Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Squeeze-film Effects in MEMS Devices with Perforated Plates for Small Amplitude Vibration

Squeeze-film effects of perforated plates for small amplitude vibration are analyzed through modified Reynolds equation (MRE). The analytical analysis reckons in most important influential factors: compressibility of the air, border effects, and the resistance caused by vertical air flow passing through perforated holes. It is found that consideration of air compressibility is necessary for high operating frequency and small ratio of the plate width to the attenuation length. The analytical results presented in this paper agree with ANSYS simulation results better than that under the air incompressibility assumption. The analytical analysis can be used to estimate the squeeze-film effects causing damping and stiffness added to the system. Since the value of Reynolds number involved in this paper is low (< 1), inertial effects are neglected.

Variation of added mass and its application to the calculation of amplitude response for a circular cylinder

In the present study, analyzed are the variation of added mass for a circular cylinder in the lock-in ( synchronization) range of vortex-induced vibration (VIV) and the relationship between added mass and natural frequency. A theoretical minimum value of the added mass coefficient for a circular cylinder at lock-in is given. Developed are semi-empirical formulas for the added mass of a circular cylinder at lock-in as a function of flow speed and mass ratio. A comparison between experiments and numerical simulations shows that the semi-empirical formulas describing the variation of the added mass for a circular cylinder at lock-in are better than the ideal added mass. In addition, computation models such as the wake oscillator model using the present formulas can predict the amplitude response of a circular cylinder at lock-in more accurately than those using the ideal added mass.

Chaos of liquid surface waves in a vessel under vertical excitation with slowly modulated amplitude

Free surface waves in a cylinder of liquid under vertical excitation with slowly modulated amplitude are investigated in the current paper. It is shown by both theoretical analysis and numerical simulation that chaos may occur even for a single mode with modulation which can be used to explain Gollub and Meyer's experiment. The implied resonant mechanism accounting for this phenomenon is further elucidated.

Standing wave of finite-amplitude in an circular basin with uneven bottom

The effect of the particle cover over the density interface between two layers of fluids and of the suspended solid particles in the upper turbulcnt layer on the turbulent entrainment has been studied experimentally. The entrainment distance D is a function of the time of power: D=kt, where =0.200-0.130p. For suspended particles in the upper layer and pure 2-layer fluid is equal to 0.200, but the value of k for the suspended particles is smaller than that for the pure 2-layer fluid. The non-dimensional entrainment velocity is E=KRiln, where n=1.50+0.93 p. It is shown that the particle cover over the interface changes the power of Ril in the entrainment and hinders the turbulent entrainment. The variation rule of E for the suspended particles is the same as that for the pure 2-layer fluid, but the K value of the former is smaller than that of the latter. The turbulent mixing mechanism has been discussed.

Parametric studies of tension leg platform with large amplitude motions

Tension leg platform (TLP) is an important kind of working station for deep water exploration and development in ocean, whose dynamic responses deserve a serious thought. It is shown that for severe sea state, the effects of nonlinearities induced by large displacements of TLP may be noteworthy, and then employment of small displacements model should be restrained. In such situation, large amplitude motion model may be an appropriate alternative. The numerical experiments are performed to study the differences of dynamic responses between the two models. It is shown that for most cases, differences between results of the two models are significant. The variances of the differences vs. the wave period are the most remarkable, and that of the differences vs. wave heading angle are also apparent.

Optical bistability via amplitude and phase control of a microwave field

We investigate the steady-state optical bistability behavior in a three-level A-type atomic system closed by a microwave field under the condition that the applied fields are in resonance with corresponding atomic transitions. It is shown that the bistable hysteresis cycles can be controlled by both the amplitude and the phase of the microwave field. (c) 2006 Elsevier B.V. All rights reserved.

Comparison between complex amplitude envelope representation and complex analytic signal representation in studying pulsed Gaussian beam

Analytic propagation expressions of pulsed Gaussian beam are deduced by using complex amplitude envelope representation and complex analytic signal representation. Numerical calculations are given to illustrate the differences between them. The results show that the major difference between them is that there exists singularity in the beam obtained by using complex amplitude envelope representation. It is also found that singularity presents near propagation axis in the case of broadband and locates far from propagation axis in the case of narrowband. The critical condition to determine what representation should be adopted in studying pulsed Gaussian beam is also given. (C) 2004 Elsevier B.V. All rights reserved.

Comparison of uniform amplitude beam and intercepted Gaussian beam superresolution theories

The general superresolution theories for uniform amplitude beams and intercepted Gaussian beams are investigated. For these two types of incident beam, both two-zone amplitude and pure-phase filters are adopted to provide specific numerical descriptions of their differences in superresolution performances. Simulated results of comparisons between their performances indicate that, with the same spot size ratio, the intercepted Gaussian beam achieves a higher central image brightness ratio and significantly lower side-lobe effect irrespective of the filter used. (c) 2008 Elsevier Ltd. All rights reserved.

Differential amplitude modulation of auditory evoked cortical potentials associated with brain state in the freely moving rhesus monkey

We simultaneously recorded auditory evoked potentials (AEP) from the temporal cortex (TCx), the dorsolateral prefrontal cortex (dPFCx) and the parietal cortex (PCx) in the freely moving rhesus monkey to investigate state-dependent changes of the AEP. AEPs obtained during passive wakefulness, active wakefulness (AW), slow wave sleep and rapid-eye-movement sleep (REM) were compared. Results showed that AEP from all three cerebral areas were modulated by brain states. However, the amplitude of AEP from dPFCx and PCx significantly appeared greater attenuation than that from the TCx during AW and REM. These results indicate that the modulation of brain state on AEP from all three cerebral areas investigated is not uniform, which suggests that different cerebral areas have differential functional contributions during sleep-wake cycle. (C) 2002 Elsevier Science Ireland Ltd.. All rights reserved.

Amplitude/frequency of spontaneous mEPSC correlates to the degree of long-term depression in the CA1 region of the hippocampal slice

Prior synaptic or cellular activity influences degree or threshold for subsequent induction of synaptic plasticity, a process known as metaplasticity. Thus, the continual synaptic activity, spontaneous miniature excitatory synaptic current (mEPSC) may correlate to the induction of long-teen depression (LTD). Here, we recorded whole-cell EPSC and mEPSC alternately in the Schaffer-CA1 synapses in brain slice of young rats, and found that this recording configuration affected neither EPSC nor mEPSC. Low frequency stimulation (LFS) induced variable magnitudes of LTD. Remarkably, larger magnitudes of LTD were significantly correlated to smaller amplitude/lower frequency of the basal mEPSC. Furthermore, under the conditions reduced amplitude/frequency of the basal mEPSC by exposure to behavioral stress immediately before slice preparation or low concentration of calcium in bath solution, the magnitudes of LTD were still inversely correlated to mEPSC amplitude/frequency. These new findings suggest that spontaneous mEPSC may reflect functional and/or structural aspects of the synapses, the synaptic history ongoing metaplasticity. (C) 2005 Elsevier B.V. All rights reserved.

An ambient proof and wide tuning range LC VCO with automatic amplitude control for tuner applications

This paper represents a LC VCO with AAC (Auto Amplitude Control), in which PMOS FETs are used as active components, and the varactors are directly connected to ground to widen Kvco linear range. The AAC circuitry adds little noise to the VCO and provides it with robust performance over a wide temperature and carrier frequency range. The VCO is fabricated in 50-GHz 0.35-mu m SiGe BiCMOS process. The measurement results show that it has -127.27-dBc/Hz phase noise at 1-MHz offset and a linear gain of 32.4-MHz/V between 990-MHz and 1.14-GHz. The whole circuit draws 6.6-mA current from 5.0-V supply.

Response amplitude and hydrodynamic force for a buoy over a convex

A buoy as an offshore structure is often placed over a convex such as a caisson or a submerged island. The hydrodynamic fluid/solid interaction becomes more complex due to the convex compared with that on the flat. Both the buoy and the convex are idealized as vertical cylinders. Linear potential theory is used to investigate the response amplitude and the hydrodynamic force for a buoy over a convex due to diffraction and radiation in water of finite depth. These are derived from the total velocity potential. A set of theoretical added mass, damping coefficient, and exciting force expressions have been proposed. Analytical results of the response amplitude and hydrodynamic force are given. Finally, the numerical results show that the effect of the convex on the response amplitude and hydrodynamic force for the buoy is ignored if the size of the convex is relatively smaller.