Explanation Given: Weight of motor is 400 lb . Unbalance mass of rotor is 3 -oz . Distance of unbalance mass from the axis of rotation is 6 in . 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 Write the expression for the force exerted on system. ( F t ) m = k x m ...... (3) Substitute r ( m / M ) ( ω f / ω n ) 2 1 − ( ω f / ω n ) 2 for x m and k M for ω n in above expression and simplify. ( F t ) m = r m ω f 2 ( 1 − ω f 2 M k ) ...... (4) Here, ( F t ) m is the force exerted on the system. Calculation: Substitute 6 in . for r , 3 -oz for m , 100 rpm for ω f 2 and 400 lb for M in equation (4) To determine (b) Amplitude of fluctuating force on foundation.

12th Edition

ISBN: 9781260265521

Author: BEER

Publisher: MCG

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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…

Question

Chapter 19.4, Problem 19.118P

To determine

(a)

Maximum allowable spring constant of the pad.

To determine

(b)

Amplitude of fluctuating force on foundation.

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Chapter 19.4, Problem 19.117P

Chapter 19.4, Problem 19.119P

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(a) Maximum allowable spring constant of the pad.

Solution Summary: The author explains the maximum allowable spring constant of the pad and the distance of unbalance mass from the axis of rotation.