Oscillatory Behavior of Second Order Neutral Differential Equations with Positive and Negative Coefficients

Oscillation criteria are obtained for solutions of forced and unforced second order neutral differential equations with positive and negative coefficients. These criteria generalize those of Manojlović, Shoukaku, Tanigawa and Yoshida (2006)

On Nonoscillation of Mixed Advanced-Delay Differential Equations with Positive and Negative Coefficients

For a mixed (advanced--delay) differential equation with variable delays and coefficients $$\dot{x}(t) \pm a(t)x(g(t)) \mp b(t)x(h(t)) = 0, t\geq t_0$$ where $$a(t)\geq 0, b(t)\geq 0, g(t)\leq t, h(t)\geq t$$ explicit nonoscillation conditions are obtained.Comment: 17 pages; 2 figures; to appear in Computers & Mathematics with Application

Existence and stability of limit cycles for pressure oscillations incombustion chambers

In this paper, we discuss two problems. First, using a second order expansion in the pressure amplitude, some analytical results on the existence, stability and amplitude of limit cycles for pressure oscillations in combusticm chambers are presented. A stable limit cycle seems to be unique. The conditions for existence and stability are found to be dependent only on the linear parameters. The nonlinear parameter affects only the wave amplitude. The imaginary parts of the linear responses, to pressure oscillations, of the different processes in the chamber play an important role in the stability of the limit cycle. They also affect the direction of flow of energy among modes. In the absence of the imaginary parts, in order for an infinitesimal perturbation in the flow to reach a finite amplitude, the lowest mode must be unstable while the highest must be stable; thus energy flows from the lowest mode to the highest one. The same case exists when the imaginary parts are non-zero, but in addition, the contrary situation is possible. There are conditions under which an infinitesimal perturbation may reach a finite amplitude if the lowest mode is stable while the highest is unstable. Thus energy can flow "backward" from the highest mode to the lowest one. It is also shown that the imaginary parts increase the final wave amplitude. Second, the triggering of pressure oscillations in solid propellant rockets is discussed. In order to explain the triggering of the oscillations to a nontrivial stable: limit cycle, the treatment of two modes and the inclusion in the combustion response of either a second order nonlinear velocity coupling or a third order nonlinear pressure coupling seem to be sufficient

Determination of aerodynamic damping coefficients from wind-tunnel free-flight trajectories of non-axisymmetric bodies

Aerodynamic damping coefficient from wind tunnel free flight trajectories of nonaxisymmetrical bodie

Numerical investigation of unsteady laminar incompressible co-axial boundary layer flows

Finite difference method for analysis of laminar incompressible boundary layer flows at jet exi