Analytical investigation of air squeeze film damping for bi‐axial micro‐scanner using eigenfunction expansion method

2020 ◽  
Author(s):  
Ruhollah Atabak ◽  
Hamid M. Sedighi ◽  
Arash Reza ◽  
Erfan Mirshekari
Keyword(s):  
Eigenfunction Expansion ◽  
Expansion Method ◽  
Analytical Investigation ◽  
Squeeze Film ◽  
Eigenfunction Expansion Method ◽  
Squeeze Film Damping

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

3-D Eddy Currents Analysis in Orthotropic Materials Using Truncated Region Eigenfunction Expansion Method

2012 ◽  
Vol 239-240 ◽  
pp. 258-263 ◽  
Author(s):  
Yu Jie Bai ◽  
Xiao Zhang Zhang ◽  
Lei Jiang ◽  
Chang Liang Tang
Keyword(s):  
Eigenfunction Expansion ◽  
Eddy Currents ◽  
Separation Of Variables ◽  
Expansion Method ◽  
Orthotropic Materials ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Eigenfunction Expansion Method ◽  
Vector Differential Equation ◽  
Good Agreement

A model for 3-D eddy currents analysis in orthotropic materials such as CFRPs is proposed. With artificial magnetic insulation boundary conditions, we solved a vector differential equation which describes the magnetic vector potential in the CFRPs materials with a delta coil near it using the method of separation of variables. As a result of the truncated region eigenfunction expansion method, a series solution was obtained, from which we got the eddy currents distribution. The distribution shows a good agreement with the work by others.

scholarly journals Exact Analytical Solution for 3D Time-Dependent Heat Conduction in a Multilayer Sphere with Heat Sources Using Eigenfunction Expansion Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nemat Dalir
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Eigenfunction Expansion ◽  
Radial Direction ◽  
Exact Analytical Solution ◽  
Internal Heat ◽  
Expansion Method ◽  
Time Dependent ◽  
Heat Sources ◽  
Eigenfunction Expansion Method

An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary combination of homogenous boundary condition of the first or second kind can be applied in the angular and azimuthal directions. Nevertheless, solution is valid for nonhomogeneous boundary conditions of the third kind (convection) in the radial direction. A case study problem for the three-layer quarter-spherical region is solved and the results are discussed.

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