scholarly journals Adaptive-Control of Nonlinear Systems Using Spline Function Approximation Techniques

2013 ◽  
Author(s):  
Hesham Shageer
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Function Approximation ◽  
Spline Function ◽  
Approximation Techniques ◽  
Spline Function Approximation

scholarly journals Free Vibration of Layered Circular Cylindrical Shells of Variable Thickness Using Spline Function Approximation

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
K. K. Viswanathan ◽  
Kyung Su Kim ◽  
Kyung Ho Lee ◽  
Jang Hyun Lee
Keyword(s):  
Free Vibration ◽  
Collocation Method ◽  
Variable Thickness ◽  
Function Approximation ◽  
Spline Function ◽  
Cylindrical Shells ◽  
Thickness Variation ◽  
Point Collocation ◽  
Spline Function Approximation ◽  
Circular Cylindrical Shells

Free vibration of layered circular cylindrical shells of variable thickness is studied using spline function approximation by applying a point collocation method. The shell is made up of uniform layers of isotropic or specially orthotropic materials. The equations of motions in longitudinal, circumferential and transverse displacement components, are derived using extension of Love's first approximation theory. The coupled differential equations are solved using Bickley-type splines of suitable order, which are cubic and quintic, by applying the point collocation method. This results in the generalized eigenvalue problem by combining the suitable boundary conditions. The effect of frequency parameters and the corresponding mode shapes of vibration are studied with different thickness variation coefficients, and other parameters. The thickness variations are assumed to be linear, exponential, and sinusoidal along the axial direction. The results are given graphically and comparisons are made with those results obtained using finite element method.

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