Advanced NDIF Method for Eigenvalue Analysis of Arbitrarily Shaped Acoustic Cavities With the Partially Pressure-Release Boundary

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
S. W. Kang ◽  
Satya N. Atluri
Keyword(s):  
Influence Function ◽  
Mixed Boundary ◽  
Rigid Wall ◽  
Eigenvalue Analysis ◽  
System Matrix ◽  
Acoustic Cavity ◽  
Pressure Release ◽  
Influence Function Method ◽  
Acoustic Cavities ◽  
Final System

Abstract In this paper, an advanced non-dimensional dynamic influence function method (NDIF method) for eigenvalue analysis of arbitrarily shaped two-dimensional acoustic cavities with the mixed boundary consisting of the pressure-release and rigid-wall boundaries is proposed. The existing NDIF method has the weakness of having to calculate the singularity of the final system matrix of an analyzed acoustic cavity in the frequency band of interest to obtain the eigenvalues of the cavity because the final system matrix is dependent on the frequency. The newly proposed NDIF method in this paper provides an efficient way to extract accurate eigenvalues and eigenmodes by successfully overcoming the above weaknesses. Finally, the validity and accuracy of the proposed method are shown through verification examples.

scholarly journals Advanced non-dimensional dynamic influence function method considering the singularity of the system matrix for accurate eigenvalue analysis of membranes

2022 ◽  
Vol 14 (1) ◽  
pp. 168781402110729
Author(s):  
Sangwook Kang
Keyword(s):  
Influence Function ◽  
Vibration Analysis ◽  
Function Method ◽  
Accurate Result ◽  
Low Frequency ◽  
Free Vibration Analysis ◽  
System Matrix ◽  
Frequency Range ◽  
Influence Function Method ◽  
Lower Frequency Range

An advanced non-dimensional dynamic influence function method (NDIF method) for highly accurate free vibration analysis of membranes with arbitrary shapes is proposed in this paper. The existing NDIF method has the weakness of not offering eigenvalues and eigenmodes in the low frequency range when the number of boundary nodes of an analyzed membrane is increased to obtain more accurate result. This paper reveals that the system matrix of the membrane becomes singular in the lower frequency range when the number of the nodes increases excessively. Based on this fact, it provides an efficient way to successfully overcome the weaknesses of the existing NDIF method and still maintain its accuracy. Finally, verification examples show the validity and accuracy of the advanced NDIF method proposed.

Application of the Nondimensional Dynamic Influence Function Method for Free Vibration Analysis of Arbitrarily Shaped Membranes

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Sang Wook Kang ◽  
Satya N. Atluri ◽  
Sang-Hyun Kim
Keyword(s):  
Numerical Methods ◽  
Free Vibration ◽  
Influence Function ◽  
Vibration Analysis ◽  
Function Method ◽  
Free Vibration Analysis ◽  
Frequency Parameter ◽  
Mode Shapes ◽  
System Matrix ◽  
Influence Function Method

A new formulation for the NDIF method (the nondimensional dynamic influence function method) is introduced to efficiently extract eigenvalues and mode shapes of arbitrarily shaped, homogeneous membranes with the fixed boundary. The NDIF method, which was developed by the authors for the accurate free vibration analysis of arbitrarily shaped membranes and plates including acoustic cavities, has the feature that it yields highly accurate solutions compared with other analytical methods or numerical methods (the finite element method and the boundary element method). However, the NDIF method has the weak point that the system matrix of the method is not independent of the frequency parameter and as a result the method needs the inefficient procedure of searching eigenvalues by plotting the values of the determinant of the system matrix in the frequency parameter range of interest. An improved formulation presented in the paper does not require the above-mentioned inefficient procedure because a newly developed system matrix is independent of the frequency parameter. Finally, the validity of the proposed method is shown in several case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to those calculated by exact, analytica, or numerical methods.

Analysis of the Effect of Natural Slope Stability due to Tunnel Excavation in Mountainous Areas

2013 ◽  
Vol 690-693 ◽  
pp. 938-942
Author(s):  
Xu Li Liang ◽  
Fei Wang ◽  
Gang Li Hao
Keyword(s):  
Slope Stability ◽  
Influence Function ◽  
Function Method ◽  
Mountainous Area ◽  
Mountainous Areas ◽  
Tunnel Excavation ◽  
Natural Slope ◽  
Influence Function Method ◽  
Theoretical Results ◽  
Good Agreement

The effect of natural slope stability due to the tunnel excavation in mountainous areas is studied used influence function method, and one tunnel excavation project in Hebei province was analyzed, the theoretical results obtained are in good agreement with the real monitoring data, therefore, the influence function method can be effectively used to predict the ground displacement caused by tunnel excavation in mountainous area, which could provide the basis for the evaluation of the safety of such works.

Methodology for the Design of the Geometry of a Cavity and Its Absorption Coefficients as Random Design Variables Under Vibroacoustic Criteria

2016 ◽  
Vol 24 (02) ◽  
pp. 1650006 ◽  
Author(s):  
Renata Troian ◽  
Koji Shimoyama ◽  
Frédéric Gillot ◽  
Sébastien Besset
Keyword(s):  
Energy Method ◽  
Noise Level ◽  
Optimal Solution ◽  
Cavity Surface ◽  
Nsga Ii ◽  
Acoustic Cavity ◽  
Design Variables ◽  
Material Uncertainties ◽  
Acoustic Cavities ◽  
Nondominated Sorting

Reducing the noise level in the acoustic cavities is the important problem when treating inflight conditions of commercial planes or boats. Shape optimization of the acoustic cavity that will take into account the geometrical and material uncertainties, arising during the manufacturing process, is presented in this paper. The noise level is controlled by minimizing the energy density in the cavity, obtained through an energy method called Simplified Energy Method. Such formulation is based on our previous published work where transformation function mapping 3D cavity surface on a 2D domain was proposed. The optimization process directly relies on this function and thus avoids remeshing of the geometry. Robust optimization is performed using the nondominated sorting genetic algorithm (NSGA-II) together with the Kriging surrogate model. Influence of geometrical and material characteristics on the optimal solution is identified.

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