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Sunday, 11 September 2016

Vibration Isolation and Transmissibility -- 2 Level model (2 DOF)

          If supporting floor is sufficiently flexible, then two level (or higher) model is more accurate representation. This model also useful for the case where an inertia block (seismic model) is used between the machine and the rigid foundation. 

          If we neglect damping, the motions of the masses, m1 and m2 to an input force on the upper mass of  FEQSinwt  are:
The transmissiblity  (ratio of force transmitted to foundation to the input force), is :
The natural frequencies of the system are the two values of W where the denominator is equal to zero. In the olden days, we would  have factored this equation into the form aw4 + bw2 + c = 0, then found the two roots using the quadratic equation,
now it is more convenient to put equation 12 into a spread sheet and calculate the transmissibility over a range of frequencies, as in Fig. There are now two natural frequencies, and two frequencies at which the system can resonate. The slope above the second resonance is now -40 db/decade.   


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