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Tables & Breadboards

ScienceDesk™ BreadboardsBreadboard compliance is primarily determined bythe stiffness of the table top. Transmissibility
Supports â–  At resonance, compliance is deter-mined by the degree of damping of thetable surface. Consider a ball suspended from an enor-mous mass by a spring. For now, we shallignore the pendulum motions and consid-er a system having only one degree of free- dom, i.e. capable only of vertical extension motions.In the absence of vibrational impulses, theball is stationary at its rest position.Suppose the object from which the ball issuspended is not infinitely large or not in- finitely stiff so that the point at which the spring is anchored starts to vibrate. Some of the vibration energy may be felt at the ball, causing it to vibrate at the same fre-quency. The frequency of this motion is given by:Where:
Optical Tables â–  Only at high frequencies, above reso-nance, does the mass of the table makeany significant impact on compliance. A typical transmissibility vs frequencycurve for a system with one degree of freedom
Table Supports At low or zero frequencies, the ball andspring move synchronously with the tableand with the same amplitude, i.e. the transmissibility is unity and the system be- haves as though the spring were rigid, with no vibrational isolation.As the frequency increases, a resonantcondition is approached. The ball has mass and momentum when moving and cannot change direction instantaneously in response to the rapidly changing forc-ing vibration. The vibration of the ballstarts to lag behind the forcing vibration, i.e. they are no longer in phase. Eventually, this phase lag becomes exactly 90°and at this point, the system is vibrat-ing at its natural or resonant frequency. Atthis resonant frequency, the system accu- mulates vibrational energy and increases in amplitude during the time the forcingvibration is applied, i.e. the system acts asa vibrational amplifier. As defined by the equation for transmissibility, the ampli- tude of this resonant motion does not grow to infinity because of damping.At frequencies much higher than the reso-nant frequency, the response of the ball is determined solely by the mass term, which is much larger than the stiffness term. In other words, the spring is rela-tively soft and the vibrational force travelsslowly along it in the form of compression extension waves. This slow transmission effectively spreads out the oscillatory na- ture of the forcing vibration. Essentially,the ball experiences a time-averaged forcedue to the fast moving vibration and, un- less the vibration involves a net displace- ment, this time-averaged force tends to ze- ro with increasing vibrational frequency.
Non-Magnetic Implications for Table Selection For optimum performance, an opticaltable must meet several conditions. Thefirst resonant frequency should be as highas possible, at least above the frequency of the noise sources. The table should be as stiff as possible and it should also be well damped, particularly near the resonantfrequency of the table. Thorlabs optical ta-bles and breadboards are designed to be light but stiff structures which incorporate good damping. fn is the resonant frequency of the oscillation m is the mass moving during the oscillation. k is the spring constant (related to thestiffness of the spring).The transfer function most commonlyused to express this flow of vibrational en- ergy is termed transmissibility, and is de- fined as the ratio of the dynamic output to the dynamic input, i.e. the ratio of theamplitude of the transmitted vibration tothat of the forcing vibration. Selecting the Isolation System Vibration isolation or elimination at anoptical surface is a two part problem. As discussed in the notes on optical tabletops, an optical table is designed to have zero or minimal response to a deflective force or vibration. This in itself is not sufficient toensure a vibration free working surface.The rigid table may still vibrate without deforming, i.e. vibrations of the table on the mounting system. These types of vibra- tion are constrained translations and/or ro-tations of the optical table.The entire table system is subjected con-tinually to vibrational impulses from the laboratory floor. These vibrations may be caused by large machinery within thebuilding or even by wind or traffic-excitedbuilding resonances (swaying).Vibrations of a floor in a building can bedivided into two basic types: vertical and horizontal. Typically, vertical componentsare in the range 10 to 50Hz, and horizon-tal components are in the 1 to 20Hz range. To prevent such vibrations from disturbing a setup or test, it is important to mount the table in such a way as to iso-late it vibrationally from the laboratoryfloor, i.e. mount the table such that its in- stantaneous position is independent of the periodic motions of the laboratory floor. This type of mounting is termed 'seismic'mounting. When an object is seismicallymounted with respect to the floor, the motions of the object and the floor are completely uncoupled and separate. Resonance In the example just outlined, the transmis-sibility of the spring is very dependent on the frequency of the forcing vibration. The idealized transmissibility of this sys-tem is given by: Where:ƒ is the frequency of the forcing function, ƒnis the natural resonant frequency of thesystem, ℘ is the damping ratio C/CC, which isexplained later in these notes.The following graph shows a plot of thisidealized transmissibility as a function of frequency. Note the similarity to the com- pliance transfer function previously dis- cussed in the table vibration text. Againthere are three distinct regions on the curve
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