MATH 6760
Continuum Mechanics: Solids
Instructor: Andrej Cherkaev Fall 2004
3 credit hours
M,W,F
2:00-2:50 PM
Homework projects
First project. Due September 10.
Modelling of dissipation and heating
Consider a chain of 15 equal unit masses joined by nonlinear massless
springs with the force-versus elongation characteristics
f= x - 1/x
At the end of the chain, a mass m=100 is attached.
Initially, the chain is in equilibrium position, and an impulse is applied
to the end mass which has the initial speed v0=4
Model the dynamics of this chain. Simulate the motion of masses.
Graph the motion and energy of the large mass versus time.
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Compute kinatic energy of each of small masses.
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Approximate the chain with a single nonliear spring and dash pot.
- Observe the transport of energies to high-frequency modes of oscillations.
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Calculate the time average of the length of the excited chain.
- Why are the bodies expand when heated?