# Chap95 - Harmonic Response Analysis(Frequency Response Analysis The amplitude of response is sought under sinusoidal excitation There may be

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1 Harmonic Response Analysis (Frequency Response Analysis) ± The amplitude of response is sought under sinusoidal excitation. ± There may be multiple external forces , possibly out of phase with one another, but the loading is considered harmonic only when all loads are of the same frequency . •• F 1 =Asin5t F 2 =Bsin(5t-30 ° ) d 1 (t) d 2 (t) ± Loads of different frequency require dynamic response analysis as opposed to harmonic analysis . ± When first applied, harmonic loading does not invoke harmonic response. ± An initial transient exists that decays to zero in time because of damping. ± What remains is the steady-state response , which is the subject of harmonic response analysis .

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2 Harmonic Response of sdof System ± Harmonic load r(t) on the system ± Equation of motion: ± The steady-state displacement response :
3 Parameters Affecting Response Amplitude ± β here is the frequency ratio , ratio of the load frequency to the natural frequency ω of the system. ± It is not just the value of the load frequency but its value relative to the system’s natural frequency that governs how the system responds. ± α is the phase angle , i. e., how much response lags the loads. ± For small damping ratio ξ , is either very small (for <1) or close to 180 ° (for >1). ± F 0 / k is the static displacement, solution of the governing equation when velocity and acceleration are zero. ± Steady-state response amplitude is proportional to F 0 / k . u

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4 Amplitude Response Spectra for a sdof System
5 Characteristics of Amplitude Spectrum ± For ξ < 0.55 and when is near the natural frequency ω (frequency ratio near unity), response amplitude has a peak ± The smaller the damping, the larger the peak.

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## This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.

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Chap95 - Harmonic Response Analysis(Frequency Response Analysis The amplitude of response is sought under sinusoidal excitation There may be

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