Parametric resonances in a base-excited double pendulum

Two parametrically-induced phenomena are addressed in the context of a double pendulum subject to a vertical base excitation. First, the parametric resonances that cause the stable downward vertical equilibrium to bifurcate into large-amplitude periodic solutions are investigated extensively. Then the stabilization of the unstable upward equilibrium states through the parametric action of the high-frequency base motion is documented in the experiments and in the simulations. It is shown that there is a region in the plane of the excitation frequency and amplitude where all four unstable equilibrium states can be stabilized simultaneously in the double pendulum. The parametric resonances of the two modes of the base-excited double pendulum are studied both theoretically and experimentally. The transition curves (i.e., boundaries of the dynamic instability regions) are constructed asymptotically via the method of multiple scales including higher-order effects. The bifurcations characterizing the transitions from the trivial equilibrium to the periodic solutions are computed by either continuation methods and or by time integration and compared with the theoretical and experimental results.

Microstructure and metal-insulator transition in single crystalline KMo4O6

High quality KMo4O6 single crystals with tetragonal structure (space group P4/mbm) have been prepared by fused salt electrolysis. The crystals were studied by scanning electron microscopy (SEM), X-ray diffractometry, electrical resistivity, and magnetization measurements. X-ray powder diffraction patterns and SEM have given some information on the growth of single crystals. Electrical resistivity as a function of temperature shows that the KMo4O6 compound is a bad metal with resistivity change of approximately 30% in the temperature range from 2 to 300K. A metal-insulator transition (MIT), observed at approximately 110K, has been also confirmed for this material. Magnetization as a function of temperature agrees with previous report, however a magnetic ordering has been observed in M(H) curves in the whole temperature range.