TY - GEN
T1 - Multiresolution reproducing kernel particle methods in acoustic problems
AU - Liu, W. K.
AU - Chang, C. T.
AU - Chen, Y.
AU - Liras, R. A.
N1 - Funding Information:
The support of this research by ONR to Northwestern University is gratefully acknowledged. A part of this work (R. A. Uras) was supported by the U.S. Department of Energy, Technology Support Program, under contract W-31-109-Eng-38.
Publisher Copyright:
© 1995 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1995
Y1 - 1995
N2 - In the analysis of complex phenomena of acoustic systems, the computational modeling requires special attention for a realistic representation of the physics. As a powerful tool, the finite element method has been widely used in the study of complex systems. In order to capture the important physical phenomena, p-finite elements and/or hpfinite elements are employed. The reproducing kernel particle methods(RKPM) are emerging as an effective alternative due to the elimination of a mesh, and the ability to analyze a specific frequency range. Additionally, a wavelet particle method based on the multiresolution analysis encountered in signal processing has been developed. The interpolation functions consist of spline functions with built-in window. A variation in the size of the window implies a geometrical refinement, and allows the filtering of the desired frequency range. Preliminary analysis of the wave equation shows the effectiveness of this approach. The frequency/wave number relationship of the continuum case can be closely simulated by using the reproducing kernel particle methods. A similar methodology is also developed for the Timoshenko beam.
AB - In the analysis of complex phenomena of acoustic systems, the computational modeling requires special attention for a realistic representation of the physics. As a powerful tool, the finite element method has been widely used in the study of complex systems. In order to capture the important physical phenomena, p-finite elements and/or hpfinite elements are employed. The reproducing kernel particle methods(RKPM) are emerging as an effective alternative due to the elimination of a mesh, and the ability to analyze a specific frequency range. Additionally, a wavelet particle method based on the multiresolution analysis encountered in signal processing has been developed. The interpolation functions consist of spline functions with built-in window. A variation in the size of the window implies a geometrical refinement, and allows the filtering of the desired frequency range. Preliminary analysis of the wave equation shows the effectiveness of this approach. The frequency/wave number relationship of the continuum case can be closely simulated by using the reproducing kernel particle methods. A similar methodology is also developed for the Timoshenko beam.
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U2 - 10.1115/DETC1995-0483
DO - 10.1115/DETC1995-0483
M3 - Conference contribution
AN - SCOPUS:85103444200
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 881
EP - 890
BT - 15th Biennial Conference on Mechanical Vibration and Noise - Acoustics, Vibrations, and Rotating Machines
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 1995 Design Engineering Technical Conferences, DETC 1995, collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium
Y2 - 17 September 1995 through 20 September 1995
ER -