Bad Vibes! Page 4
One example of this misconception, frequently applied in audio, is the use of massive slabs of granite or marble alone. Many audiophiles expect that "isolation" will be guaranteed occur for any component or speaker so supported---as if the vibrations wouldn't be able to pass through such a massive object. As we will see, the different problems of floor- and stand-borne vibrations require different practical approaches. Once you understand the basic elements of physical law that affect each, and the different roles required of a platform and its isolating suspension, their proper relationship should become clear.
Every structure associated with a typical stereo system---floor, shelf, component chassis, speaker cabinet, equipment rack---will have a number of natural resonant frequencies. Each resonant frequency of a solid object corresponds to a specific bending mode unique to that frequency. These mode shapes define the direction of motion and correlate to the peak amplitude of displacement that results when the particular natural frequency of a platform is excited into resonance by external vibrations of the same frequency.
Every solid object, particularly irregularly shaped ones, will have numerous modes, yet the lowest natural frequency of a given platform will usually be the most dominant, with the next few adding a significant contribution to its overall "resonant signature." Modal analysis begins with the concept of "degrees of freedom" of a system or object. This refers to the minimum number of directions of motion necessary to define how an object can move in its particular environment. For instance, a single, independent particle has three degrees of freedom, while our ideal rigid body has six: up and down, front to back, left to right, and rotation around each of these three axes. There is a direct relationship between the number of degrees of freedom an object has and the number of natural resonant frequencies and modes it is subject to. Most fixed objects or enclosed acoustic spaces have many hundreds of degrees of freedom and related modes (see sidebar 1, "The Rigid Body Concept").
Because audio components are non-ideal three-dimensional objects, it doesn't take much imagination to see how complex the twisting, bending, and flexing of modal forces can become when random and variable vibrations stimulate multiple resonant frequencies in such structures. As a result, vibrations in the horizontal and vertical planes must be dealt with. (Keep this requirement in mind; it has a major impact on the real-world performance of most vibe-reduction products.)
When you multiply the modal signature of a platform by those simultaneously at work on shelves connected to a rack or stand---which is contributing its own complex resonant pattern to the mix---and include vibrations from the floor that the stand is coupled to, you have a real problem. Toss in a few stereo components whose non-uniform chassis contain vibration-generating transformers that make their resonant frequencies particularly complex, and an incredibly elaborate set of mode interactions will likely occur that will add sonic colorations and can result in a genuine limit to a system's resolution.
In vibration analysis, the minimum resonant frequency of a platform or suspension and the maximum amplitude of that resonance are of paramount importance. This is due to the effect of displacement. In vibration analysis, "compliance" is often used interchangeably with displacement as a measure of the tendency of an object to move in response to vibration. As such, it is directly related to mode shape and defines a structure's dynamic rigidity. Compliance is a ratio of displacement to the amount of applied force, and is also the inverse of stiffness, whether of a solid object like a shelf, or of a spring-like suspension; in the latter case, the stiffer the spring, the lower the compliance, and vice versa.
There are several reasons why the minimum resonant frequency of a rigid structure is so important. For starters, a reduction in frequency leads to an increase in displacement and a corresponding amplification of the resonance, resulting in a "noisier," less stable platform.
Realistically, the lowest natural frequency of any practical platform or table-top is around 80Hz or so, meaning that all vibrations of frequencies lower than this will transmit through the platform with little change in amplitude. Actually, most materials and shapes used for platforms have natural frequencies ranging from around 120Hz up to 400Hz or more---well into the midrange. The lower the resonant frequency of a platform, the less desirable---the associated increase in amplitude will cause more serious ringing that damping can only partially reduce. A very stiff structure will have a higher dominant resonance, and, since an increase in frequency correlates with a reduction in physical displacement, less complex mode shapes will form, even though the total amount of energy remains the same.
This, then, is the most practical solution for a good supporting platform: Employ specific materials and geometry that increase the platform's stiffness:weight ratio so that the improved rigidity raises the resonant frequency, reduces its amplitude, and minimizes the structure's bending mode shapes. In addition, enough damping should be applied to the platform to further lower the displacement of resonances over a broad frequency range without degrading the structure's stiffness. As we've seen, damping is particularly important for supporting platforms used in audio systems, to help dissipate equipment-borne and acoustically coupled resonances.