(a) Explanation Given information: The mass of the motor ( m ) is 45 kg. The static deflection ( δ s t ) is 6 mm. The unbalance mass of the motor ( m’ ) is 110 g. The axis of rotation ( r ) is 75 mm. The amplitude of vibration of the motor ( x m ) is 0.25 mm. The speed of the motor ( N ) is 300 rpm. Calculation: Calculate the natural circular frequency ( ω n ) using the formula: ω n = g δ s t Here, g is the acceleration due to gravity. Substitute 6 mm for δ s t and 9.81 m/s 2 for g. ω n 2 = 9.81 ( 6 mm× 1 m 1000 mm ) = 1635 s − 2 Calculate the frequency of the periodic force ( ω f ) using the relation: ω f 2 = 2 π N 60 Substitute 300 rpm for N . ω f 2 = ( 2 π ( 300 rpm ) 60 ) 2 = 987 s -2 Calculate the spring constant of the beam ( k ) using the formula: k = m ω n 2 Substitute 45 kg for m and 1635 s -2 for ω n 2 . k = 45 ( 1635 ) = 73.575 kN/m Calculate the unbalance force ( P m ) using the formula: P m = m ′ r ω f 2 Substitute 110 g for m ′ , 75 mm for r , and 987 s -2 for ω f 2 . P m = ( 110 g× 1 kg 1000 g ) ( 75 mm × 1 m 1000 mm ) ( 987 ) = ( 0.110 N/m ) ( 75 mm × 1 m 1000 mm ) ( 987 ) = 8 (b) To determine The coefficient of damping ( c ).

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

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Chapter 19.5, Problem 19.145P

(a)

To determine

The damping factor (ccc).

(b)

To determine

The coefficient of damping (c).

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Chapter 19.5, Problem 19.144P

Chapter 19.5, Problem 19.146P

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Vector Mechanics for Engineers: Statics and Dynamics

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The damping factor ( c c c ) .