Explanation Given: Unbalanced weight of tail rotor is 1 lb . The distance of unbalance weight to axis of rotation is 6 in . Equivalent stiffness of tail and tail rotor is 8800 lb/ft . Equivalent weight of tail and tail rotor is 165 kg . Operating speed of rotor is 500 rpm . Concept used: Write the expression for natural frequency of system. ω n = k M ...... (1) Here, ω n is the natural frequency of system, k is the equivalent stiffness of tail and tail rotor and M is the equivalent mass of tail and tail rotor. Write the expression for amplitude of vibration of motor. x m = e ( m / M ) ( ω f / ω n ) 2 1 − ( ω f / ω n ) 2 ..... (2) Here, x m is the amplitude of vibration of motor, e is the distance between mass center of rotor and its axis of rotation, m is the mass of rotor, M is the mass of tail and tail rotor and ω f is the forced frequency of rotor Write the expression for the forced response of tail. x p ( t ) = x m sin ( ω t − ϕ ) ...... (3) Here, x p ( t ) is the forced response of tail section and ϕ is the phase difference. Calculation: Substitute 8800 lb/ft for k and 165 lb 32.2 ft/s 2 for M in equation (1). ω n = 8800 ( 165 32.2 ) = 41.44 rad/s Substitute 41.44 rad/s for ω n , 500 rpm for ω f , 1 lb for m , 6 in for e and 165 lb for M in equation (2)

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 19.120P

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The forced response of the tail section.

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Chapter 19.4, Problem 19.119P

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The forced response of the tail section.

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