Thermal convection with generalized friction

A model for thermal convection with generalized friction is investigated. It is shown that the linear instability threshold is the same as the global stability one. In addition, decay of the energy in the $$L^2$$ L 2 norm is shown for the perturbation velocity and temperature fields. However, due to the presence of the generalized friction we establish exponential decay in the $$L^{\beta +1}$$ L β + 1 norm for the perturbation temperature, where $$\beta >1$$ β > 1 .

STABILITY AND VIBRATION ANALYSES OF AN INTERNALLY DAMPED TAPERED COMPOSITE DRIVESHAFT USING THE FINITE ELEMENT METHOD

The present study considers the linear vibration and stability analyses of an internally damped rotating tapered composite shaft supported on rolling bearings. The Timoshenko beam theory is utilized to model the tapered drive-shaft based on Equivalent Single Layer Theory (ESLT). The ESLT considers a laminated driveshaft that consists of several lamina with different fiber orientations. Since the bearings are considered as rolling element bearings, the bearings stiffnesses are modeled using linear translational springs and dampers. The equations of motion are derived by applying Lagrange’s equation, including the hysteretic internal damping of composite material, and then finite element formulation is utilized to solve the equations. The effects of various system parameters on the natural frequencies and instability threshold are investigated. An extensive parametric study has been carried out to determine the effects of various system parameters including hysteresis internal damping, fiber orientation, stacking sequence, taper angle, rotational velocity, and bearings stiffness and damping on the natural frequencies, critical speeds, and instability thresholds of internally damped tapered composite drive-shafts. Furthermore, Campbell and critical speed map diagrams are depicted to present the effects of rotational velocity and bearings stiffness on natural frequencies and critical speeds. It is shown that the stability of the driveshaft is enhanced by increasing the damping of the bearings, whereas increasing the internal damping of the composite driveshaft may reduce the instability threshold.

Observation of direction instability in a fiber ring laser

We report on the observation of a new phenomenon occurring in a fiber ring laser. This phenomenon is about the transition from an initially bidirectional emission of a reciprocal fiber ring laser to a unidirectional emission at a certain pump power threshold. In addition, the final direction is not predefined but appears to be randomly chosen every time the threshold is exceeded. Therefore, we term this new phenomenon direction instability. Furthermore, we provide a first discussion of how the instability threshold is influenced by the length and the loss of the cavity. We show that the threshold follows a power times length scaling, indicating a nonlinear origin.