Explanation Given: Mass of motor is 180 kg . Unbalance mass of rotor 28 g . Distance of unbalance mass of rotor and axis of rotation is 150 mm . Static deflection is 12 mm . Amplitude of vibration should be less than 60 μ m . Speed of motor should be more than 300 rpm . Concept used: Write the expression for amplitude of vibration of motor. x m = r ( m / M ) ( ω f / ω n ) 2 1 − ( ω f / ω n ) 2 ..... (1) Here, x m is the amplitude of vibration of motor, r is the distance between mass center of rotor and its axis of rotation, m is the mass of rotor, M is the mass of motor, ω f is the forced frequency of rotor and ω n is the natural frequency of system. Write the expression for natural circular frequency of system. ω n = k M ...... (2) Here, k is the equivalent stiffness of spring. Rearrange equation (2) for k . k = M ω n 2 ...... (3) Write the expression for natural frequency in terms of deflection for beam. ω n = g δ s t ...... (4) Here, g is the acceleration due to gravity and δ s t is the amplitude of static deflection. Substitute g δ s t for ω n in equation (3). k = M g δ s t ...... (5) Consider the plate being added to the system, consider then new mass of the system as M ' . Write the expression for new natural circular frequency of system. ω n ' = k M ' ...... (6) Here, ω n ' is the new natural frequency and M ' is the mass of system with plate. Write the expression for mass of the plate. M plate = M ' − M ...... (7) Here, M plate is the mass of plate. Substitute M ' ω n ' 2 for k , ω n ' 2 for ω n 2 in equation (1). x m = r ( m k ) ( ω f 2 ) 1 − ( ω f 2 ω n ' 2 ) ...... (8) Calculation: Substitute 180 kg for M , 9

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

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Chapter 19.4, Problem 19.117P

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The required mass of plate.

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Chapter 19.4, Problem 19.116P

Chapter 19.4, Problem 19.118P

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The required mass of plate.

Solution Summary: The author explains the amplitude of vibration of motor, the force of rotor, and the natural frequency of system.

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