scholarly journals Vibration analysis of a mass on a spring by means of magnus expansion method

2016 ◽  
Vol 4 (2) ◽  
pp. 90-90
Author(s):  
Musa Basbuk ◽  
Aytekin Eryilmaz ◽  
Mehmet Tarik Atay
Keyword(s):  
Vibration Analysis ◽  
Expansion Method ◽  
Magnus Expansion

Vibration Analysis of Composite Beams With End Effects via the Formal Asymptotic Method

2009 ◽  
Author(s):  
Jun-Sik Kim ◽  
K. W. Wang
Keyword(s):  
Finite Element ◽  
Asymptotic Expansion ◽  
Cross Section ◽  
Asymptotic Method ◽  
Vibration Analysis ◽  
Eigenvalue Problems ◽  
Free Vibration Analysis ◽  
Expansion Method ◽  
Composite Beams ◽  
Asymptotic Expansion Method

Free vibration analysis of composite beams is carried out by using a finite element-based formal asymptotic expansion method. The formulation begins with three-dimensional equilibrium equations in which cross-sectional coordinates are scaled by the characteristic length of the beam. Microscopic 2D and macroscopic 1D equations obtained via the asymptotic expansion method are discretized by applying a conventional finite element method. Boundary conditions associated with macroscopic 1D equations are also considered in order to investigate the end effect. We then describe how to form and solve the eigenvalue problems derived from the asymptotic method beyond the classical approximation. The results obtained are compared to those of 3D FEM and those available in literature for composite beams with solid cross-section and thin-walled cross-section.

Vibration analysis of a Mindlin elastic plate under a moving mass excitation by eigenfunction expansion method

2013 ◽  
Vol 62 ◽  
pp. 53-64 ◽  
Author(s):  
Javad Vaseghi Amiri ◽  
Ali Nikkhoo ◽  
Mohammad Reza Davoodi ◽  
Mohsen Ebrahimzadeh Hassanabadi
Keyword(s):  
Elastic Plate ◽  
Eigenfunction Expansion ◽  
Vibration Analysis ◽  
Expansion Method ◽  
Moving Mass ◽  
Eigenfunction Expansion Method

Vibration Analysis of Composite Beams With End Effects via the Formal Asymptotic Method

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Jun-Sik Kim ◽  
K. W. Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Asymptotic Expansion ◽  
Cross Section ◽  
Asymptotic Method ◽  
Vibration Analysis ◽  
Expansion Method ◽  
Composite Beams ◽  
Asymptotic Expansion Method ◽  
Element Method

Vibration analysis of composite beams is carried out by using a finite element-based formal asymptotic expansion method. The formulation begins with three-dimensional (3D) equilibrium equations in which cross-sectional coordinates are scaled by the characteristic length of the beam. Microscopic two-dimensional and macroscopic one-dimensional (1D) equations obtained via the asymptotic expansion method are discretized by applying a conventional finite element method. Boundary conditions associated with macroscopic 1D equations are considered to investigate the end effect. It is then described how one could form and solve the eigenvalue problems derived from the asymptotic method beyond the classical approximation. The results obtained are compared with those of 3D finite element method and those available in the literature for composite beams with solid cross section and thin-walled cross section.

scholarly journals The norm convergence of a Magnus expansion method

2011 ◽  
Vol 10 (1) ◽  
pp. 150-158
Author(s):  
András Bátkai ◽  
Eszter Sikolya
Keyword(s):  
Expansion Method ◽  
Norm Convergence ◽  
Magnus Expansion
Sign in / Sign up

Export Citation Format

Share Document