Vibrations in Electronics

Many modern electrical devices make use of microelectromechanical, or MEM, resonators and filters (pictured above) in their circuitry, especially those involving the wireless transmission of data such as cell phones and computers. One possible use for an MEM resonator would be to act as a bandpass filter, regulating the frequency output of a circuit (a possibility which has been researched by Purdue Mechanical Engineering professor Jeffrey Rhoads). The filter acts by having negligible motion until a signal is passed which results in the MEM device oscillating at resonance (approximately its natural frequency), at which point the vibrations of the structure reach a magnitude large enough for the wave to pass through. The following article discusses some recent breakthroughs in the area and the advantages of using MEM technology:

Article

A simulation related to Problem 8/72

In today's lecture, we talked about how the amplitude of response depends on the ratio of omega/omega_n in base-excited systems (such as Problem 8/72):

• For small omega/omega_n, the response tracks closely with that of the base.
• For omega/omega_n near 1, near-resonance (large response) is expected. This is usually undesirable for obvious reasons.
• For large omega/omega_n, the response is diminished as compared to the base motion. This is usually good.

One way to make omega/omega_n small is to increase the value of the excitation frequency omega. For Problem 8/72, this means driving fast. This is undesirable since, as was pointed out in class, this creates a large transmitted force in the suspension (and possible an undesirable ticket from the police!). Another way to make omega/omega_n large is to decrease the value of omega_n. Note that omega_n can be decreased by INCREASING the apparent mass of the system. This is called "vibration isolation".

Earlier in the system, Ryan (rvanklom) posted an interesting idea in vibration isolation for Formula 1 vehicles called an "inerter" (see the following post). This inerter allows for the apparent mass to increase without a large increase in actual mass (it converts translational motion into rotational motion).

Shown below is a simulation of the response of one quarter of the body of a car without and with an inerter. Carefully compare the two responses. 

• As you can see, the response with the inerter is less than half of that response without the inerter. 
• Also note that the damping ratio has also decreased with the inerter (the transients take longer to die away) although the damping constant c is unchanged. Do you know why this is true? (Look at how the damping ratio is related to the damping constant and the mass of the system.)

Let us know if you have any thoughts on this.

An "inerter" and vibrations (posted for rvanklom)

Ryan has provided us with another blog challenge topic. This time it is related to a new idea for vibration control in the suspension of Formula 1 racing cars. This device is called an "inerter" that adds effective mass to the suspension system through the conversion of translation motion into rotational motion.

Click here to see the analysis provided by Ryan for the inerter.

What do you think? Do you follow his analysis?

Vibration modeling of guitar strings (posted for Dale Szul)

See attached file for a single degree of freedom model for the vibration of a guitar string. This work focuses on determining the value for the string mass to be used in the model so that the natural frequencies match up with those of the physical string.

Spring-Mass Simulator

This is a MATLAB program that simulates how a mass acts under the influence a spring system. It takes inputs derived from the EOM and outputs an XY plot of time (x axis) vs. displacement of the mass (y-axis). I suggest using EOM's from homework problems.

To use the simulator, right-click to download both files (SpringSim.m and SpringSimulator.mdl ) and put them in the same directory. Then start MATLAB and run the script called "SpringSim". The simulator should explain the rest.

I used MATLAB to create the interface and Simulink to create the simulator itself, which is the block diagram you will see when you run the program. If you have any questions about how it works or have any problems using the simulator, please comment.

NOTE: This simulator will work with any inputs, however the results may not show up on the XY plot if the applied force is substantially bigger than the product, k * (max value of displacement). If you run the simulator, don't receive an error, and nothing shows up on the XY plot, you need to use different values.

Critical Frequency - Tacoma Narrows Bridge Collapse

Here is a short documentary on the Tacoma Narrows Bridge (courtesy of YouTube). It is very interesting to see how the critical frequency can play a role in design. The bridge suffered a collapse when steady winds at the critical frequency caused the bridge to oscillate up and down before ultimately destroying it. As in class, whenever an object is being oscillated at the critical frequency, the oscillations keep getting larger and larger. Just thought it might be interesting since it covers the same topics as we have been covering in lecture.

The pitcher's mound and dynamics (posted for rvanklom)

Click here to see an explanation provided by Ryan for having a pitcher's mound in baseball. 

What do you think -- is this the reason for the mound?

Blog Challenge Question No. 2

In Homework Problem No. 3/177 (see problem figure in post below), the system is released from rest with y > 0 (block A above the horizontal path of B).

The mathematics of your work-energy equation should show that the speed of B reaches a (local) maximum for some position of A for which y > 0. Can you provide a physical argument as to why this local maximum for vB must exist for y > 0? [HINT: Consider the initial speed of B and the speed of B when AB is horizontal.]

In order to give everyone a chance to see this question, do not submit any responses prior to 5PM on Wednesday, October 15.

Blog Challenge Question No. 1

In the solution provided for Quiz No. 6, there is a question posed related the minimum rotation rate for bar OA such that the particle does not slip on bar OA. In particular, it was noted that if mu_s > tan(theta) the solution provides an imaginary value for omega_min. It was asked what physical significance does an imaginary solution for omega_min have.

For this blog challenge question, provided a written answer to this question. Submit your answer by either a comment to this post or an email attachment of a scan of your handwritten answer that will be posted by your instructor.

This challenge question is worth 10 blog participation points.

In order to give everyone a chance to see this question, do not submit any responses prior to 5PM on Wednesday, October 8.