李萨茹图形的几种实验方法

李萨茹图形在频率测量中有重要作用,本文总结了李萨茹图形的三种实验方法和特点,并简单介绍其应用.

ON POSITIVE SOLUTIONS OF ONE CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, we establish a 1-1 correspondence between positive solutionsof one class of nonlinear differential equations and a class of harmonic functions.These results give an explicit description of E.B.Dynkin's class Ha of positive harmonic functions.

Kinematics and dynamics of a particle on a non-simple harmonic vibrating screen

The motion of a particle on a screen is directly affected by the motion of the screen if airflow and inter- granular friction are ignored. To study this effect, a mathematical model was established to analyze the motion of a planar reciprocating vibrating screen, and a matrix method was employed to derive its equa- tion of motion. The motion of the screen was simulated numerically and analyzed using MATLAB. The results show that the screen undergoes non-simple harmonic motion and the law of motion of each point in the screen is different. The tilt angle of the screen during screening is not constant but varies according to a specific periodic function. The results of numerical simulations were verified through experiments. A high-speed camera was used to track the motion of three points in the longitudinal direction of the screen. The balance equation for forces acting on a single particle on the screen was derived based on the non-simple harmonic motion of the screen, These forces were simulated using MATLAB. Different types of particle motion like slipping forward, moving backward, and being tossed to different parts of the screen were analyzed. A vibro-impact motion model for a particle on the non-simple harmonic vibrating screen was established based on the nonlinear law of motion of the particle. The stability of fixed points of the map is discussed. Regimes of different particle behaviors such as stable periodic motion, period-doubling bifurcation motion, Hopf bifurcation motion, and chaotic motion were obtained. With the actual law of motion of the screen and the behavior of a particle on the screen, a theoretical basis for design optimization of the screen is provided.

Investigation of a ship resonance through numerical simulation

Understanding dynamic stability of a ship on a resonance frequency is important because comparatively smaller external forces and moments generate larger motions.The roll motion is most susceptible because of smaller restoring moments.Most studies related to the failure modes such as parametric roll and dead ship condition,identified by second generation of intact stability criteria(SGISC)are performed at a resonance frequency.However,the nature of resonance,where the model experiences an incremental roll motion,has not been well understood.In this study,nonlinear unsteady computational fluid dynamics(CFD)simulations were conducted to investigate the resonance phenomenon using a containership under a sinusoidal roll exciting moment.To capture the complexity of the phenomenon,simulations were conducted over a range of frequencies to cover the resonance frequency including lower and higher amplitudes.In addition to the resonance frequency,the phase shift between roll exciting moment and roll angle,as well as the phase difference between acceleration and roll angle,were found to have significant effects on the occurrence of resonance.

Advances on numerical and experimental investigation of ship roll damping

This paper presents recent developments towards efficient and reliable methods for roll damping estimation based on numerical simulations as well as model tests using the harmonic excited roll motion(HERM)technique.A newly designed automatic roll damping estimation procedure shows the advantage of a just-in-time post processing of experimental measurement results.Real-time analysis of the measured roll damping values permits a considerable shortening of the test times.Thus,a large number of investigations can be carried out with relatively manageable effort in order to determine the roll damping behavior of different keel configurations or at operating conditions,e.g.,different sized keels or Froude numbers.In addition,HERM measurement method is applied to investigate the memory effect.For this purpose,different excitation schemes are introduced and the results are analyzed.Moreover,a study of the scale effect on the roll damping properties is conducted,in which experimental and numerical investigations are performed for two scales of a ship model.Furthermore,a method is developed that significantly reduces the effort of Reynolds average Navier-Stokes(RANS)-based simulations of roll motion.The reduction of simulation time is achieved by introducing an artificial damping.The obtained results show that the developed method is very well applicable for numerical as well as in experimental investigations.During the model tests using HERM technique,the model is free and the rudder is used to keep the straight-ahead course.The analysis of the numerical and experimental results shows that the influence of the rudder induced force and moment during HERM tests is not negligible and the contribution of the rudder must be taken into account by estimating the roll damping.Finally,a new concept is developed to investigate the parametric roll behavior of ships,which allows neglecting the consideration of the complex modelling of free surface waves in the simulations.During the RANS computations,a potential-based method is applied to compute the variation of restoring terms due the roll motion.

Equilibrium state of axially symmetric electric solar wind sail at arbitrary sail angles

This paper studies the equilibrium state and trajectory dynamics of an axially symmetric Electric solar wind sail(E-sail)at arbitrary sail angles.The E-sail is assumed operating in a heliocentric-ecliptic orbit at approximately one astronomic unit(au)from the Sun,and experiencing various dynamic disturbances like solar wind pressure,tether tension oscillations,and centrifugal forces.The study derives analytical expressions for the E-sail's equilibrium state and its maximal coning angle under small coning angle assumption.Subsequently,an improved propulsion model is developed for the E-sail in this equilibrium state.To assess the precision of these formulations,a high-fidelity E-sail dynamic model is constructed using the nodal position finite element method,where the tethers are modeled as two-noded tensile elements and the central spacecraft and remote units are simplified as lumped masses.Through thorough parametric analyses,this paper conclusively demonstrates that the operation of the E-sail at the equilibrium state can be achieved in accordance with the derived analytical prediction of the equilibrium state.Furthermore,the improved propulsion model is employed in trajectory analyses for a mission to reach the solar system's boundary.The study provides valuable insights and findings and foundation for the practical application and further advancement of the E-sail technology.