ASE 365 - Practice Test 3

ASE 365 - Practice Test 3 - ASE 365Structural Dynamics Dr J...

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ASE 365—Structural Dynamics Name: Dr. J. K. Bennighof April 30, 2009 TEST 3 This test is closed-book, except that you are allowed to use one two-sided sheet of notes that you have prepared beforehand. Do all of your work neatly , with each problem beginning on a separate page. Clearly designate each of your answers with a box or circle. All numerical answers should either be exact or accurate to four decimal places. When you hand in your test, place the test handout, with your name on it, on top, followed by your work, with your sheet of notes on the bottom. Staple all pages together. Problem 1 (30%) The two degree of freedom system shown below has two masses, two springs, two dashpots, two displacements, and is excited by one force. (a) Show with two sketches the non-conservative virtual work δW nc done as virtual displacements δx 1 and δx 2 take place. Find the kinetic energy T and potential energy V for this system in terms of generalized coordinates x 1 and x 2 and their time derivatives. Write δW nc , T , and V in terms of matrices and vectors.
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