Large initial velocity

weak layer buckling or collapse

o Compress a beam -- the observations

  • If you compress a beam with increasing force
    • Small forces, the beam doesn't move
    • Large enough force, the beam buckles
  • Buckling equations

    k A ziv + P z'' = 0

    z(0) = z''(0) = z(L) = z''(L) = 0

    • k - Hookes spring stiffness of material
    • A - beam cross section area
    • P - compressive load

o Eigenvalue problem for z

  • Add a compressive load (i.e. a skier or new snow)
  • Single mode buckling solution

    P = pi2 k A / L2

o Mechanism for creating an initial velocity

  • This model does not give the amplitude
  • Worst case
    • Assume the layers free fall a distance L
    • Using gravity as the force, find the velocity
  • Provides for large initial velocities

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