scholarly journals A Fast Frequency Domain Method for Steady-State Solution of Forced Vibration of System with Complex Damping

2020 ◽  
Vol 10 (10) ◽  
pp. 3442
Author(s):  
Wenrui Qi ◽  
Danguang Pan ◽  
Yongtao Gao ◽  
Wenyan Lu ◽  
Ying Huang
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Steady State ◽  
Frequency Domain ◽  
Imaginary Part ◽  
Complete Solution ◽  
Time History ◽  
Frequency Domain Method ◽  
Domain Method ◽  
Complex Damping

The conventional frequency domain method (CFDM) and dual-force-based time domain method (DTDM) are often used to solve the steady-state response of system with complex damping under an arbitrary force. However, the calculation efficiency of the DTDM is low due to the straightforward summation operation of series even if the solution of the DTDM is the exact real part of the solution. In addition, since the CFDM only can obtain the real part of solution not the complete solution, it gives misleading information that the solution does not have an imaginary part. In this paper, a fast frequency domain method (FFDM) is proposed to calculate the complete response of complex damping system including the imaginary part with a higher accuracy in a much faster manner. The new FFDM uses half of the Fourier series of the discrete Fourier transform of the actual arbitrary force to construct the Fourier series of the dual force, followed by calculating the time history response using the inverse fast Fourier transform. The new developed method is validated through three numerical examples with harmonic and seismic excitations. The numerical results show that the accuracy of the new FFDM is compatible to the DTDM but with much higher computational efficiency.

scholarly journals The Comparison of the Effect of Haimming Window and Blackman Window in the Time-Scaling and Pitch-Shifting Algorithms

2011 ◽  
Vol 1 ◽  
pp. 221-225
Author(s):  
Zhi Wei Lin ◽  
Li Da ◽  
Hao Wang ◽  
Wei Han ◽  
Fan Lin
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Domain Method ◽  
Domain Type ◽  
Domain Method ◽  
Time Scaling ◽  
Window Functions ◽  
Inherent Frequency ◽  
The Time Domain

The real-time pitch shifting process is widely used in various types of music production. The pitch shifting technology can be divided into two major types, the time domain type and the frequency domain type. Compared with the time domain method, the frequency domain method has the advantage of large shifting scale, low total cost of computing and the more flexibility of the algorithm. However, the use of Fourier Transform in frequency domain processing leads to the inevitable inherent frequency leakage effects which decrease the accuracy of the pitch shifting effect. In order to restrain the side effect of Fourier Transform, window functions are used to fall down the spectrum-aliasing. In practical processing, Haimming Window and Blackman Window are frequently used. In this paper, we compare both the effect of the two window functions in the restraint of frequency leakage and the performance and accuracy in subjective based on the traditional phase vocoder[1]. Experiment shows that Haimming Window is generally better than Blackman Window in pitch shifting process.

HARMONIC DISTORTION ANALYSIS BASED ON HOPF BIFURCATION THEOREM AND FAST FOURIER TRANSFORM

2007 ◽  
Vol 17 (05) ◽  
pp. 1623-1635 ◽  
Author(s):  
F. I. ROBBIO ◽  
E. E. PAOLINI ◽  
J. L. MOIOLA ◽  
G. CHEN
Keyword(s):  
Fourier Transform ◽  
Hopf Bifurcation ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Harmonic Distortion ◽  
Period Doubling ◽  
Frequency Domain Method ◽  
Colpitts Oscillator ◽  
Eighth Order ◽  
Domain Method

A frequency domain method is used to estimate the harmonic contents of a smooth oscillation arising from the Hopf bifurcation mechanism. The harmonic contents up to the eighth-order are well estimated, which agree with the results obtained from a completely different approach that measures the frequency content of a signal by using digital signal processing techniques such as the Fast Fourier Transform (FFT). The accuracy of the approximation is evaluated by computing the Floquet multipliers of the variational system based on the fact that for periodic solutions one multiplier must be +1. The separation from this theoretical value is proportional to the error of the approximation. A limitation of the frequency domain method is encountered when being used for continuing the secondary branch of limit cycle bifurcations, such as pitchfork and period-doubling bifurcations. Two examples are shown to illustrate the main results: Colpitts' oscillator with a pitchfork bifurcation of cycles, and Chua's circuit with a period-doubling bifurcation of cycles.

Leak detection in pipelines by exclusively frequency domain method

2012 ◽  
Vol 55 (3) ◽  
pp. 743-752 ◽  
Author(s):  
XinLei Guo ◽  
KaiLin Yang ◽  
YongXin Guo
Keyword(s):  
Frequency Domain ◽  
Leak Detection ◽  
Frequency Domain Method ◽  
Domain Method
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