Engineering Applications of Correlation and Spectral Analysis, 2nd Edition

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CEE619 – Advanced Structural Dynamics & Smart Structures Winter Semester 2006-2007 Homework #2 (Due: February 21, 2007 – In Class) 1. Fourier Integral . A structure will be loaded by a blast load with the aperiodic function depicted in Figure 1.1. As part of complete dynamic analysis of a structure exposed to this load, you decide to use the frequency domain to determine the structural response. Calculate the components A( ω ) and B( ω ) of the Fourier transform of the function, x(t) . x(t) x(t) = 0 for t < 0 x(t) = e -at for t > 0 t 0 Figure 1.1 An aperiodic blast loading function applied to structure As part of your solution, pleas provide a plot A( ω ) and B( ω ) in MATLAB . It has been stated that at time discontinuities, the inverse Fourier intergal would provide x(t) to be the average of the discontinuity. Please illustrate this property of the inverse Fourier integral at t=0 for the aperiodic function of Figure 1.1. 2. Fourier Transform. Use the equations for the formal definition of the Fourier transform to determine X( ω )
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