Viscoelastic Material Characterization

Successful design of passive damping treatments using viscoelastic materials (VEM) such as elastomers depends upon several factors. One important factor is accurate knowledge of the way in which the properties of viscoelastic materials vary with temperature and frequency. These materials are generally more difficult to characterize than are structural materials such as metals.

This occurs for two basic reasons.

  1. When an elastomer is dynamically loaded, even at levels well within its linear range, it converts a much larger fraction of the input energy into heat than does a metal. It is therefore necessary to measure both the energy storage property (stiffness) and energy dissipation property (damping).
  2. Both stiffness and damping of elastomers tend to vary significantly with frequency and temperature. Generally, the more dissipative a material, the greater the variation.

Both problems are accommodated by describing the mechanical properties of the material in terms of a frequency and temperature-dependent complex modulus, G*.[i] The stress-to-strain ratio for the material is treated as a complex quantity. Complex arithmetic provides a convenient means for keeping track of the phase angle by which an imposed cyclic stress leads the resulting cyclic strain. The complex shear modulus, for example, is usually expressed in the form

G^* = G_0(f,T)[1.0+j\eta(f,T)]

The real and imaginary parts of the modulus are then G0(f,T) and G0(f,T)⋅η(f,T), respectively. The two frequency-temperature functions on the right in the equation are commonly called the storage modulus and loss modulus. Fourier transform theory and the correspondence principle of viscoelasticity allow complex moduli to be used for calculating response to arbitrary dynamic inputs. Material properties are most often specified and measured in terms of their complex shear modulus because it allows greater flexibility in choosing the size and shape of the test specimen.

Most VEMs can be assumed to be thermorheologically simple, which can be characterized using frequency-temperature equivalence.[ii] (Simply stated, the frequency-temperature equivalence theory says that a decrease in temperature gives equivalent dynamic behavior to an increase in frequency.) A temperature shift curve, αT, which is a function of temperature only, is constructed for each particular set of complex modulus data. The real part, GR, the imaginary part, GI, and the material loss factor, η = GI/GR, of the complex modulus data are plotted as a function of the reduced frequency, fR, where fR is the product of the experimental frequency, fE, and αT, (i.e., fR = αT⋅fE). Historically, the temperature shift function for a particular damping material has been defined empirically by the experimental complex modulus data. The value of αT at each experimental temperature is selected such that it simultaneously shifts horizontally the three complex modulus data points GR, GI, and η to define curves and minimize scatter. With the use of computers, it is convenient to fit the empirical temperature shift function with a suitable analytical function of parametric nature.

Once the master curves for GR, GI, and η versus fR are created, a reduced temperature nomogram, or international plot, may be created by placing the experimental frequency on the right hand scale and then using the frequency-temperature equivalence principle to superimpose lines of constant temperature on the plot. A damping designer may then read modulus and loss factor values off this plot for any particular frequency and temperature of interest (Figure 1).


Figure 1: VEM data reduction

The use of this international plot to read values of modulus and loss factor is demonstrated in the figure. To get modulus and loss factor values corresponding to 100 Hz and 311K (100ºF), one reads the 100 Hz frequency on the right-hand scale and proceeds horizontally to the 311K temperature line. Then proceed vertically to intersect the curves along a line of reduced frequency. Finally, proceed horizontally from these intersections to the left-hand scale to read the values of 20.5 MPa (2970 psi) for the real modulus and 0.89 for the loss factor.

The main difficulty in performing characterization lies in correctly choosing parameters for the master curve equations so that they accurately represent the VEM. Interactive computer graphics have greatly improved the process of choosing and adjusting the correct parametric values.

Lynn Rogers and I have written a state-of-the-art computer program owned by CSA Engineering that implements frequency-temperature equivalence through the Ratio of Factored Polynomials model and fit of the Wicket Plot[iii] to interactively characterize viscoelastic materials.

[i]A.D. Nashif, D.I.G. Jones, J.P. Henderson, Vibration Damping, John Wiley and Sons, New York, 1985.

[ii] J.D. Ferry, Viscoelastic Properties of Polymers, John Wiley and Sons, 3rd ed., 1980.

[iii] B. Fowler, L. Rogers, “A New Approach to Temperature Shift Functions in Modeling Complex Modulus Damping Data,” Proceedings of the 75th Shock and Vibration Symposium, Virginia Beach, VA, October 18-22, 2004.

TRENDnet 500 Mbps Compact Powerline Ethernet AV Adapter

TRENDnet 500 Mbps Compact Powerline Ethernet AV AdapterI have been having trouble with the WiFi connection between the DVD player in the master bedroom and the WiFi router in the study. The rooms are just down the hallway from each other, but there is a bathroom and lots of walls between the DVD player and switch.

The trouble was most noticeable when streaming Netflix movies over the connection. The DVD player would often recalibrate the connection with Netflix and the movie quality was typically poor. I read online that a good replacement for poorly performing wireless Ethernet was the TRENDnet 500 Mbps Compact Powerline Ethernet AV Adapter. These adapters transmit and receive Ethernet over your house’s electrical wiring. You plug them into nearby electrical sockets and attach Ethernet cable between the adapter and the Ethernet-capable device. I do not know how they work if the electrical sockets are on different circuits in your circuit breaker panel, but they are working great for my situation. Netflix streaming is now always HD quality. I have seen a few reports about poor reliability on Amazon. I have only had the adapters for a week, but so far am pleasantly surprised.

There does appear to be a small problem with the adapters. They put out a very high-frequency sound. I cannot hear it, nor can my wife, but our son can hear it and it bothers him when he is in the same room with an adapter. I will have to put a wall socket box cover around the adapters to damp the high-frequency noise.

I would recommend these adapters to anyone who is experiencing poor WiFi signal quality due to too many walls, mirrors, etc., between their Ethernet transmitter and receiver.

Messing with Javascript

9-dotsThe “9-dots” puzzle was discussed on PBS the other day. The 9-dots puzzle consists of 9 dots arranged in a 3 x 3 grid. A person is asked to use 4 connected straight line segments to pass through all 9 dots. It is a simple puzzle that lead to the saying, “Think outside the box.” I decided it would be interesting and fun to see if I could program an interactive web version of the 9-dots puzzle.

With the problems surrounding java on the web, I decided to use javascript and html. I found a useful javascript framework for interactive graphics called paper.js. The paper.js website is here. I coded an interactive 9-dots program in a few hours. I spent more hours trying to figure out how to allow users to enter their initials. That ended up being a bit of a kludge using an intermediate text file. I would not use that technique for a work project, but it was good enough for my 9-dots test case. Click here to try my 9-dots code.

CSA Engineering Has Been Purchased

On May 1, 2008, CSA Engineering, Inc., became a wholly-owned subsidiary of Moog, Inc. Moog specializes in precision actuators, as well as control systems. Moog makes military and commercial aircraft flight controls, satellite positioning controls, controls for positioning gun barrels and automatic ammunition loading for military combat vehicles, controls for steering tactical and strategic missiles, and thrust vector controls for space launch vehicles.

It will be interesting times ahead. They have told us that they will not make major changes to the structure of CSA, but our president, Conor Johnson, will be retiring in a year or so. Another co-founder and vice-president, Dave Keinholz, will not be far behind.

CSA will continue to work with our existing customer base as before. We will also continue to go after commercial and military contracts on our own. But Moog apparently has need for our engineering expertise in damping, isolation, and the control systems that CSA has developed and sells. We have heard good stories about working as a subsidiary of Moog from other Moog acquisitions. I was impressed with the facility and the people I met when I visited Moog’s Chatsworth facility.

I have my fingers crossed.

Presidential Candidates Senior Moments

The current crop of presidential candidates are pretty laughable. I would laugh if the job they were seeking wasn’t President of the United States.

First John McCain has a news conference in Jordan where he goes on for a while talking about Iran working with Al Qaeda to cause problems in Iraq. His exact words were,

“We continue to be concerned about Iranian taking Al Qaeda into Iran, training them and sending them back.”

Asked about that statement, Mr. McCain said,

“Well, it’s common knowledge and has been reported in the media that Al Qaeda is going back into Iran and receiving training and are coming back into Iraq from Iran. That’s well known. And it’s unfortunate.”

He was then corrected by Senator Lieberman, who is a pretty strange fellow, himself. McCain then said

I’m sorry, the Iranians are training extremists, not Al Qaeda.

Okay. This is coming from the person who bills himself as the best leader from the standpoint of American Security. He forgot that Iranians generally hate Al Qaeda. And he wants to be President. I could go on about his singing, “Bomb, bomb, bomb,… bomb, bomb Iran.” Whoo boy!

Next up is Hillary Clinton. She decided to embellish a visit she made to Bosnia in 1996 when she was First Lady. Her recollection of her arrival in Bosnia was,

I certainly do remember that trip to Bosnia, and as Togo said, there was a saying around the White House that if a place was too small, too poor, or too dangerous, the president couldn’t go, so send the First Lady. That’s where we went. I remember landing under sniper fire. There was supposed to be some kind of a greeting ceremony at the airport, but instead we just ran with our heads down to get into the vehicles to get to our base.

(“Togo” she referred to was former Army Secretary, Togo West.) In reality, she was on a USO tour with her daughter, Sinbad, and Sheryl Crow. They got off the plane, talked to the President of Bosnia, heard a poem by an 8-year old girl, talked to a bunch of other children and their teachers, and then got into cars to go to the nearby Air Force base. She now says she misspoke.

Again, this person is close to becoming President of the USA.

Barak Obama has not had any senior moments but he co-sponsored a Senate bill that would dedicate 0.7 percent of the U.S. gross national product to foreign aid, which over 13 years he said would amount to $845 billion over and above what the U.S. already spends.

The bill would “declare” that the official U.S. policy is to eliminate global poverty, that the president is “required” to “develop and implement” a strategy to reach that goal and requires that the U.S. efforts be “specific and measurable.”

That is all very noble stuff, but I don’t think it can be done that way, and $845 billion dollars in additional foreign aid right now is not a good plan.

So, who would you vote for: Moe, Larry, or Curly?

Financial posts have moved

I have moved the finance and investment portion of this blog to I will continue to post things I find interesting here, but the personal finance stuff did not seem to fit at

mysql stuff

I did a pretty silly thing just now as I was trying to decide how to best back up the mysql database files for this blog. I followed the scripts from to create a backup file containing the mysql database for No problems with that, but I noticed that when I installed mysql, I had neglected to set a password for the root account. I proceeded to do that with

>mysqladmin -u root password NEWPASSWORD

I then tried to check the root password by logging in with

>mysql -u root -p

After entering the password I had set above (which is not really NEWPASSWORD, by the way), I got

ERROR 1045 (28000): Access denied for user ‘root’@’localhost’ (using password: YES)


I had set the global root password, but my installation of mysql wants to differentiate passwords between domains, such as ‘’ and ‘localhost’. So now I was screwed. Time to Google.

The web site has a page for “access denied” errors, but none of the solutions on that page worked. They had stuff like try, “mysqladmin –no-defaults -u root -p” and then reset the password. Still got the error, above.

After searching around some more, I found a less secure way on their web site that allowed me to reset the password. The full instructions are at

First I had to kill the mysqld process with a simple ‘kill’ command on the running process. Then restarted it with

>/usr/bin/mysqld_safe –skip-grant-tables –user=root &

This allows anyone to log in without passwords, so it should not be done while connected to the internet.

Then I logged in as root and reset the password

>mysql -u root
mysql> UPDATE mysql.user SET Password=PASSWORD(‘NEWPASSWORD’)
-> WHERE User=’root’;
mysql> exit

Killed the mysqld process again, and then restarted the daemon correctly

>service mysqld start

I tested the root login and got what I expected.

>mysql -u root -p
Enter password:
Welcome to the MySQL monitor. Commands end with ; or \g.

mysql> exit

So, that is now correct. I feel like such a noob. Oh, and as far as backups, I decided to just add the entire mysql database directory into my rsnapshot.conf file so that all databases get backed up every night. I may write about my use of rsnapshot later. It is a pretty awesome tool for making current and archival backups in the least amount of disk space.