Analytical solutions of the simplified Mathieu’s equation
Journal Title: INCAS BULLETIN - Year 2016, Vol 8, Issue 1
Abstract
Consider a second order differential linear periodic equation. The periodic coefficient is an approximation of the Mathieu’s coefficient. This equation is recast as a first-order homogeneous system. For this system we obtain analytical solutions in an explicit form. The first solution is a periodic function. The second solution is a sum of two functions, the first is a continuous periodic function, but the second is an oscillating function with monotone linear increasing amplitude. We give a formula to directly compute the slope of this increase, without knowing the second numeric solution. The periodic term of the second solution may be computed directly. The coefficients of fundamental matrix of the system are analytical functions.
Authors and Affiliations
Nicolae MARCOV
Keywords
Related Articles
- EP ID EP148983
- DOI 10.13111/2066-8201.2016.8.1.11
- Views 93
- Downloads 0
Velocity distribution as a result of the interaction between organizational processes in shear flows
This paper continues the recent research of the authors concerning the interaction between the micro and macro flow structure domains (further on called IPmMD). The authors propose a probabilistic type approach of the IP...
Investigation of the flow around an aircraft wing of section NACA 2412 utilising ANSYS fluent
The aim of this paper is to produce and validate a simulated model of the external flow around the NACA 2412 using ANSYS Fluent; utilising experimental data for a low velocity case (20.73 m/s) from literature. This model...
Methods of flow visualization
Flow visualization is an important topic in scientific visualization and has been the subject of active research for many years. Typically, data originates from numerical simulations, such as those of computational fluid...
CFD Analysis for Industrial Applications using xGrid Environment
Relevant CFD computations are performed in a GRID environment in order to evaluate this technology as a reliable infrastructure for HPSC for complex industrial applications. Several aspects of this environment are presen...
A Coordinate Transformation for Unsteady Boundary Layer Equations
This paper presents a new coordinate transformation for unsteady, incompressible boundary layer equations that applies to both laminar and turbulent flows. A generalization of this coordinate transformation is also propo...