Question

IlI. Vibration isolation taking into account the stiffness of the beam A machine subject to a single frequency harmonic excitation of the form F()Fo sin at is to be analyzed over a range of frequencies ω, < ω < ω.. The machine is mounted on a beam at a location where the of equivalent stiffness is keg. The model of a machine mounted on a damped isolator then attached to a beam of negligible mass is Fosinut xit) yit) kea Figure 1 A. Calculate the equivalent stiffness of the beam at the location where the mass is attached assuming the mass of the beam is negligible Plot the maximum stiffness of an undamped isolator versus the maximum transmitted force to the beam for various frequencies within the operating range. Use the model in Figure 1 Consider the model of the vibrations of the machine on a damped isolator with the stiffness of the beam considered. This model is shown in Figure 1. Derive expressions for the force transmitted to the beam through the isolator, the steady-state amplitude of the machine and the maximum deflection of the isolator. You may use concepts from SOR such as the sinusoidal transfer function. Does the basic isolator design still work when the stiffness of the beam is taken into account? Explain using both mathematical (calculating the transmitted force) and physical reasoning. Determine the absolute amplitude of vibration of the machine and the amplitude of deflection of the isolator when the basic isolator design is used. B. C. D. E.

Answer 1

Fes lK Dc. Fo=. Applied Cot cot

(ous) Fo MO u규- tonn t-

Gng. @k +he Yuti o 15 Tonts you