Question

Fun vibrations project, discussion

Answer 1

So, I was given a task to calculate the maximum tip displacement of the lightning rod on top of the empire state building.

My professor hinted that I would need the mass, natural frequency, stiffness, moment of inertia to calculate this

However, I'm having a heck of a time figuring out where to start, I have the mass and the dimensions of the building so the moment of inertia isn't a problem *estimated anyways*

But where can I start? Time for a discussion? ideas?

Answer 2

Eventually I will be making a general solidworks flow simulation to get some of the pressures up top etc...but I want to deal with the theory for now!

Answer 3

At first glance, I would probably calculate the wind force and get an approximation of the maximum displacement by equating the wind force to the restoring force provided by the stiffness. Then I would probably do something using the damped harmonic oscillator equation but you probably need to linearise the wind force in some way. I am a first year physics undergrad and I am no engineer. Physicists deal with much nicer things...

Answer 4

"fun" johnny says

Answer 5

Hey @thomas5267 thanks for the response!

So in all, I made the model in solidworks *Though I can NOT find the lengths and widths of the various levels of the building which makes this the ULTIMATE rough sketch lol*

Since I'm going to treat this as a solid rectangular prism, I use the stiffness to be \(\large K = \frac{3EI}{l^3}\)

Making this entire model of material A36 steel *common in construction and I can NOT find more detailed results* I was able to find the other information I needed

Then I converted the wind speed to a dynamic pressure \(\large Q = \frac{1}{2}\rho \bar{v}^2\)

Used that pressure along the entire cross section of the model I made in solidworks and came out with a displacement of about 18mm

Sounds good to me!

Answer 6

Hey @IrishBoy123

What else do you think I could do here to make it interesting? Or at least, a little more realistic? :)

Answer 7

hi john

thomas is a either a shy or a recalcitrant engineer. as his suggestions are simply excellent.


if you are taking this into the real world, most buildings are sails. big rectangle just waiting to be knocked over.

i'm thinking at a very low level, but as this is a maths site, we have to think small! and pernickerity lol!

so if you wanna go really nuts, streamline the edges of the thing. and use the drop in air pressure to power the buildling!

http://www.rd.com/advice/work-career/james-dyson-on-creating-a-vacuum-that-actually-well-sucks/

Answer 8

Haha I agree completely! Thomas, we all know your secret!

But awesome, I appreciate your response as well @IrishBoy123 ! That's actually a cool way to check this out...lets have some fun here!

Answer 9

!!!

Answer 10

Today I learned that apparently I am an engineer.... I am just a first year student studying theoretical physics...