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.

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