Explanation Given that, The equation for the motion of the machine is x = x m sin ( ω f t − ϕ ) Force transmitted to the foundation is Springs: F s = k x = k x m sin ( ω f t − ϕ ) Dashpot: F d = c x . = c x m ω f cos ( ω f t − ϕ ) So, F t = F s + F d = x m [ k sin ( ω f t − ϕ ) + c ω f cos ( ω f t − ϕ ) ] F t = [ x m k 2 + ( c ω ) 2 ] sin ( ω f t − ϕ + ψ ) Thus the amplitude of F t is, F m = x m k 2 + ( c ω ) 2 ……………….(Eq.1) Amplitude of the force transmitted to the foundation is given by: x m = P m k ( 1 − ( ω ω n ) 2 ) 2 + [ 2 ( c c c ) ( ω ω n ) ] 2 Here, ω denote ω f

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Author: BEER

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All the components used in civil engineering and mechanical engineering applications undergo deformations due to induced internal stresses under the application of external loads. Under repeated application of loads, there is a high possibility of failur…

Question

Chapter 19.5, Problem 19.147P

To determine

The amplitude of the fluctuating force transmitted to the foundation is:

Fm=Pm1+[2(ccc)(ωωn)]2(1−(ωωn)2)2+[2(ccc)(ωωn)]2

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Chapter 19.5, Problem 19.146P

Chapter 19.5, Problem 19.148P

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The amplitude of the fluctuating force transmitted to the foundation is: F m = P m 1 + [ 2 ( c c c ) ( ω ω n ) ] 2 ( 1 − ( ω ω n ) 2 ) 2 + [ 2 ( c c c ) ( ω ω n ) ] 2

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The amplitude of the fluctuating force transmitted to the foundation is: Fm=Pm1+[2(ccc)(ωωn)]2(1−(ωωn)2)2+[2(ccc)(ωωn)]2

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Chapter 19 Solutions

The amplitude of the fluctuating force transmitted to the foundation is:

Fm=Pm1+[2(ccc)(ωωn)]2(1−(ωωn)2)2+[2(ccc)(ωωn)]2