What is vibration transmissibility?

Vibration transmissibility T is the ratio of the response amplitude to the excitation amplitude in a vibration isolation system. T 1 means amplification is occurring, especially near resonance.

When does vibration isolation begin?

For an undamped system, isolation begins when the frequency ratio r = f/fn exceeds √2 ≈ 1.414. Below this ratio, the mount amplifies vibration. The T = 1 crossover at r = √2 holds for any damping ratio.

What is a good damping ratio for isolation?

Low damping (ζ = 0.01–0.1) gives better isolation at high frequency ratios but higher resonance peaks. Moderate damping (ζ = 0.1–0.3) limits resonance amplification at the expense of some high-frequency isolation.

How do I calculate isolation efficiency?

Isolation efficiency = (1 − T) × 100%. For example, T = 0.1 means 90% isolation. This metric is only meaningful when T √2).

What is the frequency ratio r?

The frequency ratio r = f/fn, where f is the forcing (excitation) frequency and fn is the natural frequency of the isolation system. The system response depends primarily on this ratio and the damping ratio ζ.

免費工程工具 — #013

振動傳遞率計算器

計算振動隔絕系統的傳遞函數 T。輸入激勵頻率、自然頻率與阻尼比，即可獲得傳遞率與隔絕效率。

SDOF 系統傳遞率 T 隔絕率 %

結果

傳遞率 T

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隔振效率

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頻率比 r

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傳遞率 (dB)

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相位角

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SDOF 系統的傳遞率

對於具有黏性阻尼的單自由度 (SDOF) 系統，傳遞率 T 為：

其中 r = f / f_n 為頻率比，而 ζ 為阻尼比。

關鍵區域

r < 1 — 低於共振：T ≈ 1（無隔絕效果）
r ≈ 1 — 共振：T 達峰值（放大）
r = √2 ≈ 1.414 — 交叉點：T = 1，與阻尼無關
r > √2 — 隔絕區域：T < 1，振動減弱

隔振效率

隔絕效率僅在 T < 1（即 r > √2）時有意義。

相位角

實務範例

範例 — 機台置於橡膠墊上

已知： 激勵頻率 = 50 Hz，自然頻率 = 15 Hz，ζ = 0.05

r = 50 / 15 = 3.333

T = √(1 + (2 × 0.05 × 3.333)²) / √((1 − 3.333²)² + (2 × 0.05 × 3.333)²)

T = √(1.111) / √(102.23 + 0.111) = 1.054 / 10.117 = 0.104

隔絕效率 = (1 − 0.104) × 100 = 89.6%

⚠️ 注意： 此公式適用於 SDOF 系統。實際結構可能具有多個共振點。請務必以量測結果驗證。