Bad Vibes! Page 9
The concept of a successful suspension is simple. Once we've done everything practical to reduce the amount of added resonant energy generated in our stand and platform, the next step is to reduce the propagation of baseline external vibrations into our components through isolating as much of the remaining energy as possible with an effective suspension.
A suspension's resonant frequency is determined solely by the ratio of the coupled mass (composed of the supporting platform and component) to the stiffness of the spring support. As in our platform discussion, the natural frequency of a suspension is amplified at resonance. For frequencies well below the suspension's natural resonance, transmission is close to 100%. Then isolation begins for all frequencies greater than 1.4 times the resonant frequency. For undamped or sophisticated pneumatic and NSM (negative stiffness mechanism) designs, the reduction in amplitude continues to decrease at a nice, steep rate of nearly 12dB/octave.
Obviously, the issue of vibration in solid objects and the issue of isolation have resonance as a common problem. However, as we pointed out at the beginning of our discussion, there are important differences between these two aspects of vibration control in both theory and practice. Unlike the platform example, in which we pushed the resonant frequency as high as possible to reduce displacement from modal activity, a suspension will only begin to offer effective isolation at frequencies significantly above its natural resonance. Since a really effective suspension will need to isolate all structure-borne vibrations that can have an audible impact, we must push its natural frequency as low as possible so that the resulting zone of amplification is as far away as possible from the audio band---the main source of disturbance.
Two basic models are used by engineers to define an isolating suspension. First is the example of a "simple harmonic oscillator" which is formed by a rigid mass suspended by an ideal linear spring, yet has no method for dissipating the mechanical energy of its movement. There are some basic characteristics of this model that are important to remember: Any vibrations that are at or near the resonant frequency of the suspension will be significantly amplified. If the suspension truly lacked any damping, the displacement at the resonance peak would be infinite (you won't find many of these at your local hi-fi hut). The frequency at which the height of the resonant peak has fallen back to unity is equal to the natural frequency multiplied by the square root of two.. Another way of looking at this relationship is to multiply the resonant frequency of any suspension by 1.4; the result will approximate the frequency at which isolation actually begins.
Transmissibility is the ratio of vibrational amplitude that is transmitted through the suspension to the total vibration input. The transmissibility of vibration is constant for all frequencies well below the resonant point. In other words, essentially all of the low-frequency energy transmitted to the system will pass right on through without modification---as if the suspension wasn't even there.
The amount of vibration transmitted to the isolated elements will continue to attenuate for all frequencies above the zone of amplification---ie, after the resonance has subsided to the baseline level of unity. This is, in effect, like a low-pass filter at 12dB/octave, or 40dB per decade. Therefore, the lower you can establish the suspension's resonant frequency, the greater the degree of isolation for all frequencies above that point. Remember, too, that the suspension's resonant frequency is different from the inherent natural frequency of either the isolated platform or the component.
Unfortunately, the large displacement accompanying super-low frequencies---particularly those well below 10Hz---in an undamped suspension can make it very unstable and can lead to severe operational problems. The practical solution for the stability problem employed in most real-world suspensions is some variation of the second model called, appropriately, a "damped simple harmonic oscillator." This system differs from the first example by adding a damping mechanism to the spring that reduces the amplitude and shape of the resonance. In contrast to the first model, the damped isolation system not only curtails the maximum displacement of the suspension, making it more stable---a desirable trait---but can also, unfortunately, reduce the rate of attenuation for all frequencies above that point, in effect flattening the low-pass rolloff characteristics from a 12dB/octave slope to as shallow as 6dB/octave for some heavily damped suspensions (see Sidebar 2, fig.2).
Actually, the zone of amplification for a damped suspension is broadened on both sides of the resonance, though the low-pass region is of greater importance. For any given point above resonance---say, 20Hz for a system with a 10Hz resonant frequency---the damped system will usually provide less isolation than the undamped suspension! Also, some materials used to damp the action of a typical isolator can add stiffness to a spring which, in turn, would raise its resonant frequency. All things considered, we have a classic Catch-22 that defines the fundamental limitation of the steel-spring and elastomer-based suspensions commonly used in audio.
Fortunately, this dilemma can be solved with good pneumatic isolation systems. Traditional isolators tend to have "reactive" damping characteristics, while the more sophisticated, dual-chambered pneumatic designs combine real-time damping along with other unique qualities. These factors allow good air-based systems to achieve the fast rolloff of a simple harmonic oscillator above resonance, and the low amplitude at peak resonance of a damped harmonic oscillator---resulting in a clearly superior suspension all the way around.