# hwk12 - ME563 Fall 2011 Purdue University West Lafayette,...

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Unformatted text preview: ME563 Fall 2011 Purdue University West Lafayette, IN Homework Set No. 12 Assignment date : Friday, November 18 Due date : Friday, December 9 (last day of lecture) Please attach this cover sheet to your completed homework assignment. Name PUID Problem 12.1 Problem 12.2 TOTAL Problem 12.1 Consider the undamped, four-DOF system shown below. This system has 4x4 symmetric and positive definite mass and stiffness matrices M and K , respectively. However, we are not given the details of the problem in terms of masses and individual spring stiffnesses. The fundamental natural frequency for this system is 1A with the corresponding modal vector X A 1 ( ) . a) Consider now System B shown below. This system is the same as System A above except a particle of mass m has been rigidly attached to one of the original particles. Use the Rayleighs method to prove that the fundamental natural frequency is decreased by this addition of mass to the system; that is, show that 1A > 1 B . Consider the following suggestions for your proof: If the mass matrix for System B is written as M B = M +...
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hwk12 - ME563 Fall 2011 Purdue University West Lafayette,...

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