An elastic bar of length L = 1m and cross section A = 1cm² spins with angular velocity w about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = w²x, where w = 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: (σ(x)) + pa(x) = 0 PDE d dx σ(x) = Edu dx u(0) =?? σ(L) =?? Hooke's law (1) essential BC natural BC where σ(x) is the axial stress in the rod, p = 2700kg/m³ is the mass density, and E = 70 GPa is the Young's modulus. 3 M L 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. 4. Solve the problem using COMSOL's Weak Form PDE module.

An elastic bar of length L = 1m and cross section A = 1cm² spins with angular velocity w about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = w²x, where w = 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: (σ(x)) + pa(x) = 0 PDE d dx σ(x) = Edu dx u(0) =?? σ(L) =?? Hooke's law (1) essential BC natural BC where σ(x) is the axial stress in the rod, p = 2700kg/m³ is the mass density, and E = 70 GPa is the Young's modulus. 3 M L 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. 4. Solve the problem using COMSOL's Weak Form PDE module.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.3.18P: A stepped shaft ABC consisting of two solid, circular segments is subjected to uniformly distributed...

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