Question

A 50 lb motor is bolted to the middle of a 72-inch long plank, and x is the displacement of the motor from its equilibrium position. The plank may be modeled as a simply supported beam with EI 18 x 10 lb-in2. Use the inch-pound-second system of units to work this problem, and use g 386 in/sec2 a) Neglect the mass of the plank and find the system's undamped natural frequency of vibration (ansuwer: f 21.3 Hz) b) Suppose the plank weighs 20 lb and the plank's deflection is similar to one-half of a sine wave: y(z) x(t)sin where zA 0 and z = l = 72 in. Include the equivalent mass of the plank and find the system's undamped natural frequency of vibration (answer: f 19.4 Hz). A x ZB=1= 72 in. 0= 2 ATO 72 in. P 48EI The stiffness of a simply-supported beam is keam where P is the force applied to the midpoint of the beam and S is the deflection at the midpoint

Answer 1

Calculate the stiffness of a simply supported beam 48(18x100 48EI - 2314.8 lb/in (72) Calculate the undamped natural frequency of vibration k 2314.8 1 = 21.276 Hz z 21.3 Hz = 2Tm 50 27T 386

Calculate the equivalent mass considering the weight of the plank 50 20 0.5 386 - 0.15544 lb-s2/in М +0.5m тор 386 Calculate the undamped natural frequency of vibration (2314.8) 1 k 1 19.422 Hz 19.4 Hz 27 (0.15544) 27T m eq