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.

Enhancement of laser induced Au nanoparticle formation by femtosecond pulse shaping

We report the control of Au nanoparticle (NP) formation by using shaped 30 fs pulses, in a solution containing HAuCl4 and chitosan. By using a sinusoidal spectral phase, a periodic train of pulses is generated. When the period of the pulse train matches certain Raman resonances of chitosan, the reducing agent of the process, an enhancement of the Au NP formation is observed. Theoretical quantum chemical calculations indicate that the outer groups of the chitosan are mostly influenced by low Raman frequencies, which is in reasonably agreement with the experimental data and indicates an enhancement in the Au NP formation as the pulse train period increases (low frequency).