Uwiano wa upunguzaji ζ ni nini?

Damping ratio ζ (zeta) is the ratio of actual damping to critical damping. ζ = 0 means undamped, ζ = 1 is critically damped, 0 < ζ < 1 ni pungufu ya upunguzaji (inayoteleza). Mifumo mingi ya mitambo ina ζ kati ya 0.01 na 0.1.

Jinsi gani mbinu ya kipimo cha logarithmic decrement inavyofanya kazi?

Measure successive peak amplitudes x₁ and x₂ in free vibration. The log decrement δ = ln(x₁/x₂). For n cycles: δ = (1/n)ln(x₁/xₙ₊₁). Then ζ = δ/√(4π² + δ²) ≈ δ/(2π) for small damping.

Jinsi gani mbinu ya upana wa bandwidth ya half-power inavyofanya kazi?

From a frequency response function, measure the natural frequency fn and the two frequencies f₁, f₂ where amplitude drops to 1/√2 of peak (−3 dB). Then ζ = (f₂ − f₁)/(2fn) = Δf/(2fn).

Mbinu gani ina usahihi zaidi?

Logarithmic decrement inafaa zaidi kwa mifumo yenye kudhibitiwa kwa upole (ζ < 0.1) yenye mtetemo huru unaopungua wazi. Upana wa bandwidth ya half-power unafanya kazi vizuri kwa vipimo vya mtetemo unaolazimishwa na kudhibitiwa kwa wastani. Kwa kudhibitiwa kwa upole sana, wastani wa mizunguko mingi huimarisha usahihi wa logarithmic decrement.

Je, sababu ya ubora Q ni nini?

Quality factor Q = 1/(2ζ). A high Q indicates low damping and a sharp resonance peak. Q = 50 means ζ = 0.01. Q is commonly used in acoustics, electronics, and structural dynamics.

Zana ya Uhandisi ya Bure #066

Kikokotoo cha Uwiano wa Kunyamazisha

Amua uwiano wa udhibiti ζ kutoka kwa logarithmic decrement (vilele vya mfululizo vya amplitude) au mbinu ya upana wa half-power bandwidth. Inasaidia wastani wa mizunguko mingi.

Log DecrementUpana wa Half-Power BandwidthAuto-Calc

Method

Peak Amplitude x₁

Amplitude ya Kilele x₂ (baada ya mizunguko n)

Idadi ya Mizunguko n (between x₁ and x₂)

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Results

Uwiano wa Udhibiti ζ

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Damping (%)

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Kupungua kwa Logarithm δ / Upana wa Bendi Δf

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Sababu ya Ubora Q

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Uainishaji wa Unyoofu

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Njia ya Kupungua kwa Logarithm

Njia ya Upana wa Bendi wa Nguvu-Nusu

Quality Factor

Mfano — Kupungua kwa Logarithm

Given: x₁ = 10 mm, x₂ = 6 mm, n = 1 cycle

δ = (1/1) × ln(10/6) = ln(1.667) = 0.5108

ζ = 0.5108 / √(4π² + 0.5108²) = 0.5108 / 6.304 = 0.0811 (8.11%)

⚠️ Note: The log decrement approximation ζ ≈ δ/(2π) is accurate to within 1% for ζ < 0.1. Kwa unyoofu mkubwa zaidi, tumia formula sahihi.

Kikokotoo cha Uwiano wa Udhibiti | Logarithmic Decrement & Upana wa Half-Power Bandwidth | Zana ya Bure #066

Published by Nikolai Shelkovenko on Febuari 15, 2026 Febuari 15, 2026

Results

Njia ya Kupungua kwa Logarithm

Njia ya Upana wa Bendi wa Nguvu-Nusu

Quality Factor

Duka

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