Closed form solution for acoustic wave equation between two parallel plates using Euler–Maclaurin sum formula

2004 ◽  
Vol 277 (1-2) ◽  
pp. 123-132 ◽  
Author(s):  
M.J. Panza
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parallel Plates ◽  
Acoustic Wave Equation ◽  
Sum Formula

scholarly journals Acoustic Wave Propagation in a Trifurcated Lined Waveguide

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Ayub ◽  
M. H. Tiwana ◽  
A. B. Mann ◽  
H. Zaman
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Closed Form ◽  
Integral Transform ◽  
Closed Form Solution ◽  
Form Solution ◽  
Kernel Functions ◽  
Acoustic Wave Propagation ◽  
Proper Selection ◽  
Selection Of

The diffraction of sound from a semi-infinite soft duct is investigated. The soft duct is symmetrically located inside an acoustically lined but infinite duct. A closed-form solution is obtained using integral transform and Jones' method based on Wiener-Hopf technique. The graphical results are presented, which show how effectively the unwanted noise can be reduced by proper selection of different parameters. The kernel functions are factorized with different approaches. The results may be used to design acoustic barriers and noise reduction devices.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

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