Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm

2001 ◽  
Vol 124 (1) ◽  
pp. 36-45 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang

The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Green’s function for the cases with known Green’s functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC-FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.

Author(s):  
Zhanjiang Wang ◽  
Xiaoqing Jin ◽  
Shuangbiao Liu ◽  
Leon M. Keer ◽  
Jian Cao ◽  
...  

This paper presents a new method of contact plasticity analysis based on Galerkin vectors to solve the eigenstresses due to eigenstrain. The influence coefficients relating eigenstrains to eigenstresses thus can be divided into four terms the one due to the eigenstrains in the full space, others due to the mirrored eigenstrains in the mirror half space. Each term can be solved fast and efficient by using the three-dimensional discrete convolution and fast Fourier transform (DC-FFT) or the three-dimensional discrete correlation and fast Fourier transform (DCR-FFT). The new method is used to analyze the contact plastic residual stresses in half space.


1996 ◽  
Vol 118 (1) ◽  
pp. 95-99 ◽  
Author(s):  
J. Ling ◽  
Y. Cao

This paper introduces frequency response functions, analyzes the relationships between the frequency response functions and influence coefficients theoretically, and derives corresponding mathematical equations for high-speed rotor balancing. The relationships between the imbalance masses on the rotor and frequency response functions are also analyzed based upon the modal balancing method, and the equations related to the static and dynamic imbalance masses and the frequency response function are obtained. Experiments on a high-speed rotor balancing rig were performed to verify the theory, and the experimental data agree satisfactorily with the analytical solutions. The improvement on the traditional balancing method proposed in this paper will substantially reduce the number of rotor startups required during the balancing process of rotating machinery.


2007 ◽  
Vol 347 ◽  
pp. 583-588
Author(s):  
Simon P. Shone ◽  
Brian R. Mace ◽  
Tim P. Waters

A method is presented for locating discontinuities in a uniform waveguide from two or more point frequency response functions (FRFs). The phase of the FRF exhibits modulation when plotted against wavenumber because of interference of waves reflected from the discontinuity, and this is related to the distance of the excitation point from the discontinuity. Such discontinuities might be known boundaries or unknown damage sites. An inverse Fourier transform is used to transform from the wavenumber domain to the spatial domain in order to extract the locations of the discontinuities. The use of the transform relies upon knowledge of the dispersion relation for the waveguide. Experimental results are presented for several uniform isotropic beams which were damaged to differing extents by sawing transverse slots in them. The results show the method to be successful in locating the slots.


Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1117
Author(s):  
Bin Li ◽  
Zhikang Jiang ◽  
Jie Chen

Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for a long time because of its high efficiency and wide practicability. More than twenty different sFFT algorithms compute discrete Fourier transform (DFT) by their unique methods so far. In order to use them properly, the urgent topic of great concern is how to analyze and evaluate the performance of these algorithms in theory and practice. This paper mainly discusses the technology and performance of sFFT algorithms using the aliasing filter. In the first part, the paper introduces the three frameworks: the one-shot framework based on the compressed sensing (CS) solver, the peeling framework based on the bipartite graph and the iterative framework based on the binary tree search. Then, we obtain the conclusion of the performance of six corresponding algorithms: the sFFT-DT1.0, sFFT-DT2.0, sFFT-DT3.0, FFAST, R-FFAST, and DSFFT algorithms in theory. In the second part, we make two categories of experiments for computing the signals of different SNRs, different lengths, and different sparsities by a standard testing platform and record the run time, the percentage of the signal sampled, and the L0, L1, and L2 errors both in the exactly sparse case and the general sparse case. The results of these performance analyses are our guide to optimize these algorithms and use them selectively.


Author(s):  
W. Schünemann ◽  
R. Schelenz ◽  
G. Jacobs ◽  
W. Vocaet

AbstractThe aim of a transfer path analysis (TPA) is to view the transmission of vibrations in a mechanical system from the point of excitation over interface points to a reference point. For that matter, the Frequency Response Functions (FRF) of a system or the Transmissibility Matrix is determined and examined in conjunction with the interface forces at the transfer path. This paper will cover the application of an operational TPA for a wind turbine model. In doing so the path contribution of relevant transfer paths are made visible and can be optimized individually.


1998 ◽  
Vol 120 (2) ◽  
pp. 509-516 ◽  
Author(s):  
J. A. Morgan ◽  
C. Pierre ◽  
G. M. Hulbert

This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.


Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.


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