APPLICATION OF FREE VIBRATION ANALYSIS OF MEMBRANES USING THE NON-DIMENSIONAL DYNAMIC INFLUENCE FUNCTION

2000 ◽  
Vol 234 (3) ◽  
pp. 455-470 ◽  
Author(s):  
S.W. KANG ◽  
J.M. LEE
Keyword(s):  
Free Vibration ◽  
Influence Function ◽  
Vibration Analysis ◽  
Free Vibration Analysis

scholarly journals Green’s function approach to frequency analysis of thin circular plates

2016 ◽  
Vol 64 (1) ◽  
pp. 181-188
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Influence Function ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Circular Plates ◽  
Natural Modes ◽  
Good Agreement ◽  
Analytical Frequency

Abstract The free vibration analysis of homogeneous and isotropic circular thin plates by using the Green’s functions is considered. The formulae for construction of the influence function for all nodal diameters are presented in a closed form. The limited independent solutions of differential Euler equations were expanded in the Neumann power series using the method of successive approximation. This approach allows to obtain the analytical frequency equations as power series rapidly convergent to exact eigenvalues for different number of nodal diameters. The first ten dimensionless frequencies for eight different natural modes of circular plates are calculated. A part of obtained results have not been presented yet in open literature for thin circular plates. The results of investigation are in good agreement with selected results obtained by other methods presented in literature.

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.

Numerical Stability of GFEM Evaluation for Free Vibration Analysis in Trussed Structures

2017 ◽  
Author(s):  
Thamara Petroli ◽  
Marcos Arndt ◽  
Paulo de Oliveira Weinhardt ◽  
ROBERTO Dalledone Machado
Keyword(s):  
Free Vibration ◽  
Numerical Stability ◽  
Vibration Analysis ◽  
Free Vibration Analysis
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