scholarly journals Higher-order theories and radial basis functions applied to free vibration analysis of thin-walled beams

2016 ◽  
Vol 23 (9) ◽  
pp. 1080-1091 ◽  
Author(s):  
A. Pagani ◽  
E. Carrera ◽  
A.J.M. Ferreira
Keyword(s):  
Free Vibration ◽  
Radial Basis Functions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Basis Functions ◽  
Radial Basis ◽  
Thin Walled

scholarly journals Analysis of Laminated Shells by Murakami’s Zig-Zag Theory and Radial Basis Functions Collocation

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
D. A. Maturi ◽  
A. J. M. Ferreira ◽  
A. M. Zenkour ◽  
D. S. Mashat
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Basis Functions ◽  
Transverse Displacement ◽  
Laminated Shells ◽  
Radial Basis

The static and free vibration analysis of laminated shells is performed by radial basis functions collocation, according to Murakami’s zig-zag (ZZ) function (MZZF) theory . The MZZF theory accounts for through-the-thickness deformation, by considering a ZZ evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by Carrera’s Unified Formulation and further interpolated by collocation with radial basis functions.

FREE VIBRATION ANALYSIS OF TIMOSHENKO BEAMS AND MINDLIN PLATES BY RADIAL BASIS FUNCTIONS

2005 ◽  
Vol 02 (01) ◽  
pp. 15-31 ◽  
Author(s):  
A. J. M. FERREIRA
Keyword(s):  
Free Vibration ◽  
Radial Basis Functions ◽  
Basis Function ◽  
Vibration Analysis ◽  
Function Method ◽  
Free Vibration Analysis ◽  
Basis Functions ◽  
Timoshenko Beams ◽  
Radial Basis ◽  
Radial Basis Function Method

A study of free vibration of Timoshenko beams and Mindlin plates is presented whereby the analysis is based on the radial basis function method. Various approaches for computing eigenvalues using radial basis functions are also discussed together with the numerical results for various thickness-to-length ratios.

scholarly journals Higher-Order Hierarchical Models for the Free Vibration Analysis of Thin-Walled Beams

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
G. Giunta ◽  
S. Belouettar
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Approximation Order ◽  
Higher Order ◽  
Geometrical Parameters ◽  
Thin Walled ◽  
Three Dimensional Finite Element

This paper addresses a free vibration analysis of thin-walled isotropic beams via higher-order refined theories. The unknown kinematic variables are approximated along the beam cross section as aN-order polynomial expansion, whereNis a free parameter of the formulation. The governing equations are derived via the dynamic version of the Principle of Virtual Displacements and are written in a unified form in terms of a “fundamental nucleus.” This latter does not depend upon order of expansion of the theory over the cross section. Analyses are carried out through a closed form, Navier-type solution. Simply supported, slender, and short beams are investigated. Besides “classical” modes (such as bending and torsion), several higher modes are investigated. Results are assessed toward three-dimensional finite element solutions. The numerical investigation shows that the proposed Unified Formulation yields accurate results as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam.

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