Explanation Given information: The impressed force ( P ) is P m sin ω f t . The equation of ( y ) is δ m sin ω f t . Calculation: The expression for the amplitude of forced vibration ( x m ) as follows: x m = P m k 1 − ( ω f ω n ) 2 The expression for the force transmitted ( P T ) m as follows: ( P T ) m = k x m Substitute P m k 1 − ( ω f ω n ) 2 for x m . ( P T ) m = k P m k 1 − ( ω f ω n ) 2 ( P T ) m = k × P m k [ 1 1 − ( ω f ω n ) 2 ] ( P T ) m = P m [ 1 1 − ( ω f ω n ) 2 ]

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, 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 19.4, Problem 19.121P

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Show the equation of transmissibility ωfωn>2.

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Chapter 19.4, Problem 19.120P

Chapter 19.4, Problem 19.122P

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A mass of flexible machine part, m, of 10 x 2 kg was observed to vibrate badly at frequency of 10 Hz. The vibration was caused by the application of a harmonic force, F of 10 x 10 N to the flexible part. A judgment was made by a mechanical engineer that the vibration was excessive because the frequency of the harmonic force coincides with the natural frequency of the flexible part. (c) Analyze the mass and stiffness of an absorber that would eliminate vibrations of the flexible part at frequency of 10 Hz, if the amplitude motion of the absorber mass, Xa at 10 Hz was observed to be 0.1 x 9 cm. (d) If the flexible machine part is operated in the speed range of 500 to 750 rpm, justify whether the design of vibration absorber in Q3(c) is safe to be used or not.

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Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.2P Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - Prob. 19.8P Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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