Explanation Given information: The vibration is forced vibration. Write the expression for the magnification factor in terms of amplitude of steady state response to the static deflection under the action of force. M F = X m δ m ..... (I) Here, the amplitude of steady state response is X m , the static deflection under the action of force is δ m . Write the expression for the magnification factor in terms of frequency ratio and damping factor. M F = 1 [ 1 − ( ω f ω n ) 2 ] 2 + [ 2 ( c c c ) ( ω f ω n ) ] 2 ...... (II) Here, the angular frequency of force damped vibration is ω f , the natural angular frequency is ω n , the damping coefficient is c , the critical damping coefficient is c c . Equate the Equations (I) and (II): X m δ m = 1 [ 1 − ( ω f ω n ) 2 ] 2 + [ 2 ( c c c ) ( ω f ω n ) ] 2 Square the terms on both sides. ( X m δ m ) 2 = 1 [ 1 − ( ω f ω n ) 2 ] 2 + [ 2 ( c c c ) ( ω f ω n ) ] 2

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

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 19.5, Problem 19.141P

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The range of values of damping factor for which magnification factor will always decrease as the frequency ratio increases.

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Chapter 19.5, Problem 19.140P

Chapter 19.5, Problem 19.142P

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The range of values of damping factor for which magnification factor will always decrease as the frequency ratio increases.

Solution Summary: The author explains the range of values of damping factor for which magnification factor will always decrease as the frequency ratio increases.

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The range of values of damping factor for which magnification factor will always decrease as the frequency ratio increases.

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