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Please help with the question. Thank you. A thin solid disk of radius b rotates

ID: 1862169 • Letter: P

Question

Please help with the question. Thank you.

A thin solid disk of radius b rotates (in a state of plane stress) with constant angular velocity omega within a rigid cylindrical casing of the same radius. The disk is a homogeneous linear elastic material of Young's modulus E, Poisson's ratio v, and mass density rho. The contact between the outer edge of the disk and the inner surface of the casing is frictionless. Find the radial displacements ur(r) throughout the disk. Sketch the variation with r of the radial displacement found in part a), and compute both the maximum value u max of u r and find the value of location r at which it occurs. Find the stresses sigma rr (r) and sigma theta theta (r) throughout the disk. Find the pressure p applied by the inside surface of the casing on the outer edge of the disk as a result of the rotation. Sketch the variations of the stresses found in part c), determine the values of r at which each of the stresses vanishes, and the regions of the disk in which each stress is positive, and the regions in which each stress is negative. Find the variation with r of the magnitude |tau| max of the maximum in-plane shear stress throughout the disk. In particular, determine the maximum value M of |tau| max and the value of r at which it occurs.

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