We investigate the double-diffusive instability in an inclined porous layer with a concentrationbased internal heat source by conducting linear instability and nonlinear energy analyses. The effects of different dimensionless parameters, such as the thermal (Ra T ) and solutal (Ra S ) Rayleigh numbers, the angle of inclination (φ), the Lewis number (Le) and the concentration-based internal heat source (Q) are examined. A comparison between the linear and nonlinear thresholds for the longitudinal and transverse rolls provides the region of subcritical instability. We found that the system becomes more unstable when the thermal diffusivity is greater than the solute and the internal heat source strength increases. It is observed that the system is stabilized by increasing the angle of inclination. While the longitudinal roll remains stationary without the region of subcritical instability, as the angle of inclination increases, the transverse roll switches from stationary-oscillatory-stationary mode. Our numerical results show that for Ra S < 0, for all Q values, the subcritical instability only exists for transverse rolls. For Ra S ≥ 0, however, the subcritical instability appears only for Q = 0 and Q ≥ 0, respectively, for longitudinal and transverse rolls.
The present article focuses on suppressing mode-coupling instability in frictional systems, which can cause unwanted vibrations such as squeal in braking systems. Mode-coupling instability occurs when two or more modes of a system approach each other. This article proposes the use of resonant velocity feedback control to eliminate friction-induced oscillations generated by mode-coupling instability. A two degree-of-freedom linear model is used to capture the instability due to friction-induced mode coupling. The efficacy of the control is demonstrated through linear stability analysis, and by optimizing control parameters using pole crossover method to minimize the transient time of the response. The robustness analysis demonstrates the ability of the control to effectively mitigate the instability even under parametric perturbations. The controlled system is simulated in MATLAB Simulink to validate analytical results. The effects of time delay, which is commonly present in feedback systems, are also investigated. Finally, the effectiveness of the control is studied in the presence of nonlinearity in the system. The nonlinear dynamics are analyzed by creating bifurcation diagrams with different bifurcation parameters.
The present paper investigates the effect of time delay in a particular type of single degree-of-freedom self-excited oscillator. The self-excited vibration is generated in the system by using linear velocity feedback (to destabilize the static equilibrium of the system) with a nonlinear Rayleigh type feedback (to limit the growth of the instability into a stable limit cycle). The general method of describing function is employed to study the dynamics with the presence of time delay. Also, the analytical results are verified with the simulation result. Without time delay, the control law can generate a stable limit cycle with the proper choice of control parameters. However, the presence of time delay introduces a globally unstable limit cycle in the system with a stable one. Though the amplitude of the stable limit cycle dies down with the increase of time delay and finally vanishes by stabilizing the static equilibrium of the system. The effect of control parameters is also studied.
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