency.

Meta-materials are the most current method researched in dissipating earthquake waves. This

technology has the potential to reduce the severe effects of catastrophes such as the 1906 San

Francisco Earthquake.

Meta-materials are a new, innovative method that could be a potential source of

protection for buildings against earthquakes. This could reduce the number of lives lost as well

as damage. Countless amounts of property damage are caused by earthquakes yearly. The

earthquake that hit Japan caused about $235 billion in damage (Property Damage Japan

Earthquake…, 2011). Massive property damage to an area could dramatically affect the

economy. Earthquakes can also cause other natural disasters. Reducing the effects of earthquakes

can prevent much more traumatic disasters from occurring. The havoc from earthquakes can

cause economic downfall, which would eventually affect the entire world. Although immediate

assistance to areas affected by earthquakes is provided by organizations such as Red Cross and

Rotary Club, it is not as effective as is needed.

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Previous year’s project gave evidence to support the idea that meta-materials are effective

in reducing the acceleration of a mimicked seismic wave that reaches the building. The

researcher is now investigating if using different materials could have a significant effect on the

efficiency of the meta-materials.

The research hypothesis for this project states that if different materials are used to

construct meta-materials, then it will have a significant effect on the meta-material’s efficiency.

Earthquakes destroy buildings by weakening and breaking the supports of the building (Why

buildings respond differently…, 2011). Taller, narrower buildings can withstand a higher

frequency better than a building with short, wide dimensions. This is because high frequency

waves have short periods, which affects the building less. A low frequency wave has long, low

periods. This affects a tall narrow building much more than a short, wide building. The null

hypothesis is that if meta-materials surround a building, then they will not have a significant

effect of earthquake protection for the building.

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Literature Review:

In doing this project, there are certain terms that require some prior knowledge. Some of

these are meta-materials, seismic waves, and earthquake. Meta-materials are materials

engineered to have optical, thermal, or other specific properties that naturally occurring

substances do not. These materials can block, bend, and manipulate many different types of

waves (Ross, 2012). Meta-materials were first discovered in 1986 by a Russian theorist, Victor

Veselago (Murray, 2009). Meta-materials work mostly because of their shape. The material used

to make meta-materials does not have a huge impact on the functionality of the meta-material

itself. The only conditions are that it must be strong enough to withstand seismic waves and be

made of different materials than what it surrounds.

For this project, the shape of the meta-material can be determined using a formula,

ω=√ Sl ' V

∗v, from a journal article with a theoretical experiment of this project (Kim & Das,

2012). The equation mainly relies on the speed of sound in the material that is going to be used

and the frequency of the waves. As the meta-material for this project will be in the shape of a

cylinder, the volume and dimensions of the meta-material can be found using this equation.

Seismic waves are waves of energy that are mainly caused by earthquakes. The waves are caused

by a sudden breaking of rock in the earth or an explosion. Seismic waves are recorded by

seismographs when they are travelling through the earth (Wood, 2007). Earthquakes occur when

a fault moves in the Earth, causing waves of energy to go outward from the fault (Wald, 2009).

There have been many previous studies on preventing buildings from collapsing due to

earthquakes. Buildings have been designed to be strong and stable against earthquakes. The

foundations of buildings are created to distribute the force of earthquakes that hit the buildings to

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make them more resistant to damaging waves. The soils around buildings are modified in order

to absorb and lessen the earthquake vibrations. This would lessen the amount of vibrations sent

through buildings.

Before technology was fully developed, buildings were not designed to reduce the effect

of earthquake waves. When steel and reinforced concrete were developed and implemented into

construction, reinforcement on building designs began. Between the 1930s to 1960s, the

common earthquake resistant design for buildings was to add horizontal strength into them. This

created a stronger structure, although it made the building much stiffer. In the late 1960s,

research at the University of Canterbury led to a better design for buildings to withstand

earthquakes. These designs are now the most common designs for buildings(Wald, 2009).

There are three concepts used as the basis for seismic design. The first concept is that all

buildings should not be designed to withstand the largest earthquake they would encounter. This

would have a serious economic effect on the area. The second concept is that the energy received

by the building from the earthquake must be absorbed in a controlled manner. In order for this to

happen, essential elements of the building must be ductile. This is because ductile elements can

yield and absorb energy without completely breaking. The third concept is to create a hierarchy

of strength. This creates strong unyielding columns and weaker yielding beams to be part of the

buildings. This is because if the energy output of the earthquake to the building is too great, the

building would not collapse. (Wald, 2009)

The materials used to build the meta-materials are Polyvinyl Chloride (PVC) pipes,

wood, and concrete. PVC pipes can be easily obtained from a hardware store. These are used

because it can easily be replaced and adjusted for the meta-materials for function correctly.

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Wood can be obtained from the hardware store and can be used to easily recreate the meta-

materials needed for this research project. Concrete can be easily obtained as well and can also

be easily used to create specific shapes and sizes using molds.

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Methodology:

In this project, there are three independent variables. There are three different materials

that will be tested: PVC, wood, and concrete. These materials were created as meta-materials and

tested. They were compared to an experiment without any meta-materials. This is so that the data

can be compared to see how effective the different materials will be as meta-materials. They

were tested at eight different frequencies: 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, 1000 Hz,

1500 Hz, and 2000 Hz.

The dependent variable of this project is the acceleration of earthquake

vibrations/amplitude. The actual vibrations that were measured were the ones that exist after they

have passed through the meta-materials when they read the model building and the 1-axis

accelerometer that is mounted to it. The unit of measurement is meters per second per second.

For this project, the values of the meta-materials will be calculated. The formula used to

do this isω=√ Sl ' V

∗v (Kim & Das, 2012) (Sang Hoon Kim, Personal Communication, April

16th, 2012). This will result in a 1” diameter with a height of 3”. This will be consistent

throughout all of the different meta-materials. They will be created by creating a hollow cylinder

of 1” diameter and 3” height. Then holes will be drilled in the meta-materials piece at four equal

points along the side of the evenly divided and centered pieces. Then tape will cover the top and

bottom holes as well as the side holes. There will be a total of 18 meta-materials per material.

In this project, a model building was used as a tool to aid in testing the protection of

buildings by meta-materials from seismic waves. The model building was a block of wood with a

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shape altered to mimic typical behavior of buildings. The model building was used by placing

them on top of dirt that houses the meta-materials.

The experiment was set up with the meta-materials inside of dirt for the testing with

treatment. The dirt with meta-materials was placed in a container. The container was placed next

to the loud speaker with the loud speaker pressed up against the container. Then the loud speaker

was connected to the function generator. The model building was placed in the center formed by

meta-materials. Then the 1-axis accelerometer was mounted on the model building with screws.

The 1-axis accelerometer was used to calculate the magnitude of total acceleration of seismic

waves.

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D ata Analysis:

After the experimentation, the accelerations were recorded. All of the data was inputted

into MINITAB in order to obtain inferential and descriptive statistics. One ANOVA test was

done on the variables of this experiment. The ANOVA test was done on the material and

frequency variables, and the results showed that the meta-materials significantly reduced the

acceleration of the mimicked seismic waves through the dirt (Materials DF: 2; F: 805.17;

P<0.05) (Frequency DF: 7; F: 109.91; P<0.05).

Figure 1: This graph shows the standard deviation of the acceleration for each material.

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Figure 2: This picture displays the orientation of the PVC meta-materials prior to

experimentation.

An ANOVA test was run on the average of the acceleration that resulted from the

experiment data. It averaged the acceleration of frequencies per material.

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Figure 3. This graph shows the average of the acceleration for each frequency per material.

The information gathered with the use of ANOVA testing and descriptive statistics

showed that the research hypothesis was accepted. This is because the data of one material’s

meta-material deviated from the data of another material’s meta-material. The null hypothesis

was rejected.

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Discussion & Conclusion

The purpose of this project is to test different materials to determine its effects on the

meta-materials’ efficiency. From the data obtained, it is concluded that the research hypothesis

was accepted (Materials DF: 2; F: 805.17; P<0.05) (Frequency DF: 7; F:109.91; P<0.05). The

null hypothesis was rejected. The research goal was achieved.

Figure 1 displays the Interval Plot of Acceleration, which shows the standard deviation of

the data. As show in Figure 1, the data did not deviate much from the mean, especially

accounting for the y-axis interval of 0.025. Figure 3 displays the Chart of Mean of Acceleration

for material per frequency. This chart graphed the average of the data for each trial per frequency

per material. The general trend of the average acceleration of the concrete independent variable

is the lowest compared to the average acceleration of the PVC and Wood independent variable,

showing that the concrete independent variable was more effective in dissipating sound waves

than the PVC and the wood independent variables.

Limitations to a more accurate data would be the possibility of human error when

constructing the meta-materials. As the meta-materials had to be as precise as possible and they

were built by hand, there was always the possibility for a human error. Another limitation was

the inability to specify the exact frequency used for the experimentation. Figure 6 shows the

function generator that was used in this experiment. The control used to set the frequency are

dials and not numerical values, causing a possibility of wavering frequencies in between trials. A

source of error in this research project could be that the positions of the meta-materials might

have altered in between different variables, potentially affecting the acceleration measured.

Compared to other research, this project did follow the trend that meta-materials reduce

the acceleration. However, the research it is compared to is a theoretical analysis and not an

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actual experimentation. For future research, the shape of the meta-materials could be tested as

well as the material of the meta-materials.

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Acknowledgments

I would like to thank the following people for their continued support throughout the

course of this experiment; David Bonar for providing the function generator, providing the lab

area, helping set up the experiment, and helping analyze data; Sang-Hoon Kim and Mukunda P.

Das for providing the basis of my project; Jesse Smith for providing insight on how to efficiently

create meta-materials and providing access to the uPrint 3D Printer.

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Bibliography:

(2012). Retrieved from USGS website:

http://earthquake.usgs.gov/earthquakes/eqarchives/year/eqstats.php

Kim, S. H., & Das, M. P. (2012). Seismic waveguide of meta-materials. Retrieved from

http://arxiv.org/pdf/1202.1586v1.pdf

Murray, J. (2009, September 7). 10 uses for meta-materials. beyond star trek. way beyond harry

potter.. Retrieved from http://delamagente.wordpress.com/2009/09/07/10-uses-for-meta-

materials-beyond-star-trek-way-beyond-harry-potter/

Ross, V. (2012, February 14). Theoretical metamaterial could protect buildings form

earthquakes by dissipating energy. Retrieved from

http://blogs.discovermagazine.com/80beats/2012/02/14/theoretical-metamaterial-could-

protect-buildings-from-earthquakes-by-dissipating-energy/

Wald, L. (2009, October 27). The science of earthquakes. Retrieved from

http://earthquake.usgs.gov/learn/kids/eqscience.php

Why buildings respond differently to earthquakes. (2011, March). Retrieved from

http://www.ipenz.org.nz/ipenz/forms/pdfs/ChchFactSheets-

BuildingsRepsonsdDifferently.pdf

Wood, M. M. (2007, April 16). What is seismology and what are seismic waves?. Retrieved from

http://www.geo.mtu.edu/UPSeis/waves.html

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Appendix A:

Title: Varying the Constituents of Meta-materials to Improve EfficiencyHypothesis: If different materials are used to construct meta-materials, then it will have a significant effect on the meta-materials’ efficiency.IV: Different constituent of Meta-materials; Frequency

Level of IV None PVC Wood Concrete

Frequency

100 Hz 3 Trials 3 Trials 3 Trials 3 Trials

200 Hz 3 Trials 3 Trials 3 Trials 3 Trials

300 Hz 3 Trials 3 Trials 3 Trials 3 Trials

400 Hz 3 Trials 3 Trials 3 Trials 3 Trials

500 Hz 3 Trials 3 Trials 3 Trials 3 Trials

1000 Hz 3 Trials 3 Trials 3 Trials 3 Trials

1500 Hz 3 Trials 3 Trials 3 Trials 3 Trials

2000 Hz 3 Trials 3 Trials 3 Trials 3 Trials

DV: Acceleration (m/s/s)Constant: Loud Speaker, 1-Axis Accelerometer, Vernier Lab Quest, Frequency, 17.1 kg of dirt, 37x24x28cm box, Model Building, Position of meta-materials

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Appendix B

This experiment required various materials and equipment to be conducted. It required

numerous amounts 4 pieces of wood 10x10x4cm for the construction of the model building and

wood glue. The construction of meta-materials required 1” PVC pipes, concrete mix,

10x10x243cm wood, uPrint 3D Printer, a drill, and tape. The experimental setup required 1

37x24x28cm container, 17.1kg of dirt, 1 loud speakers, 1 function generator, 1 1-axis

accelerometer, and 1 Vernier Lab Quest.

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Appendix C :

Safety Discussion

The main hazard in this experiment is the usage of tools to build the meta-materials.

When using the tools, it will be under the supervision of a teacher and goggles have to be worn.

For this project, the forms 1, 1A, 1B, continuation projects form 7, research plan, previous

research abstract, and previous research plan. These forms are standard forms required for all

research projects as well as the necessary forms for a continuation project. No other forms are

needed as there are no risk assessments.

Procedures

Construct Model Building

1. Obtain a 4 wooden blocks of 10x10x4cm

2. Glue the wooden blocks together with wood glue.

Construct Meta-Materials (PVC Pipes)

1. Obtain 2.54cm PVC pipe and cut into lengths of 7.62cm.

2. Drill 0.635cm holes in PVC pipe pieces at four equal points along the side of the evenly

divided and centered piece (figure 1).

3. Use tape to cover the top and bottom holes of the PVC pipes.

4. Cover the top and bottom holes of the PVC pipes.

5. Cover the side holes of the PVC pipes by wrapping the tape around the PVC pipes.

6. Repeat step 2-6 until 18 meta-materials are made.

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Construct Meta-Materials (Wood)

1. Obtain wooden beam of 4”x4”x8’

2. Cut wooden beam into 4”x4”x3” pieces

3. Drill a 1” hole in the center of the piece.

4. Sand the outside of the wooden piece until appropriate thickness

5. Drill holes in wooden pieces at four equal points along the side of the evenly divided and

centered piece

6. Obtain tape to cover the top and bottom holes of the wooden piece

7. Cover the top and bottom holes of the wooden pieces

8. Cover the side holes of the wooden pieces by wrapping the tape around the wooden

pieces.

9. Repeat steps 3-8 until 18 meta-materials are made

Create Concrete Meta-Material mold

1. Use SolidWorks 2013 Software to draw a 3D drawing of the concrete mold

2. Use the uPrint SE 3D printer to print out 18 sets of the concrete mold.

Construct Meta-Materials (Concrete)

1. Obtain non-aggregate concrete

2. Prepare concrete mix and pour into the concrete molds.

3. Allow concrete to dry minimum 2 days

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Set Up Experiment: W/ Meta-materials

1. Place meta-materials inside of the dirt inside of the container

2. Place back together and place them in the box

3. Place container next to the loud speaker, with the loud speaker pressing up against the

container

4. Connect loud speaker to function generator

5. Place model building in the center of the circle formed by meta-materials

6. Mount 1-Axis Accelerometer on model building with screws.

Set Up Experiment: W/O Meta-materials

1. Place dirt in the container

2. Place container next to the loud speaker, with the loud speaker pressing up against the

container

3. Connect loud speaker to function generator

4. Place model building in the center of the circle formed by meta-materials

5. Mount 1-Axis Accelerometer on model building with screws.

Conducting Experiment

1. Turn on equipment (Function generator, Vernier Lab Quest, loud speaker)

2. When everything is ready, turn on loud speaker for 2 seconds

3. Observe and record qualitative data

4. After 2 seconds, turn off loud speaker and record data from Vernier Lab Quest

5. Repeat steps for each trial and IV

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Materials

(4) Wood 10x10x4cm

(1) Wood 3.175cm dowel

(1) 2.54cm PVC Pipes

(1) 36.29 kg Concrete Mix

(1) Drill

Tape

(2) Container

Dirt

(1) Loud Speaker

(1) Function Generator

(1) 1-Axis Accelerometer

(1) Vernier Lab Quest

uPrint 3D Printer

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Figure 1: Life-size technical drawing of meta-material

Figure 3: Function Generator used in experimentation

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Figure 2: experimental setup drawing

Dirt