1-60 Section 1 The magnification factor for the amplitude of the oscillations is (1.4.11) This quantity is sketched as a function of the frequency ratio Ω/ω for several damping factors in Figure 1.4.3. Note that the amplitude of vibration is reduced at all values of Ω/ω if the coefficient of damping c is increased in a particular system. Vibration Control Vibration Isolation It is often desirable to reduce the forces transmitted, or the noise and motions inside or in the neighbor- hood of vibrating machines and structures. This can be done to some extent within the constraints of space and additional weight and cost by the use of isolators, such as rubber engine mounts and wheel suspension systems in cars. Many kinds of isolating materials and systems are available commercially. The effectiveness of vibration isolation is expressed by the transmissibility TR, the ratio of the force transmitted F T to the disturbing force F o . A simple isolation system is modeled as a spring and a dashpot in parallel, for which the transmissibility is given by Equation 1.4.12 and sketched in Figure 1.4.4. (1.4.12) FIGURE 1.4.3Magnification factor in damped forced vibration. FIGURE 1.4.4Transmissibility patterns of a vibration isolator. MF A Fk A d oo === () [] +− () [] 1 21 2 2 2 ζω ωΩΩ TR F F T o == + () − () [] + () 14 14 2 2 2 2 2 2 ζω ωζω Ω ΩΩ . that the amplitude of vibration is reduced at all values of Ω/ω if the coefficient of damping c is increased in a particular system. Vibration Control Vibration Isolation It is often desirable to. inside or in the neighbor- hood of vibrating machines and structures. This can be done to some extent within the constraints of space and additional weight and cost by the use of isolators, such as. in cars. Many kinds of isolating materials and systems are available commercially. The effectiveness of vibration isolation is expressed by the transmissibility TR, the ratio of the force transmitted