The expression for the value of the transverse mount stiffness, k, as a function of the relative speed of the bird, v, the bird mass, the mass of the engine and the maximum displacement is k = 1 / m ( m[tex]_{b}[/tex] v / I x I )²
m x ( t ) + k x ( t ) = F δ ( t )
I x I = F / m ω[tex]_{n}[/tex]
m = Mass of engine
k = Stiffness of transverse mount
F = Magnitude of impulse
ω[tex]_{n}[/tex] = Natural frequency
ω[tex]_{n}[/tex] = √ k / m
I x I = F / m ( √ k / m )
I x I = F / √ k m → ( 1 )
For bird,
F = m[tex]_{b}[/tex] v
Substitute this momentum value in ( 1 ),
I x I = m[tex]_{b}[/tex] v / √ k m
√ k = m[tex]_{b}[/tex] v / I x I √ m
k = 1 / m ( m[tex]_{b}[/tex] v / I x I )²
Therefore, the expression for the value of the transverse mount stiffness, k, as a function of the relative speed of the bird, v, the bird mass, the mass of the engine and the maximum displacement that the engine is allowed to vibrate is k = 1 / m ( m[tex]_{b}[/tex] v / I x I )²
The question is incomplete. The complete question is :
Consider the jet engine and mount indicated in fig.3 and model it as a mass on the end of a beam. the mass of the engine is usually fixed. find an expression for the value of the transverse mount stiffness, k, as a function of the relative speed of the bird, v, the bird mass, the mass of the engine and the maximum displacement that the engine is allowed to vibrate. Fig 3. is shown in the image attached below.
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