hwk06 - Homework 6.1 For this problem: 1. Derive the mass...

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Unformatted text preview: Homework 6.1 For this problem: 1. Derive the mass and stiffness matrices for the system in terms of the absolute generalized coordinates x1 and x2 . Assume the disk to be homogeneous. 2. Determine the natural frequencies for the system. Leave your natural frequencies in terms of k /m and α. 3. Determine the beat period for the free response of the system corresponding to α << 1. Homework 6.2 For this problem: 1. Derive the mass, damping and stiffness matrices for the system in terms of the absolute generalized coordinates x1 and x2 . 2. Show that the system possesses Rayleigh damping. Does the system possess either mass proportional (external) or stiffness proportional (internal) damping? 3. Determine the undamped natural frequencies in terms of k /m. 4. Write down the uncoupled EOMs in terms of modal coordinates p1 (√ and p2 (t). Determine t) the modal damping ratios for the two modes of the problem. Use c/ km = 0.3. Homework 6.3 Consider the longitudinal motion u(x, t) of the thin rod shown below. Determine the natural frequencies and modal functions for this rod. ...
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This document was uploaded on 12/23/2011.

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hwk06 - Homework 6.1 For this problem: 1. Derive the mass...

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