Asymptotic Behaviour to a Von Karmrman System with Internal Damping

In this work we consider the Von Kármán system with internal damping acting on the displacement of the plate and using the Theorem due to Nakao [1] we prove the exponential decay of the solution.

An internally damped inertial platform for marine gravimetry and a test case in the South China Sea

To dampen periodic off-levelling motions within an inertial platform while undergoing horizontal accelerations of the same period and to achieve a levelling accuracy of a few tens of arcseconds with that system,an internally damped inertial platform for a marine scalar gravity system was the developed.Methods for attenuating horizontal acceleration and reducing off-levelling error by a satisfactory gyro-levelling loop,which are fundamental to the internally damped inertial platform,were designed and implemented.In addition,phase delays are introduced by the levelling loop.The resulting off-levelling gravity errors were analyzed and modeled.A series of tests on a motion simulator were performed in laboratory for a variety of simulated sea conditions.We found that the motion of the platform is a function of the amplitude and period of the simulated ship motions and ranges between 10 and 40 arcseconds.In addition,the phase lag between platform motion and ship motion is not constant but ranges 180°-270°,depending on the period and amplitude of the motion.Then,the platform,on which a gravimeter was mounted,was installed on the R/V Shiyan 2 to conduct a gravity survey in the South China Sea.Despite rough sea conditions,it was shown that in short periods of 2-30 s,the off-levelling angle was less than 30 arcseconds,and the phase lagged the horizontal acceleration by 230°-260°.From a repeated survey line and intersecting survey points,the estimated errors of gravity measurements were between 1.3 and 1.7 mGal.The marine measurements results were compared with those of satellite altimetry data and show a mean value of 0.5 mGal in a standard deviation of 1.5 mGal.

Nonlinear Internal Damping of Wave Equations with Variable Coefficients

For wave equations with variable coefficients on regions which are not necessarily smooth, we study the energy decay rate when a nonlinear damping is applied on a suitable subrigion.

Estimation of the internal and external damping from the forward and backward spectrum of a rotor with a fatigue crack

Both internal and external damping are concurrently present in a rotor system.However,the internal damping that originates from various sources often leads to instability in the rotor system,and hence its accurate estimation is crucial.The goal of the present paper is to distinctly estimate both external and internal damping in a Jeffcott rotor containing transverse crack.The modelling of the fatigue crack is based on the assumption of a switching crack,which additionally provides the internal damping due to rubbing on crack faces,which is hardly addressed in literature.Moreover,the fatigue crack leads to the forward and backward whirls due to asymmetry in the rotor.In the process of development of the identification procedure in the form of the regression equation for the estimation of internal damping,other important unknown rotor system parameters,like the external damping,unbalance and loss of stiffness of the shaft due to the crack,are also identified.This reduces the estimation error of the internal damping due to reduction in deviations of other model parameters.Numerically simulated responses are obtained from equations of motion of the rotor system in the form of a closed-form expression and by the Runge-Kutta integration method.The full-spectrum response data(both magnitude and phase)are utilized during the testing of the proposed identification procedure.Phase corrections have been incorporated in the full-spectrum.Measurement noise is added in numerical responses during identification of parameters to check the robustness of the algorithm and found to be working satisfactorily.

Determination of the thermal noise limit in test of weak equivalence principle with a rotating torsion pendulum

Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.

Inner Attitude Integration Algorithm Based on Fault Detection for Strapdown Inertial Attitude and Heading Reference System

This article proposes a new inner attitude integration algorithm to improve attitude accuracy of the strapdown inertial attitude and heading reference system （SIAHRS） , which, by means of a Kalman filter, integrates the calculated attitude from the accelerometers in inertial measuring unit （IMU） , called damping attitudes, with those from the conventional IMU. As vehicle＇ s acceleration could produce damping attitude errors, the horizontal outputs from accelerometers are firstly used to judge the vehicle＇ s motion so as to determine whether the damping attitudes could be reasonably applied. This article also analyzes the limitation of this approach. Furthermore, it suggests a residual chi-square test to judge the validity of damping attitude measurement in real time, and accordingly puts forward proper information fusion strategy. Finally,the effectiveness of the proposed algorithm is proved through the experiments on a real system in dynamic and static states.