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.

  1. Compute kinatic energy of each of small masses.
  2. Approximate the chain with a single nonliear spring and dash pot.
  3. Observe the transport of energies to high-frequency modes of oscillations.
  4. Calculate the time average of the length of the excited chain.
  5. Why are the bodies expand when heated?