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Unformatted text preview: Assigned on 07.12.2009 Monday Due date 14.12.2009 Monday, beginning of the lecture ME429 Fall 2009 HW7 You are expected to provide clear explanation of each step in your solution, units, well annotated scaled plots (title, axis labels, units, ..), not random hand sketches, source code attached to your solution if you use a software package. 1) A SDOF system with mass m = 1 kg and stiffness k = 100 N/m is subjected to each of the forcing functions given below. Note that the forcings are applied until t = 1s and then removed, that is the forcing is zero after t = 1s. 10 F(t) [N] 5 0 0 0.2 0.4 0.6 time [s] 0.8 1 10 F(t) [N] 5 0 0 0.2 0.4 0.6 time [s] 0.8 1 10 F(t) [N] 5 0 F(t)=10sin(t) 0 0.2 0.4 0.6 time [s] 0.8 1 Find the response of the system to each of the forcings by using a) convolution integral b) Laplace transform. 2) A building frame is modeled as an undamped SDOF system and is subjected to a loading represented by a triangular pulse as shown below. Note that the equivalent stiffness elements are given in the x direction. F(t) m x(t) Fo k/2 k/2 to a) Find the response expression of the frame using convolution integral. b) If m = 5000 kg, k = 7.5 × 109 N/m and to = 0.4 s, determine maximum Fo if the displacement is to be limited to 10 mm. c) Plot the response of the frame using the values from part b). ...
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