The comparison between the MIM product to a press and sinter P/M part.

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Chapter 16, Problem 55RQ

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The comparison between the MIM product to a press and sinter P/M part.

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An elastic bar of length L = 1m and cross section A = 1cm2 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω2x, where ω= 100rad/s is the angular velocity. The bar is pinned on the rotation axis at x = 0. A mass M = 1kg is attached to the right end of the bar. Due to the radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) solves the BVP (strong form) sketched below:              d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (1) u(0) =?? essential BC σ(L) =?? natural BC where σ(x) is the axial stress in the rod, ρ= 2700kg /m3 is the mass density, and E = 70GPa is the Young’s modulus 1. Define appropriate BCs for the strong BVP 2. Find the solution of the strong BVP analytically 3. Derive the weak form of the BVP.

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