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Vibration Analysis Tool

Vibration Isolation Mount Design Calculator
Transmissibility & Isolation Design

Back-calculate required mount stiffness from equipment mass and excitation frequency. Compute vibration transmissibility, insertion loss, and static deflection in real time while visualizing the danger zone near resonance.

$$\text{TR} = \sqrt{\frac{1+(2\zeta r)^2}{(1-r^2)^2+(2\zeta r)^2}}, \quad r = \frac{f_{\text{exc}}}{f_n}$$
Parameter Settings
Equipment Mass m 100 kg
Mass of the equipment to be isolated
Excitation Frequency f_exc 50 Hz
Motor speed, etc. (e.g. 1500 rpm → 25 Hz)
Target Natural Frequency f_n 5.0 Hz
Isolation effective when f_exc / f_n > √2
Damping Ratio ζ 0.05
Natural rubber ≈ 0.05–0.1, viscoelastic ≈ 0.2
Number of Mounts n 4
Near resonance region (TR > 0.5)
No isolation effect (resonance amplification region, TR > 1)
Design Guidelines
Isolation effective: r = f_exc/f_n > √2 ≈ 1.41
Typical design: r ≈ 3–5 (TR ≈ 5–15%)
Precision equipment: r > 5 (IL > 20 dB)
Transmissibility TR
—
dimensionless
Insertion Loss IL
—
dB
Natural Frequency f_n
—
Hz
Total Stiffness k_total
—
N/mm
Mount Stiffness k_mount
—
N/mm
Static Deflection δ_st
—
mm
Frequency Ratio r
—
f_exc / f_n
Load per Mount
—
N/unit
Transmissibility TR vs Frequency Ratio r (Log Scale)
Theory — Vibration Transmissibility & Isolation Design

Transmissibility TR

$$\text{TR} = \sqrt{\frac{1+(2\zeta r)^2}{(1-r^2)^2+(2\zeta r)^2}}$$

$r = f_{\text{exc}}/f_n$: frequency ratio

Mount Stiffness and Natural Frequency

$$k_{\text{mount}} = \frac{m(2\pi f_n)^2}{n}$$

n: number of mounts, m: equipment mass

Static Deflection

$$\delta_{\text{st}} = \frac{g}{(2\pi f_n)^2} = \frac{mg}{k}$$

Lower f_n results in larger δ_st

Insertion Loss IL

$$\text{IL} = -20\log_{10}(\text{TR}) \quad [\text{dB}]$$

TR=0.1 → IL=20 dB (90% reduction)