Discrete singular convolution method and applications to free vibration analysis of circular and annular plates

2008 ◽  
Vol 29 (2) ◽  
pp. 237-240 ◽  
Author(s):  
Omer Civalek
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Annular Plates ◽  
Discrete Singular Convolution ◽  
Convolution Method

scholarly journals Discrete singular convolution–polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams

2021 ◽  
pp. 107754632098819
Author(s):  
Abdullah Seçgin ◽  
Murat Kara ◽  
Neil Ferguson
Keyword(s):  
Free Vibration ◽  
Young’S Modulus ◽  
Vibration Analysis ◽  
Polynomial Chaos ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Discrete Singular Convolution ◽  
Convolution Method

This article enhances the discrete singular convolution method for free vibration analysis of non-uniform thin beams with variability in their geometrical and material properties such as thickness, specific volume (inverse of density) and Young’s modulus. The discrete singular convolution method solves the differential equation of motion of a structure with a high accuracy using a small number of discretisation points. The method uses polynomial chaos expansion to express these variabilities simulating uncertainty in a closed form. Non-uniformity is locally provided by changing the cross section and Young’s modulus of the beam along its length. In this context, firstly natural frequencies of deterministic uniform and non-uniform beams are predicted via the discrete singular convolution. These results are compared with finite element calculations and analytical solutions (if available) for the purpose of verification. Next, the uncertainty of the beam because of geometrical and material variabilities is modelled in a global manner by polynomial chaos expansion to predict probability distribution functions of the natural frequencies. Monte Carlo simulations are then performed for validation purpose. Results show that the proposed algorithm of the discrete singular convolution with polynomial chaos expansion is very accurate and also efficient, regarding computation cost, in handling non-uniform beams having material and geometrical variabilities. Therefore, it promises that it can be reliably applied to more complex structures having uncertain parameters.

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