On the semicontinuity of the solution map to a parametric boundary control problem

This paper studies solution stability of a parametric boundary control problem governed by semilinear elliptic equation and nonconvex cost function with mixed state control constraints. Using the direct method and the first-order necessary optimality conditions, we obtain the upper semicontinuity and continuity of the solution map with respect to parameters.     

On unpredictable ship rolling in irregular seas

Indirectly excited large amplitude roll motions of container ships and roll-on/roll-off ferries represent a considerable threat to goods and life in modern navigation. Especially when ships are heading into rough seas, or sailing away from following seas, large roll responses have been reported to occur in an unpredictable, random way. We approach this topic from deterministic bifurcation theory and generalize the analysis by characterizing the seaway as narrow band stochastic processes. It is demonstrated how the intermittent behavior of zero and large amplitude motions in irregular seas is related to the deterministic bifurcation scenario. Further, we identify parameter regions of intermittent roll motions and show how the on-/off intermittency can be characterized by the probability density function of the response amplitude.     

非共线相位匹配LBO飞秒光参量放大器的理论分析

对非共线相位匹配LBO飞秒光参量放大器的参量特性进行了分析,结果表明利用这种参量放大器不仅可以实现高的参量增益,还可以获得极宽的参量带宽.因此它特别适合以纳秒级高功率激光作为抽运光,利用OPCPA技术放大飞秒脉冲.     

Parametric Amplification in Four-Layered QPM Leaky Waveguides

Parametric amplification of signal wave in a four-layered leaky waveguide configuration in Z-cut LiNbO 3 , where the pump and signal waves are guided modes and the idler is radiated into the substrate has been studied using coupled mode approach. It is shown that in this configuration, the signal gain can be greatly enhanced as compared to the case of a three-layered QPM Cerenkov-idler configuration. The studies show that by appropriately choosing the waveguide parameters, one can have a trade-off between signal gain bandwidth and the peak signal gain achieved. These studies should find application in designing optical parametric amplifiers and oscillators.     

Arbitrary amplitude periodic solutions for parametrically excited systems with time delay

Periodic solutions for parametrically excited system under state feedback control with a time delay are investigated. Using the asymptotic perturbation method, two slow-flow equations for the amplitude and phase of the parametric resonance response are derived. Their fixed points correspond to limit cycles (phase-locked periodic solutions) for the starting system. In the system without control, periodic solutions (if any) exist only for fixed values of amplitude and phase and depend on the system parameters and excitation amplitude. In many cases, the amplitudes of periodic solutions do not correspond to the technical requirements. On the contrary, it is demonstrated that, if the vibration control terms are added, stable periodic solutions with arbitrarily chosen amplitude and phase can be accomplished. Therefore, an effective vibration control is possible if appropriate time delay and feedback gains are chosen.     

Instability of thermally induced vibrations of carbon nanotubes

The dynamical stability of carbon nanotubes embedded in an elastic matrix under time-dependent axial loading is studied in this paper. The effects of van der Waals interaction forces between the inner and outer walls of nanotubes are taken into account. Using continuum mechanics, we apply an elastic layered shell model to solve the transverse parametric vibrations of a carbon nanotube. Both the Gaussian wide-band axial temperature changes and physically realizable temperature changes with known probability distributions are assumed as the tube axial loading. The energy-like functionals are used in the stability analysis. The emphasis is placed on a qualitative analysis of dynamic stability problem. Stability domains in the space of geometric, material and loading parameters are presented in analytical forms.     

Experimental study of liquid sloshing dynamics in a barge carrying tank

An experimental work has been carried out to study the phenomena of sloshing of liquid in partially filled tanks mounted on a barge exposed to regular beam waves. Three liquid fill levels with liquid depth, h_s to length of tank, l ratio (h_s/l) of 0.163, 0.325 and 0.488, are studied. The time histories of sloshing oscillation are measured along the length of container at predefined locations. The nonlinear behaviour of sloshing oscillation is observed for the regular wave excitation. The spectra of the sloshing oscillation and their qualitative assessment are reported. Attempts are made to evaluate the harmonics present in the sloshing oscillation and compare with the results of earlier studies. The effects of wave excitation frequency and wave height on the sloshing oscillation as well as on the response of the barge are studied.     

Stability of an equilibrium position of a pendulum with step parameters

A mathematical pendulum affected by parametric disturbance with potential energy being periodic step function is considered. Non-linear equation of the pendulum depends on two parameters characterizing the mean value in time of the parametric disturbance and range of its “ripple”. Values of the parameters can be set arbitrarily. The non-linear problem of stability for two particular solutions of the equation corresponding to a hanging and inverse pendulum is solved.     

Rotary motion of the parametric and planar pendulum under stochastic wave excitation

In this paper a rotary motion of a pendulum subjected to a parametric and planar excitation of its pivot mimicking random nature of sea waves has been studied. The vertical motion of the sea surface has been modelled and simulated as a stochastic process, based on the Shinozuka approach and using the spectral representation of the sea state proposed by Pierson–Moskowitz model. It has been investigated how the number of wave frequency components used in the simulation can be reduced without the loss of accuracy and how the model relates to the real data. The generated stochastic wave has been used as an excitation to the pendulum system in numerical and experimental studies. For the first time, the rotary response of a pendulum under stochastic wave excitation has been studied. The rotational number has been used for statistical analysis of the results in the numerical and experimental studies. It has been demonstrated how the forcing arrangement affects the probability of rotation of the parametric pendulum.