When we’re taught about vibrations, every mathematical modelisation deals with a system of a fixed spring whose end has a certain mass, but how does this relate to real-world systems like a bridge or a building? The natural frequency of the spring-mass system is the number of back-and-forth movements being done per second, but what’s the equivalent of that for let’s say a building or a bridge or any real-life application?
In: 0
The analogy is pretty direct, the bridge itself moves up and down because the atoms around bound together like with springs (by electromagnetism)
Just the parameters are very different, the springs are very strong so little movement means high forces already.
Not a direct answer to your question but just a note on why the spring-Mass model is so important in physics:
The Mass on a spring is an example of a system where the force on the mass is lineair with the displacement. If you move the mass 10cm from it’s equilibrium the force is twice as big as when you move it only 5cm. It’s often the first example you see because it’s eassy to vizualize and do experiments with.
There are accually a lot of systems that behave in the same way when they are displaced by a small amount around their equilibrium.
For example: the forces between atoms in a solid material. The full version of these forces is a very difficult equation. But we know an equilibrium: when the atoms follow the lattice perfectly. In most solids at room temperature the atoms will be very close to this equilibrium and models that simplify the forces to be lineair give good, predictive results.
For real life examples in bridgers or buildings I hope some engineers will react, but I’m certain they have many.
Explain like I’m two….. I had absolutely no idea what the title meant. I’m glad I’ve now gained the knowledge. I absorbed it completely in full….
Thank you.
key point is every solid material is actually not a ‘rigid body’
they bend twist etc in reality
metals permanently deform with great force but some metals
if you push with less force before that point of no return
they come back to original shape
because they happen over time, they’re like springs
if you composite metal beams/carbon fiber with concrete/epoxy etc
very hard to theoretically calculate accurately
since it’s not just one known value of single metal nor concrete, depends on how they’re layered what orientation where will the load be etc
so it needs to be tested in real world
as if they’re springs with mass as 1 system to calculate the resonance frequency vibration characteristics etc
and if we keep building and testing different materials, orientations
we can find out theoretical value of that specific composite material
and use that to simulate more complex things
When we’re taught about vibrations, every mathematical modelisation deals with a system of a fixed spring whose end has a certain mass, but how does this relate to real-world systems like a bridge or a building? The natural frequency of the spring-mass system is the number of back-and-forth movements being done per second, but what’s the equivalent of that for let’s say a building or a bridge or any real-life application?
In: 0
The analogy is pretty direct, the bridge itself moves up and down because the atoms around bound together like with springs (by electromagnetism)
Just the parameters are very different, the springs are very strong so little movement means high forces already.
Not a direct answer to your question but just a note on why the spring-Mass model is so important in physics:
The Mass on a spring is an example of a system where the force on the mass is lineair with the displacement. If you move the mass 10cm from it’s equilibrium the force is twice as big as when you move it only 5cm. It’s often the first example you see because it’s eassy to vizualize and do experiments with.
There are accually a lot of systems that behave in the same way when they are displaced by a small amount around their equilibrium.
For example: the forces between atoms in a solid material. The full version of these forces is a very difficult equation. But we know an equilibrium: when the atoms follow the lattice perfectly. In most solids at room temperature the atoms will be very close to this equilibrium and models that simplify the forces to be lineair give good, predictive results.
For real life examples in bridgers or buildings I hope some engineers will react, but I’m certain they have many.
Explain like I’m two….. I had absolutely no idea what the title meant. I’m glad I’ve now gained the knowledge. I absorbed it completely in full….
Thank you.
key point is every solid material is actually not a ‘rigid body’
they bend twist etc in reality
metals permanently deform with great force but some metals
if you push with less force before that point of no return
they come back to original shape
because they happen over time, they’re like springs
if you composite metal beams/carbon fiber with concrete/epoxy etc
very hard to theoretically calculate accurately
since it’s not just one known value of single metal nor concrete, depends on how they’re layered what orientation where will the load be etc
so it needs to be tested in real world
as if they’re springs with mass as 1 system to calculate the resonance frequency vibration characteristics etc
and if we keep building and testing different materials, orientations
we can find out theoretical value of that specific composite material
and use that to simulate more complex things
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