Structural Dynamics Lecture 7 闺 同桥大学 土本2程学收 COLLEGE OF CIVIL
Structural Dynamics Lecture 7
Frequency Domain Method ·Time-domain method The time domain analysis procedure can be determine the response of any linear SDOF system to any arbitrary loading Frequency Domain Method Sometime,it is more convenient to perform the analysis in the frequency domain.Especially when the structural parameter are frequency- dependent.The FD is much superior to TD
Frequency Domain Method • Time-domain method The time domain analysis procedure can be determine the response of any linear SDOF system to any arbitrary loading • Frequency Domain Method Sometime, it is more convenient to perform the analysis in the frequency domain. Especially when the structural parameter are frequencydependent. The FD is much superior to TD
Frequency Domain Method Response to period excitation Fourier series in real form Fourier series in complex form Response to arbitrary excitation Fourier integral/Fourier transform Discrete Fourier transform Fast Fourier transform
Frequency Domain Method • Response to period excitation Fourier series in real form Fourier series in complex form • Response to arbitrary excitation Fourier integral/ Fourier transform Discrete Fourier transform Fast Fourier transform
Review:Response to Periodic Excitation Response of SDOF to harmonic excitation Using Fourier series expansion to expand the periodic excitation into summation of harmonic excitations Linear elastic system,superposition principle is applicable 闺 土本2程季院
• Response of SDOF to harmonic excitation • Using Fourier series expansion to expand the periodic excitation into summation of harmonic excitations • Linear elastic system, superposition principle is applicable Review: Response to Periodic Excitation
For any periodic excitation p(t),Fourier series representation p0=a+2a,os@4+2,smo 0,=j0=j元 2π a=p()cos(o) tn=1,2,3… b,=是p0sin(o4）n=l2,3 闺 土本鞋李悦
0 1 1 1 0 0 0 0 cos sin 2 1 2 cos 1, 2,3,... 2 sin 1, 2,3,... p p p j j j j j j j p T p T j j p T j j p p t a a t b t j j T a p t dt T a p t t dt n T b p t t dt n T • For any periodic excitation p(t), Fourier series representation