Refined differential equations of deflections in axial symmetrical bending problems of spherical shell and their singular perturbation solutions

1990 ◽  
Vol 11 (12) ◽  
pp. 1175-1185 ◽  
Author(s):  
Fan Cun-xu
Keyword(s):  
Differential Equations ◽  
Singular Perturbation ◽  
Spherical Shell ◽  
Bending Problems ◽  
Perturbation Solutions

scholarly journals Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Robert Vrabel ◽  
Pavol Tanuska ◽  
Pavel Vazan ◽  
Peter Schreiber ◽  
Vladimir Liska
Keyword(s):  
Differential Equations ◽  
Singular Perturbation ◽  
Small Parameter ◽  
Nonlinear Oscillations ◽  
Frequency Control ◽  
Singularly Perturbed ◽  
Perturbation Frequency ◽  
Large Frequency

We analyze the dynamics of the forced singularly perturbed differential equations of Duffing’s type with a potential that is bounded from above. We explain the appearance of the large frequency nonlinear oscillations of the solutions. It is shown that the frequency can be controlled by a small parameter at the highest derivative.

Nonlinear Corrections for Edge Bending of Shells

1980 ◽  
Vol 47 (4) ◽  
pp. 861-865 ◽  
Author(s):  
G. V. Ranjan ◽  
C. R. Steele
Keyword(s):  
Differential Equations ◽  
Spherical Shell ◽  
Asymptotic Expansions ◽  
Axial Displacement ◽  
Exponential Functions ◽  
Spherical Cap ◽  
Influence Coefficients ◽  
Edge Loading ◽  
General Geometry ◽  
Edge Influence

Asymptotic expansions for self-equilibrating edge loading are derived in terms of exponential functions, from which formulas for the stiffness and flexibility edge influence coefficients are obtained, which include the quadratic nonlinear terms. The flexibility coefficients agree with those previously obtained by Van Dyke for the pressurized spherical shell and provide the generalization to general geometry and loading. In addition, the axial displacement is obtained. The nonlinear terms in the differential equations can be identified as “prestress” and “quadratic rotation.” To assess the importance of the latter, the problem of a pressurized spherical cap with roller supported edges is considered. Results show that whether the rotation at the edge is constrained or not, the quadratic rotation terms do not have a large effect on the axial displacement. The effect will be large for problems with small membrane stresses.

A Existence Theory for Positive Solutions to Superlinear Repulsive Singular Differential Equations with Impulse Effects

2010 ◽  
Vol 40-41 ◽  
pp. 149-155
Author(s):  
Zhang Xiao Ying ◽  
Guan Li Hong
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Singular Perturbation ◽  
Positive Solutions ◽  
Existence Theory ◽  
Singular Differential Equations ◽  
Perturbation Problem ◽  
Nonlinear Alternative

In this paper, we study positive solutions to the repulsive singular perturbation Hill equations with impulse effects. It is proved that such a perturbation problem has at least one positive impulsive periodic solution by a nonlinear alternative of Leray--Schauder.

Stresses in a Spherical Shell With a Circular Elastic Inclusion

1974 ◽  
Vol 96 (3) ◽  
pp. 228-233
Author(s):  
P. Prakash ◽  
K. P. Rao
Keyword(s):  
Differential Equations ◽  
Spherical Shell ◽  
Elastic Inclusion ◽  
Circular Inclusion ◽  
Shallow Spherical Shell ◽  
Spherical Shells ◽  
Hankel Functions ◽  
Circular Elastic Inclusion ◽  
Rigid Circular Inclusion

The problem of a circular elastic inclusion in a thin pressurized spherical shell is considered. Using Reissner’s differential equations governing the behavior of a thin shallow spherical shell, the solutions for the two regions are obtained in terms of Bessel and Hankel functions. Particular cases of a rigid circular inclusion free to move with the shell and a clamped rigid circular inclusion are also considered. Results are presented in nondimensional form which will greatly facilitate their use in the design of spherical shells containing a rigid or an elastic inclusion.

scholarly journals Singular perturbation for nonlinear boundary-value problems

1979 ◽  
Vol 2 (1) ◽  
pp. 61-68 ◽  
Author(s):  
Rina Ling
Keyword(s):  
Differential Equations ◽  
Singular Perturbation ◽  
Energy Distribution ◽  
Boundary Value Problems ◽  
Asymptotic Expansions ◽  
Nuclear Energy ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

Asymptotic solutions of a class of nonlinear boundary-value problems are studied. The problem is a model arising in nuclear energy distribution. For large values of the parameter, the differential equations are of the singular-perturbation type and approximations are constructed by the method of matched asymptotic expansions.

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