In our acoustic consultancy division, we strongly believe that adequate information and technical knowledge is critical in order to solve acoustic sensitive problems. That is as noise and vibration consultants but also as industrial soundproofing consultants.

In Alpha Acoustiki, our noise and vibration consultants team conduct vibration measurement and assessment studies and use those findings to recommend vibration isolation solutions to control and mitigate vibration generated by mechanical systems. Specifically, some principal parameters of the **vibration control studies** carried out by our noise and **vibration consultants** department are:

• Evaluation of vibration in buildings

• Vibration measurements (with 3axial accelerometers): RMS weighted acceleration, PPV (*Peak Particle Velocity*), VDV (*Vibration Dose Value*), according to BS 6472, FFT vibration analysis, etc.

• Calculation of machinery excitation frequency

• Calculation of deflection and natural frequency of the anti-vibration system

• Selection of appropriate vibration control system, for each specific application

• Protection of equipment from earthquakes or wind pressure, hurricanes etc..

We design and produce Vibration Control solutions for the following indicative categories:

• Industrial vibration control applications (i.e. Chilling Units, air- conditioning units, Gen Sets, boilers, HVAC hydraulic press etc).

Additional projects of use in vibration isolation, can be in marine, railway, aviation etc that silicone rubber pads are usually proposed to be used.

• Building applications to avoid structure borne vibration transmission (i.e. floating floors, floating walls, floating suspended ceiling etc).

• Studio noise-vibration protection applications to construct floating surfaces, using the “room in room” construction method. That includes floating ceilings, floating floors and floating walls.

• Human response to vibration at work, like Hand arms & Whole body vibration evaluation and protection, according to European Union Directive 2002/44/EC or International Standards.

Some critical terminology that needs to be clarified in regards to vibration isolation is presented below. Understanding the terminology will contribute in adequate selection of the anti-vibration method.

**Transmissibility**

**Vibrations** can be divided into two basic types: vertical and horizontal. Typically, vertical components range from 10 to 50 Hz while horizontal components range from 1 to 20 Hz range. To prevent such vibrations from disturbing a receiver, it is important to support the optical table so that the optical table’s instantaneous position is independent of the periodic motions of the laboratory floor. This type of isolation is usually described as seismic mounting. When an object is truly seismically mounted with respect to the floor, the motions of the object and the floor are completely uncoupled.

In the absence of vibrational impulses, a hanging mass (usually a ball in experiments) will remain stationary at its rest position. Suppose the object from which the mass is suspended is not infinitely large or not infinitely stiff so that the point at which the spring is anchored starts to vibrate. Some of that vibrational energy may be transmitted to the ball, causing it to vibrate at the same frequency. The frequency of this motion is given by

Where f_{n} is the resonant frequency of the oscillation, *m* is the mass moving during the oscillation, and *k* is the spring constant (related to the stiffness of the spring).

The flow of vibrational energy is expressed in terms of a transfer function. A transfer function is a method of quantifying how efficiently a forcing vibration can produce an excited vibration. The transfer function most applicable here is termed transmissibility and is defined as the ratio of the dynamic output to the dynamic input (i.e., the ratio of the amplitude of the transmitted vibration to that of the forcing vibration).

where the damping ratio ζ is defined as

Here, *f* is the frequency of the forcing function and c is a parameter describing the damping properties of the system.

The graph below shows a plot of this idealized transmissibility as a function of frequency.

**A typical transmissibility vs. frequency curve for a system with one degree of freedom**

At low frequencies, the hanging mass moves synchronously with the mass that the spring is suspended from and with the same amplitude. The system behaves as though the spring was rigid, and as a result, the ball is not isolated from the large mass.

As the frequency of the driving force increases, the momentum of the ball prevents the ball from moving in phase with the driving force (i.e., a change in the direction of the driving force does not instantly result in a change in the direction that the ball is moving due to the momentum of the ball). When the phase lag between the driving force and the vibration of the ball becomes exactly 90°, the system is vibrating at its natural (resonant) frequency *f _{n}*.

When the driving force frequency is much greater than the resonant frequency of the spring/ball system, the response of the ball is determined solely by the mass of the ball. In other words, the spring is relatively soft and the vibrational force travels slowly along as compression waves. This slow transmission effectively spreads out the oscillatory nature of the forcing vibration. Essentially, the ball experiences a time-averaged force due to its slow response to the fast moving vibrations, and unless the vibration involves a net displacement, the magnitude of the time-averaged force tends toward zero with increasing vibrational frequency. As the transmissibility approaches zero, the position of the ball is not affected by the vibration in the large mass. At this point the ball is seismically mounted.

**Damping**

This is probably the most critical term for noise and vibration consultants and for overall vibration isolation. Damping refers to any process that causes an oscillation in a system to decay to zero amplitude. It is a very important phenomenon in v**ibration control or isolation**. Successful anti-vibration products offering an effective vibration control are critically designed based on this principal. Damping causes the energy to be diverted from vibration to other sinks. Damping in a system is usually defined as the ratio of actual damping to critical damping. Critical damping is the minimum amount of damping in a system necessary to prevent resonant oscillation, following application of an impulsive force.

Damping is a resonant effect in that primarily it affects the transmissibility function at or near resonance.

At resonance,

Using this relation can be simplified to read

The height of the transmissibility peak at resonance is mainly determined by the amount of damping. In the absence of damping, the peak would be infinitely high. Also, a system with no damping would not stop vibrating, even when the driving force is removed. Clearly, all real systems contain damping to some degree. Using the suspended ball as an example, the simplest form of damping would be to immerse the ball in a viscous medium. In practical terms that would be an-antivibration products. More information on http://antivibration-systems.com/our-products/. The drag on the ball created by the viscous medium would convert the vibrational energy to heat via friction and practically the vibration would be isolated in terms of subjective receipt.

**Seismic Mounting of Tables**

That is another critical term for vibration consultants and for engineers designing anti-vibration products and **vibration isolators**. The ball and spring model suggests, a way in which an optical table could be seismically mounted. Simply suspend an optical table from a rigid ceiling by weak springs. Then, at frequencies much higher than the natural resonance of the spring isolation system, ambient building vibrations would not be transmitted to the table.

For queries, technical information and methods to resolve **mechanical or building vibration control product**s, do not hesitate to contact us at info@alphacoustic.com or info@vibro.gr

For more solutions in regards to vibration control products please visit antivibration-systems.com