Explore how well a spring-damper isolator blocks vibration arriving through the foundation. Adjust the system's natural frequency, damping ratio, excitation frequency and base amplitude to see the frequency ratio, transmissibility, isolation efficiency and resonance amplification update in real time, and design a mount that protects equipment from vibration.
Parameters
System natural frequency fₙ
Hz
Natural frequency of the spring-damper mounted system. Lower is better for isolation
Damping ratio ζ
Amount of damping in the isolator. Tames the resonance peak
Excitation frequency f
Hz
Frequency of the disturbance shaking the base (floor)
Base vibration amplitude
mm
Displacement amplitude of the shaking floor
Results
—
Frequency ratio r
—
Transmissibility T
—
Mounted-mass amplitude (mm)
—
Isolation efficiency (%)
—
Resonance amplification (ref.) (×)
—
Isolation verdict
—
Isolator and vibration transmission — animation
A mass on a spring-damper isolator and a shaking base are drawn. In the isolation region the mass moves less than the base; near resonance it moves more. The transmissibility curve and current operating point are shown alongside.
Displacement transmissibility T and frequency ratio r. f is the excitation frequency, fₙ the system's natural frequency, ζ the damping ratio. Amplitude reaching the mass = base amplitude × T.
Isolation efficiency η (meaningful only when T < 1) and the resonance amplification T_res, the transmissibility at resonance (r = 1).
Isolation (T < 1) occurs only when the frequency ratio r exceeds sqrt(2) ≈ 1.414. Making the spring soft to lower the natural frequency fₙ and raise r is the key to isolation design.
What is Vibration Isolation and Transmissibility?
🙋
People keep saying "stop floor vibration with an isolation pad" — does just slipping a rubber pad underneath really cut the vibration on its own?
🎓
Not necessarily, and that surprises people. Bolt a precision microscope straight to a trembling building floor and the floor's shaking goes right into the instrument. So you put the equipment on a spring-and-damper "isolation mount" instead. How much vibration you managed to block is the "transmissibility" — the ratio of the amplitude that actually reaches the equipment to the amplitude of the shaking floor.
🙋
So it's a ratio of amplitudes. Then the softer the rubber I use, the smaller the transmissibility gets, right?
🎓
Here is the interesting part — the story splits into three regions. The key is the "frequency ratio" r, the floor's vibration frequency divided by the natural frequency of the equipment-plus-spring system. When r is below 1, the excitation is slow and the transmissibility is about 1: the equipment just rides along with the floor and the rubber barely does any work. When r is near 1 — resonance — the transmissibility shoots far above 1, and the rubber actually amplifies the vibration. That is the point newcomers find shocking.
🙋
Wait — a pad I put in to reduce vibration can make it worse? Then where does the vibration actually drop?
🎓
Genuine isolation begins only once the frequency ratio r exceeds sqrt(2), about 1.414. Beyond that the transmissibility finally drops below 1, and the larger r grows the further it falls. So the golden rule of isolation design is: make the spring soft so the system's natural frequency is far below the floor's excitation frequency. With this tool's defaults — floor at 25 Hz, natural frequency at 5 Hz — r = 5, the transmissibility is about 0.06, and you block 94% of the vibration. On the canvas above you should see the mass shaking far less than the floor.
🙋
So is more damping always better? If it tames the resonance peak, I'd want to pile it on.
🎓
That is the double-edged nature of damping. More damping does lower the dangerous peak at r = 1 — a lifesaver when a machine passes through resonance every time it starts and stops. But in the genuine isolation region above sqrt(2), more damping slightly worsens the transmissibility. Drag the "Transmissibility vs damping ratio" chart below and you will see the line rise as damping grows in the isolation region. So in practice, damping is chosen as a compromise between "taming the resonance peak" and "keeping the isolation region effective".
🙋
Then should I just drive the natural frequency down and make the spring as soft as possible?
🎓
In theory the isolation keeps improving. But too soft and the static deflection — how far the spring sags under its own weight — becomes excessive, and the equipment wobbles instead of sitting stably. Even semiconductor lithography tools on air mounts bottom out around a 1-3 Hz natural frequency; go lower and posture control becomes the hard problem. So in the field you choose the spring rate of the isolator while watching three things together: isolation performance, support stability and acceptable static deflection. Sweep r around in this tool and you will feel how the transmissibility moves.
Frequently Asked Questions
Transmissibility is the dimensionless ratio of the vibration amplitude that reaches a spring-damper mounted object to the vibration amplitude of the shaking base (floor). If the floor vibrates with an amplitude of 2 mm and the mounted object moves only 0.12 mm, the transmissibility is 0.06, meaning 94% of the vibration was blocked. The smaller the transmissibility below 1, the better the isolation; above 1 the mount amplifies the vibration instead of isolating it. The value depends only on the frequency ratio and the damping ratio.
Vibration isolation, the state where transmissibility drops below 1, begins only when the frequency ratio r = excitation frequency / natural frequency exceeds sqrt(2) which is about 1.414. For r below sqrt(2) the transmissibility is 1 or more, so an isolator cannot block the vibration, and near resonance (r = 1) it amplifies the vibration strongly. The golden rule of vibration isolation is therefore to make the spring soft so the natural frequency is far below the excitation frequency, pushing r well beyond sqrt(2).
No, damping is double-edged. More damping lowers the dangerous resonance peak at r = 1, which is vital when a machine runs up or down through resonance at start-up and shutdown. But in the genuine isolation region, where the frequency ratio exceeds sqrt(2), more damping slightly worsens the transmissibility. This is because the numerator of the transmissibility formula contains the damping term (2 zeta r)^2, whose effect grows at higher frequencies. Damping must therefore be a compromise between taming the resonance peak and keeping the isolation region effective.
A softer spring lowers the natural frequency of the system, which raises the frequency ratio r for a given excitation frequency. Isolation begins only once r exceeds sqrt(2), and the larger r is, the lower the transmissibility and the higher the isolation efficiency. For example, if the floor vibrates at 25 Hz, lowering the natural frequency to 5 Hz gives r = 5, a transmissibility of about 0.06 and 94% of the vibration blocked. However, an excessively soft mount causes a large static deflection and the object will not sit stably, so isolator selection balances isolation performance against support stability.
Real-World Applications
Vibration isolation of precision and metrology instruments: Electron microscopes, atomic-force microscopes, semiconductor lithography tools and ultra-precision machining centres lose image quality or machining accuracy from the slightest tremor of a building floor. They are placed on air springs (air mounts) or coil springs, lowering the natural frequency to about 1-3 Hz so the frequency ratio against the tens-of-Hz floor vibration is large enough. The steep drop in transmissibility when you lower the natural frequency in this tool is exactly the design philosophy of such isolation tables.
Blocking vibration transmission into buildings and floors: Conversely, vibration-generating machines (pumps, compressors, air handlers, generators) are mounted on isolation pads or springs to stop the machine's vibration from reaching the building floor and walls. The principle is the same: make the natural frequency well below the machine's running speed and the force transmitted to the floor shrinks. In apartment buildings and hospitals this design is essential to stop vibration and structure-borne sound from reaching the floors above and below.
Vibration protection of transported and onboard equipment: Medical devices carried in an ambulance, precision parts shipped by truck, and onboard hard drives or cameras must be protected from the road vibration of travel. They are supported on isolation pads or gel mounts, and the natural frequency is set so the frequency ratio exceeds sqrt(2) for the main components of the travel vibration (a few Hz to tens of Hz). During transport, however, the excitation frequency is spread over a wide band, so amplification of components that pass through resonance must also be watched.
Pre-study of isolation design with CAE: Before running a detailed multi-degree-of-freedom model or a finite-element analysis, a single-degree-of-freedom transmissibility calculation like this tool gives a first read on "what natural frequency keeps the transmissibility below the target". Computing the natural frequency from the spring rate in an isolator catalogue and estimating the transmissibility moves the early product-selection decision forward quickly. If the FEM result differs greatly from this estimate, it is a sanity check that points to a mass or stiffness input error.
Common Misconceptions and Pitfalls
The biggest misconception is "slipping in an isolation pad always reduces vibration". As you can see by setting the frequency ratio near 1 in this tool, when the excitation frequency is close to the system's natural frequency the transmissibility shoots far above 1 and the pad amplifies the vibration. Sliding a cheap rubber pad "just in case" can land the natural frequency right on the excitation frequency and make things shake harder than before — a failure that genuinely happens in the field. When choosing an isolator, always compute the natural frequency from its spring rate and the equipment mass, and check that it falls below sqrt(2) times the excitation frequency, ideally below one third.
Next, the misconception that "more damping is always better". Looking only at the resonance peak, more damping looks reassuring, but in the isolation region above sqrt(2), more damping worsens the transmissibility. The numerator of the transmissibility formula contains (2 zeta r)^2, and this degradation grows at higher frequencies. For machines that always pass through resonance (motors that repeatedly start and stop), use generous damping; for equipment that runs steadily at a high frequency ratio, keep damping modest — tailoring damping to the application is the correct approach.
Finally, do not assume "this tool's single-degree-of-freedom model maps directly onto the real machine". What is treated here is an idealized single-degree-of-freedom system where a rigid mass moves in one direction. A real machine has six degrees of freedom — three translations (up-down, fore-aft, side-to-side) and three rotations — each with its own natural frequency. Also, an isolation pad has a dynamic spring rate that varies with frequency and amplitude, and its properties drift with temperature and age, so it does not always behave like the catalogue value. This tool is ideal for early study and grasping the principle of "how much isolation can be expected in which direction", but back the final isolation design with an eigenvalue analysis or excitation test of the real machine.
How to Use
Set the natural frequency (fnNum, Hz) of your isolated system—typical values: 5–20 Hz for machinery mounts, 2–8 Hz for sensitive equipment
Adjust damping ratio (zetaNum, 0–1) where 0.05–0.1 suits elastomeric isolators and 0.2–0.3 suits viscoelastic dampers
Input base excitation frequency (excNum, Hz) and amplitude (ampNum, mm) matching your foundation vibration source
Read Transmissibility (T) to determine how much vibration reaches the mounted mass; T < 1 indicates isolation success
A 500 kg precision grinding machine mounted on elastomeric pads: natural frequency fn=8 Hz, damping ζ=0.08, base excitation 25 Hz at 0.5 mm amplitude. Frequency ratio r=25/8=3.125 falls well above resonance. Transmissibility T≈0.10 means only 0.05 mm reaches the spindle. Isolation efficiency ≈90%. Compare this to an undamped isolator (ζ=0.02) where T≈0.12 at r=3.125; the added damping reduces peak resonance amplification from 6.3× to 4.2×, protecting against shock loads during startup.
Practical Notes
Peak transmissibility occurs near r=1 (resonance); avoid mounting natural frequencies within ±0.5 Hz of dominant foundation frequencies (pumps, motors, compressors typically 50–120 Hz)
Soft isolators (low fn) achieve better isolation at high excitation frequencies but invite larger static deflection; verify floor load rating
Damping reduces resonance spike but increases mid-range transmissibility; for HVAC chillers use ζ=0.05–0.10 to balance startup transients against steady-state isolation