An Investigation of the Aeroelastic Response of a Two-Dimensional, Structurally Nonlinear Airfoil Subject to External Excitation

2002 ◽  
Author(s):  
Catharine C. Marsden ◽  
Stuart J. Price
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Nonlinear Response ◽  
Transfer Functions ◽  
Time History ◽  
System Response ◽  
Two Dimensional ◽  
Aeroelastic System ◽  
Aeroelastic Response ◽  
Band Limited

The results of an analytical investigation are presented for the aeroelastic response of a two-dimensional, structurally nonlinear airfoil subject to a forced excitation. The system is modeled as a two-dimensional, rigid airfoil section free to move in both the bending and pitching directions and possessing a rigid flap. The airfoil is mounted by torsional and translational springs attached at the elastic axis, and the flap motion is used to provide the forcing input to the system. The airfoil is immersed in an aerodynamic flow environment, modeled using incompressible thin airfoil theory for unsteady oscillatory motion. The equations of motion for the aeroelastic system are solved using a fourth-order Runge-Kutta numerical integration technique to provide time-history solutions of the response of the airfoil in the pitch and plunge directions. The time-histories are analysed using Fourier transform-based techniques to obtain frequency-domain response and transfer functions. Results show that the nonlinear response of the aeroelastic system contains frequencies other than the forcing frequency. When modal frequencies and damping values are calculated using standard Fourier-based techniques, it is shown that the super- and sub-harmonic frequency content in the nonlinear response can contribute to errors when results are compared to those obtained for the equivalent linear system. This paper describes an investigation of a method of analysis that, while based on the Fourier transform, has been modified to recognize and accommodate the nonlinear contribution to the system response. The method, developed by Bendat [1], uses a band-limited random input and separates the linear and nonlinear components of the response within the frequency domain. Results are given for the application of this method to the specific case of the structurally nonlinear aeroelastic system. It is shown that the method may be used to successfully recover the linear frequency response function using the input and output data for the nonlinear system.

scholarly journals NUMERICAL SIMULATION FOR RANDOM AEROELASTIC RESPONSES USING INVERSE FOURIER TRANSFORM

Aviation ◽  
2016 ◽  
Vol 20 (3) ◽  
pp. 103-109
Author(s):  
Tetsuhiko UEDA ◽  
Kenichi SAITOH
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Random Noise ◽  
Unsteady Aerodynamics ◽  
Time History ◽  
Control Device ◽  
Estimation Methods ◽  
Aeroelastic System ◽  
Inverse Discrete Fourier Transform ◽  
Flutter Boundary

This paper reports a new simulation technique for an aeroelastic system which responds to random external forces. Since the aeroelastic system including the effects of unsteady aerodynamics is ordinarily described in the frequency domain, the Inverse Discrete Fourier Transform (IDFT) can be utilized to simulate its random response. The response caused by the external random noise is calculated through a transfer function first in the frequency domain and then converted to the time domain. The objective of the present study is to provide mathematical time history data for evaluating the various estimation methods of the flutter boundary from subcritical responses in flight and/or wind tunnel testing. An example application to the method of flutter prediction is shown. The technique can also be used to evaluate the effects of the active control device coping with atmospheric turbulence.

TWO-DIMENSIONAL NONLINEAR OPTICS SPECTROSCOPY: SIMULATIONS AND EXPERIMENTAL DEMONSTRATION

1996 ◽  
Vol 05 (03) ◽  
pp. 465-476 ◽  
Author(s):  
L. LEPETIT ◽  
G. CHÉRIAUX ◽  
M. JOFFRE
Keyword(s):  
Fourier Transform ◽  
Nonlinear Response ◽  
Two Dimensions ◽  
Second Order ◽  
Phase Matching ◽  
Two Dimensional ◽  
Experimental Demonstration ◽  
Spectral Interferometry ◽  
Dimensional Measurement ◽  
A New Technique

We propose a new technique, using femtosecond Fourier-transform spectral interferometry, to measure the second-order nonlinear response of a material in two dimensions of frequency. We show numerically the specific and unique information obtained from such a two-dimensional measurement. The technique is demonstrated by measuring the second-order phase-matching map of two non-resonant nonlinear crystals.

Spectrographic Analysis for the Modal Testing of Nonlinear Aeroelastic Systems

2006 ◽  
Author(s):  
Catharine C. Marsden ◽  
Stuart J. Price
Keyword(s):  
Nonlinear System ◽  
Time History ◽  
Modal Testing ◽  
System Response ◽  
Spectrographic Analysis ◽  
Input Frequency ◽  
Frequency Content ◽  
Aeroelastic System ◽  
Time Histories ◽  
Sine Sweep

The spectrograph is a signal processing tool often used for the frequency domain analysis of time-varying signals. When the signal to be analyzed is a function of time, the spectrograph represents the frequency content of the signal as a sequence of power spectra that change with time. In this paper, the usefulness of the technique is demonstrated in its application to the analysis of the time history response of a nonlinear aeroelastic system. The aeroelastic system is modeled analytically as a two-dimensional, rigid airfoil section free to move in both the bending and pitching directions and possessing a rigid flap. The airfoil is mounted by torsional and translational springs attached at the elastic axis, and the flap is used to provide the forcing input to the system. The nonlinear system is obtained by introducing a freeplay type of nonlinearity in the pitch degree-of-freedom restoring moment. The airfoil is immersed in an aerodynamic flow environment, modeled using incompressible thin airfoil theory for unsteady oscillatory motion. The equations of motion are solved using a fourth-order Runge-Kutta numerical integration technique to provide time-history solutions of the response of the airfoil in the pitch and plunge directions. Time-histories are obtained for the nonlinear responses of the linear and nonlinear aeroelastic systems to a sine-sweep input. The time-histories are analyzed using the spectrographic technique, and the frequency content of the response is plotted directly as a function of the input frequency. Results show that the combination of the sine-sweep input with the spectrographic analysis permits a unique insight into the behaviour of the nonlinear system with a minimum of testing. It is shown that the frequency of the nonlinear system response is a function of the input frequency and one other characteristic frequency that can be associated with the limit cycle oscillations of the same nonlinear system subject to a transient input.

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 Application of two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for 4k fixed format digital image of satellite data in frequency domain processing

2020 ◽  
Vol 149 ◽  
pp. 02010 ◽  
Author(s):  
Mikhail Noskov ◽  
Valeriy Tutatchikov
Keyword(s):  
Fourier Transform ◽  
Numerical Experiment ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
Satellite Data ◽  
Digital Image ◽  
Digital Images ◽  
Two Dimensional ◽  
Fast Fourier Transform Algorithm

Currently, digital images in the format Full HD (1920 * 1080 pixels) and 4K (4096 * 3072) are widespread. This article will consider the option of processing a similar image in the frequency domain. As an example, take a snapshot of the earth's surface. The discrete Fourier transform will be computed using a two-dimensional analogue of the Cooley-Tukey algorithm and in a standard way by rows and columns. Let us compare the required number of operations and the results of a numerical experiment. Consider the examples of image filtering.

Optimization of Frequency Domain Fatigue Analysis for Unbonded Flexible Risers

2021 ◽  
Author(s):  
Jiabei Yuan ◽  
Yucheng Hou ◽  
Zhimin Tan
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Transfer Functions ◽  
Hybrid Approach ◽  
Fatigue Analysis ◽  
System Response ◽  
Similar Response ◽  
Potential Cost ◽  
Spectrum Prediction ◽  
Flexible Risers

Abstract Fatigue analysis of flexible risers is a demanding task in terms of time and computational resources. The traditional time domain approach may take weeks of time in global simulation, local modelling and post-processing of riser responses to get fatigue results. Baker Hughes developed a fast hybrid approach, which is based on a frequency domain technique. The new approach was first implemented at the end fitting region and then to all other regions of the riser. Studies showed that the hybrid approach achieved convenient and conservative results in a significant shorter period of time. To improve the accuracy and reduce conservatism of the method, Baker Hughes has further optimized the analysis procedure to seek better results approaching true solutions. Several methods were proposed and studied. The duration of representative cases and noncritical cases have been extended. The steps to predict stress spectrum based on transfer functions have also been updated. From previous studies, only one transfer function was built for fatigue load cases with similar response spectra. This assumption linearizes the system response and produces certain level of discrepancy against true time domain solution. In this study, multiple ways of spectrum prediction are evaluated and compared. The paper summarizes several techniques to further optimize the hybrid frequency domain approach. The updated fatigue results are found to be more accurate. The optimized approach therefore gives more flexibility to engineers to approach the true solutions, which were originally acquired from full 3-hr time domain simulations. The approach requires less analysis time and reduces iterations in pipe structure and riser configuration design, which leads to faster project execution and potential cost reduction.

A Computationally Low-cost Method for Capturing Airframe Flexibility Effects in Landing Dynamic Simulations

2021 ◽  
Author(s):  
Terrin Stachiw ◽  
Fidel Khouli ◽  
Robert G. Langlois ◽  
Fred F. Afagh ◽  
Joseph Ricciardi
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Transfer Functions ◽  
Initial Conditions ◽  
Low Cost ◽  
Time History ◽  
Element Model ◽  
Landing Gear ◽  
Dynamic Simulations ◽  
Positive Time

Abstract Airframe flexibility effects have typically been captured by modal reduction of the airframe. Although efficient, this model may still be prohibitively expensive for preliminary design studies. This paper employs time- and frequency-domain system identification techniques to form a multi-objective optimization problem to identify equivalent transfer functions representing airframe flexibility effects. Pareto-optimal sets are first identified for an equivalent transfer function of a force element between the landing gear attachment point and the centre of gravity of a 150-passenger regional jet, and a second transfer function from the input landing gear force to the cockpit acceleration. The reduced models demonstrate the ability to generally capture flexibility effects with reduced computation times. The combination of time-domain and frequency-domain information ensures the positive time-history matches while the model remains physically realizable as it is rooted to frequency response obtained from the finite element model. It is hypothesized that this physical link allowed the model to be robust to the landing initial conditions.

scholarly journals Parseval Relationship of Samples in the Fractional Fourier Transform Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Bing-Zhao Li ◽  
Tian-Zhou Xu
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Dimensional Case ◽  
Fourier Domain ◽  
Transform Domain ◽  
Two Dimensional ◽  
Band Limited ◽  
Relationship Of ◽  
The Relationship ◽  
Fourier Transform Domain

This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained. Then, the relationship is extended to a general set of nonuniform samples of band-limited signal associated with the fractional Fourier transform. Finally, the two dimensional case is investigated in detail, it is also shown that the derived results can be regarded as the generalization of the classical ones in the Fourier domain to the fractional Fourier transform domain.

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