Name ___________________________ Section _____________________ EM406 Examination I September 28, 2006 Problem Score 1 /25 2 /35 4 /40 Total /100 Show all work for credit AND Turn in your signed help sheet AND Stay in your seat until the end of className 25 pts EM406 Examination I Problem 1 September 28, 2006 Problem 1a In the lab you used a performance index, J, to determine the goodness of fit for your models. Given experimental data, xexp, and results from a model, xmodel, how do you find J? (3 pts) Problem 1a A force versus deflection plot is made for a non-linear spring as shown. Object A weighs 2 lbs and object B weighs 6 pounds. Which will have a larger natural frequency when suspended from this spring? (3 pts) 01234567891000.10.20.30.4Displacement (in.)Force (lbf) What is the natural frequency of object B when suspended from this spring? (4 pts)Problem 1c A piece of rotating machinery is experience a bad vibrations problem and you have been asked to design a vibration isolator. The machine has two dominant frequencies 30 Hz and 50 Hz. a) Which frequency should you use when designing the isolator? (3 pts) b) Why? (3 pts) c) Using the answer you chose for part a) what minimum natural frequency, in Hz, is required to reduce the force transmitted? (3 pts) Problem 1d An engine is mounted on a rigid foundation with a set of four parallel supporting spring mounts. The static deflection under the weight of the engine is 0.2 in. What is the natural frequency of the engine? (3 pts) For a standard harmonically excited system, what is the minimum frequency ratio required to reduce the force transmitted by 70%. Neglect damping. (3 pts)Name 35 pts EM406 Examination I Problem 2 September 28, 2006 The water turbine shown in the figure is designed to operate at 360 rpm. The rotor is estimated to have a rotational imbalance of 0.1 kg-m. The mass of the rotor is 250 kg. The table has the information on the shaft connected to the rotor. We need to determine whether this rotational imbalance might cause interference with the stator. Calculate the bending displacement amplitude at steady state, in mm. Shaft Mass 123.5 kg Elastic Modulus 2.07 x 1011 N/m2 Moment of Inertia I 4.91 x 10-6 m4 Diameter 0.100 mName 35 pts EM406 Examination I Problem 3 September 28, 2006 A piece of equipment is placed on a shake table by 4 slender rods (only two are shown in the Figure 1). The mass, m, is 100 kg and k1 = 100,000 N/m. A model of this system is shown in Figure 2. a) Determine the equation of motion in terms of k1, c, kbeams and m. (Do not just write it down. Be sure to show all your work). An experiment is performed and it is found that the peak response occurs at ω = 55 rad/s and that ζ = 0.33. b) What is the value of kbeam? c) What is the steady state response, xss(t), assuming an input displacement of y(t) = 10cos70t mm. d) Determine the magnitude force transmitted to the support on the right. EI, L k1 y = Y0sinωt x m c Shake table Figure 1 – Schematic of equipment model k1 y = Y0sinωt x m c Figure 2 – Model of experiment