Understanding Resonance 1

[cjholl0]

I was wondering if anyone could explain some basic resonance ideas? If I'm designing a throttle body that incorporates a DC motor, is the concern that the motor may operate at or near the nat freq of the body, which would cause some body deformation? I'm assuming all objects have a NF right?, depending on mass of object. If an object is vibrated directly or by a component (if an assembly)at or near its NF is that when resonance ocuurs, what if the object was going through some vibration range, would it oscillate as it was transitioning through that NF range? I had the classes in school and worked the calculations but never really got a good applied, theoretical understanding of the concept. Any help is appreicated.

 

[sms]

Resonance occurs when a forcing function frequency is equal to a natural frequency.

A simple example of excitation of a natural frequency is plucking a guitar string. The string vibrates at its natural frequency and because of damping the vibration reduces in amplitude over time.

An example of resonance is the old memorex commercial. Ella Fitzgerald adjusts the frequency of the note she is singing until it is the same as the natural frequency of a wine glass. The result is that the vibrations of the wine glass build up until it shatters. If some had tapped the wine glass the natural frequency would have been excited and the wine glass would ring at that frequency. But the constant excitation over stresses the glass causing it to shatter.

In general it is advised to keep mechanical structures out of resonance. I work with screw compressors that excite resonance in piping and silencers resulting in heavy plate steel breaking resulting in hydrocarbon leaks.

"Why don't you knock it off with them negative waves? Why don't you dig how beautiful it is out here? Why don't you say something righteous and hopeful for a change?" Oddball, "Kelly's Heros" 1970

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[Ali Kara]

Hi. Actually continuous systems have infinite degree of freedom, so infinite natural frequency(i.e. resonance frequency). You mentioned about a motor. A motor has many components and all of these components have their own resonance frequencies. Due to the nature of the vibratory motion, if a component vibrates with its fundamental frequency(first natural frequency) or one of first few, the amplitude of the motion tends to go infinity. This of course causes the break, fatigue or fracture propagation.

http://en.wikipedia.org/wiki/Image:Resonanzueberhoehung.png;

here you can see what i mean.

 

[Transient1]

saglamci,

I'm not sure if I agree with the statement that the first natural frequency of a structural has an amplitude that tends to infinity. I think your saying that the amplification of a structure excited by a force with a frequency equal to its natural frequency tends to infinity.

It is correct to say this (the fundamental mode) will have the largest amplitude. Also, other natural frequencies if clustered close to the first natural frequency may be non-trivial (for example during random vibration).

 

[btrueblood]

Some gas turbine engines have shafts (coupling turbine and compressor) that operate above the first critical speed. Typically, these engines have a prescribed starting sequence, where the engine is started and operated for some time period below the critical speed, then accelerated through the critical speed within a defined time window, to reach a final operating speed. The forcing function in this case can usually be pretty well defined, or at least bounded, by knowledge of the rotor's mass balance (or imbalance limits), and the analysis proceeds by examining how much energy can be deposited to the shaft/rotor by said imbalance at a given speed or by conducting other dynamic analyses, resulting in a maximum speed-time envelope that can be allowed before vibrations will build to levels that are damaging to the equipment. Often, accelerometers are attached to the bearings, and real-time measurements can be used to force a shut-down of the engine.

 

[Ali Kara]

Hi again. Transient is right. Saying that i was thinking what you said. But i couldn't express myself i guess. Thank you for correction. One more thing also i forgot; damping. As you say excitation at first fundamental frequency makes the system tend to go infinity. However; this actually occurs when there is no damping effect. So, in damped systems(actually undamped system is an assumption to make things simple) although excitation having the natural frequency of the system effects on it, excitation does not go to infinity but will be the maximum.