Natural Frequency और Damping का Relation क्या है? | Forced Vibration in Hindi


Natural Frequency और Damping का Relation क्या है? | Forced Vibration in Hindi

Natural Frequency (ωₙ) और Damping Ratio (ζ) किसी vibrating system के dynamic response को determine करते हैं। ये forced vibrations, resonance, और amplitude response पर direct effect डालते हैं।

1. Natural Frequency

SDOF system में natural frequency:

ωₙ = √(k/m)

यह वह frequency है जिस पर system free vibration में oscillate करता है जब damping absent हो।

2. Damping Ratio (ζ)

Damping ratio system की resistance को describe करता है। Viscously damped SDOF system में:

ζ = c / (2√(mk))

जहाँ c = damping coefficient, m = mass, k = stiffness।

3. Relation Between Natural Frequency and Damped Frequency

Damped system में oscillation की frequency slightly कम होती है:

ωd = ωₙ √(1 – ζ²)

ζ < 1 होने पर underdamped system में frequency decrease होती है। ζ = 0 होने पर ωd = ωₙ (undamped case)।

4. Significance in Forced Vibration

  • Resonance occurs when forcing frequency ≈ ωₙ
  • Higher damping reduces peak amplitude at resonance
  • ζ and ωₙ together determine dynamic amplification factor
  • Engineering design ensures safe amplitude response by selecting appropriate damping

5. Applications

  • Machine foundations and vibration control
  • Seismic design of structures
  • Vehicle suspension systems
  • Dynamic load analysis in mechanical and civil systems

6. Conclusion

Natural frequency और damping ratio vibration analysis के core parameters हैं। Damped frequency ωd इनके relation से determine होती है और forced vibration में system response safe और controlled बनाता है।

Related Post