How Does Building Height Affect Resonance During Earthquakes?

[bob4000]

i have undertaken an investigation, where the aim is to establish a relationship between the frequencies of an earthquake, and the height of the building(at maximum deflection parallel to motion). to do this, a model was created; a building of lego blocks and a vibration generator set to reciprocate at frequencies 2,4,6,8,10 Hz (all frequencies investigated separately). the height at which maximum deflection was acheived was takes as the resonant point. the building started at 2 blocks, increasing in increments of 2 blocks each time. the deflection and height was then plotted. graphs were plotted to illustrate height vs deflection and frequency vs max deflection.

now how would i relate this to relevant physics theories/laws. it MAY not seem difficult to yourself, but it has baffled both of my teachers. the ones that I know we have to discuss are simple harmonic motion and resonance. but we have trouble applying even these to this investigation. how would i deduce any information/analyse from such graphs as mentioned above.

I AM NOT ATTEMPTING TO GET SOMEONE TO DO THIS FOR ME, JUST POSITIVE IN DEPTH GUIDANCE.

Thank You for reading this.

PLEASE E-MAIL ME AT surjmann2907@hotmail.com FOR ANY PROOF OF WORK DONE

 

[berkeman]

It seems like the first step would be to write the harmonic analysis equations for a finite thickness rod, or maybe a finite thickness rectangular tower in the direction of the flat faces.

Then the next step toward understanding a building's motion would be to perform a finite element analysis using a computer. In the simplest version, you could just use Excel to construct a 10-floor building with known masses, spring constants, dampings, etc. In a more complicated analysis, you could use existing FEA software, or write your own code. In the end, you should be able to correlate the experimental results with your FEA results, as long as you have modeled the physical situation well in your code.

 

[kyle8921]

Hello,

I am happy to provide guidance on your investigation on the relationship between earthquake frequencies and building height. It is a challenging task to relate this experiment to relevant physics theories and laws, but with some guidance, I believe you can make sense of the data you have collected.

Firstly, it is important to understand the concept of resonance. Resonance occurs when an object is subjected to a periodic force at its natural frequency, causing it to vibrate with a larger amplitude. In your investigation, the building made of lego blocks represents the object, and the vibration generator represents the periodic force. The frequencies you have investigated (2, 4, 6, 8, and 10 Hz) can be considered as the natural frequencies of the building.

Now, let's look at the graphs you have plotted. The height vs deflection graph shows the relationship between the height of the building and the maximum deflection it experiences at each frequency. This graph can be related to simple harmonic motion, which is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. In your experiment, the height of the building can be considered as the displacement from equilibrium, and the maximum deflection can be considered as the amplitude of the motion. The graph should show a sinusoidal curve, with the maximum deflection occurring at the resonant frequency of the building.

Next, the frequency vs max deflection graph shows the relationship between the frequency of the vibration generator and the maximum deflection of the building. This graph can be related to the concept of resonance. As mentioned earlier, resonance occurs when an object is subjected to a periodic force at its natural frequency. In your experiment, the maximum deflection occurs at the resonant frequency of the building, which is the frequency at which the building vibrates with the largest amplitude.

To deduce information and analyze the data, you can use the equations for simple harmonic motion and resonance. The equation for simple harmonic motion is x(t) = A*sin(ωt + φ), where x(t) is the displacement, A is the amplitude, ω is the angular frequency, and φ is the phase angle. You can use this equation to calculate the amplitude of the building's motion at each frequency and compare it to the maximum deflection data you have collected.

The equation for resonance is f = ω/2π, where f is the resonant frequency and ω is the angular frequency.