Söndirish koeffitsienti ζ nima?

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 bo'lsa — kam söndirish rejimi (tebranma). Ko'pchilik mexanik tizimlarda ζ 0,01 dan 0,1 gacha bo'ladi.

Logaritmik dekrement usuli qanday ishlaydi?

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.

Yarim quvvat kengligi usuli qanday ishlaydi?

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).

Logaritmik dekrement kam söndiriladigan tizimlar uchun yaxshiroq (ζ < 0,1) va erkin tebranish so'nishining aniq ko'rinib turishi sharti bilan. Yarim quvvat kengligi usuli majburiy tebranish o'lchovlari va o'rtacha söndirish uchun qulay. Juda kuchsiz söndirish holatida ko'p tsikl bo'yicha o'rtalashtirish logaritmik dekrement aniqligini oshiradi.

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.

Bepul Muhandislik Vositasi #066

So'nish koeffitsienti kalkulyatori

Logaritmik dekrement (ketma-ket cho'qqi amplitudalari) yoki yarim quvvat kengligi usuli orqali söndirish koeffitsienti ζ ni aniqlash. Ko'p tsiklli o'rtalashtirish qo'llab-quvvatlanadi.

Log DecrementYarim Quvvat KengligiAuto-Calc

Method

Peak Amplitude x₁

Cho'qqi amplitudasi x₂ (n tsikldan keyin)

Tsikllar soni n (between x₁ and x₂)

Quick presets

Results

So'nish nisbati ζ

—

Damping (%)

—

Logarifmik dekrement δ / O'tkazish polosi kengligi Δf

—

Sifat omili Q

—

So'nish tasnifi

—

Logarifmik dekrement usuli

Yarim quvvat o'tkazish polosi usuli

Quality Factor

Misol — Logarifmik dekrement

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. Yuqori so'nish uchun aniq formuladan foydalaning.

Söndirish Koeffitsienti Kalkulyatori | Logaritmik Dekrement & Yarim Quvvat Kengligi | Bepul Vosita #066

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

Results

Logarifmik dekrement usuli

Yarim quvvat o'tkazish polosi usuli

Quality Factor

Do'kon

Support

Contact