Analytical solution for a vibrating simply-supported cylinder subjected to 2-D concentric annular flow, considering friction

2012 ◽  
Vol 35 ◽  
pp. 1-20 ◽  
Author(s):  
Heung Seok Kang ◽  
Njuki W. Mureithi ◽  
Michel J. Pettigrew
Keyword(s):  
Analytical Solution ◽  
Annular Flow ◽  
Simply Supported

scholarly journals Analytical solution to bending of stiffened and continuous antisymmetric laminates

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Liecheng Sun ◽  
Issam E. Harik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Displacement Function ◽  
The Other ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Coupling Problem ◽  
Simply Supported ◽  
General Response

AbstractAnalytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

The Support Reaction of a Simply Supported and Uniformly Loaded Thin Circular Aeolotropic Plate

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Kjell Eriksson
Keyword(s):  
Analytical Solution ◽  
Series Solution ◽  
Lateral Load ◽  
Anisotropic Materials ◽  
Higher Order ◽  
Simply Supported ◽  
Support Reaction ◽  
Degree Of Anisotropy

A previous analytical solution of the deflection of a thin circular aeolotropic plate, with simply supported edge and uniform lateral load, has been used to derive approximate series expressions for the plate support reaction, which are directly applicable in practice. The support reaction, which has been calculated for some typical anisotropic materials of varying degree of anisotropy, varies significantly along the plate perimeter and strongly anisotropic materials require in general a higher order series solution. Certain solution constants of previous deflection approximations were not found to harmonize and are therefore recalculated.

Analytical solution for the buckling of rectangular plates under uni-axial compression with variable thickness and elasticity modulus in the y-direction

2009 ◽  
Vol 224 (1) ◽  
pp. 33-41 ◽  
Author(s):  
M Saeidifar ◽  
S N Sadeghi ◽  
M R Saviz
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Power Series ◽  
Boundary Conditions ◽  
Variable Thickness ◽  
Elasticity Modulus ◽  
Plate Motion ◽  
Transverse Displacement ◽  
Buckling Loads ◽  
Simply Supported

The present study introduces a highly accurate numerical calculation of buckling loads for an elastic rectangular plate with variable thickness, elasticity modulus, and density in one direction. The plate has two opposite edges ( x = 0 and a) simply supported and other edges ( y = 0 and b) with various boundary conditions including simply supported, clamped, free, and beam (elastically supported). In-plane normal stresses on two opposite simply supported edges ( x = 0 and a) are not limited to any predefined mathematical equation. By assuming the transverse displacement to vary as sin( mπ x/ a), the governing partial differential equation of plate motion will reduce to an ordinary differential equation in terms of y with variable coefficients, for which an analytical solution is obtained in the form of power series (Frobenius method). Applying the boundary conditions on ( y = 0 and b) yields the problem of finding eigenvalues of a fourth-order characteristic determinant. By retaining sufficient terms in power series, accurate buckling loads for different boundary conditions will be calculated. Finally, the numerical examples have been presented and, in some cases, compared to the relevant numerical results.

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