Engineering Applications of Correlation and Spectral Analysis, 2nd Edition

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CEE619 – Advanced Structural Dynamics & Smart Structures Winter Semester 2006-2007 Homework #3 (Due: March 23, 2007 – Hand in to my office) 1. Consider a suddenly applied pulse load, with intensity f o , which extends over a period of T o : = o o o T t T t f t f 0 0 ) ( We are interested in analyzing the 1DOF response to this loading, with f o = 1 kip and T o = 0.4 sec, by the FFT (Fast Fourier Transform) method. An associated handout lists a few MATLAB functions that will be useful in frequency domain analyses. Please read this handout before beginning to work on the problem set. You should write a general MATLAB routine (do not use Excel) that applies the FFT method to predict the response of an 1DOF oscillator – with arbitrary mass m , damping c , and stiffnes k – under an arbitrary input force history f(t) . To check your routine, first examine a system with m = c = 0 and k = 1; i.e. with zero mass and damping and unit stiffness. In this special case the response should be identical to the input force, f(t) . Check your results (including the normalization of the Fourier components) with the sample input/output plots provided in the handouts. NOTES: For simplicity, the example digitizes the force with dt = 0.1 sec. A finer discretization is requested in the questions below. At times t = 0 and t = T o , the force discontinuity is best represented, for Fourier analysis, by its average value f o /2 = 0.5 kips.
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  • Winter '06
  • Lynch
  • FFT, free vibration, Fast Fourier transform, Undamped Systems, FFT Analysis

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