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Unformatted text preview: Homework assignment 4 * Due date: Monday December 3, 2007 1. Buckling of a tower See figure 8 . 16 on p. 501 in the text. Consider the following Cauchy-Euler equation 1 which describes the deflection y ( x ) from the vertical in terms of the height x measured from the top of the untruncated tower: x 2 y 00 + Pa 2 EI y = , x ∈ ( a, a + L ) y ( a ) = y ( a + L ) = The top of the tower corresponds to x = a ( a is the part of the tower that is truncated) and the ground corresponds to x = a + L , so the height of the tower is L . The positive parameters are as follows: P for the vertical load, I for the moment of inertia, E for the modulus of elasticity. Under certain conditions -in particular when the load is high enough- the tower may buckle and the purpose of this problem is to determine when this will happen. By definition, buckling occurs if the above boundary value problem has a nontrivial solution ( y ( x ) 6 = 0)....
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- Summer '06
- Boundary value problem, nontrivial solution, boundary condition, nontrivial periodic solution, untruncated tower