On the Explicit Determination of Certain Solutions of Periodic Differential Equations of Higher Order

1996 ◽  
Vol 29 (1-2) ◽  
pp. 43-55 ◽  
Author(s):  
Anja Baesch
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Explicit Determination

scholarly journals On the asymptotic series solution of some higher order linear differential equations at turning points

1984 ◽  
Vol 7 (3) ◽  
pp. 541-548
Author(s):  
Arthur D. Gorman
Keyword(s):  
Differential Equations ◽  
Series Solution ◽  
Turning Points ◽  
Asymptotic Series ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Asymptotic Series Solution ◽  
Linear Differential

The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of second-order “wave type” differential equations at turning points. The formalism also applies to higher order linear differential equations, as we make explicit here illustrating with some4th order equations of physical significance.

Effect of Small Hub-Radius Change on Bending Frequencies of a Rotating Beam

1960 ◽  
Vol 27 (3) ◽  
pp. 548-550 ◽  
Author(s):  
Hsu Lo ◽  
J. E. Goldberg ◽  
J. L. Bogdanoff
Keyword(s):  
Differential Equations ◽  
Linear Function ◽  
Simple Relation ◽  
Higher Order ◽  
Frequency Parameter ◽  
Rotating Beam ◽  
First Order ◽  
Order Solution ◽  
Small Change

By the method of perturbation, a simple relation is formulated for the determination of the change of bending frequencies of a rotating beam due to a small change of hub radius. The first-order solution shows that a frequency parameter γ is a linear function of the hub-radius change and the constant of proportionality is readily obtainable from known parameters. The frequency ω itself can also be represented by a linear function of the hub-radius change. This confirms the results previously obtained by Boyce by repeated solutions of the differential equations for a particular beam. Higher-order solutions are also established and shown to be convergent within the limitation imposed on the amount of the hub-radius change allowable.

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

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