RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS

The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.

PERIODIC MOTIONS OF SPINNING RIGID SPACECRAFT UNDER INFLUENCE OF GRAVITATIONAL AND MAGNETIC FIELDS

The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.

Periodic Motion Planning and Control for Double Rotary Pendulum via Virtual Holonomic Constraints

Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning.We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint(VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.

Bifurcation of Periodic Motion of Rigid Rotor System Supported by Angular Contact Ball Bearings

Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.

Study on High Accuracy Hybrid Controller for Periodic Motion Control

In order to realize high accuracy control for periodic motion,a hybrid controller with grey prediction was presented in this paper.Incorporating the grey prediction,repetitive control,and the traditional Proportional-Integral-Differential(PID)control,a design method of the grey prediction repetitive PID(GRPID)control algorithm was investigated,according to the characteristics of the periodic motion control.The hybrid control algorithm can estimate unsure parameters and disturbance of system using grey prediction,and compensate control in terms of the prediction results,and this may improve control quality and robustness of repetitive control for controlling periodic motion.An example was carried out to verify the feasibility of the controller.The simulation results show that this algorithm has better performances than that of the conventional repetitive control system.It indicates the presented control method is more suitable for control system of periodic motion.

Birkhoff's conjecture and almost periodic motions on torus T^2

The relation between rotation number and almost periodic motion for almost all C5 systems on T2 which have no critical points is established. The result that every solution of such systems is a Liapunov stable and almost periodic motion is

Revealing the Fluttering Motions of Mid-Water Trawl Codend Through Sea Trials:Case Study of Antarctic Krill Trawl Codend

The dynamic coupling between the fluttering motions and hydrodynamic characteristics of codend is essential in understanding the trawl selectivity through fish response and the drag force acting on the whole trawl.This study investigated the effect of towing speed,warp length,warp tension,and catch size on the fluttering motions of Antarctic krill trawl codend during net shooting,towing,and hauling by using sea trial data.The time-periodicity of codend oscillation was analyzed by the Morlet wavelet transform method.Results indicated that the period of codend oscillation was between 50 s and 90 s and showed an increasing trend with the warp tension but a decreased value at the towing stage.The coefficient amplitude of codend oscillation was between 0 and 4 at the net shooting and hauling stages,and between 0.2 and 0.6 at the towing stage.The amplitude of codend oscillation increased with the warp tension,towing speed,and catch size,but decreased with the increase of the warp length.In addition,the period of codend oscillation increased with the towing speed at the net shooting and hauling stages,but decreased at the towing stage.These results from codend fluttering motions can improve the understanding of fish behavior and gear shape that modify the hydrodynamic force on the codend instantaneously.

Observation 20-s periodic signals on Mars from InSight,Sols 800-1,000

Seismometers of the InSight probe(Interior Exploration using Seismic Investigation,Geodesy and Heat Transport)currently operating on Mars have recorded not only seismic events but also high-frequency non-seismic periodic signals that appear to have been induced by variations in the Martian environment and the hardware.Here,we report an observation of a long-period signal with a dominant period of~20 s from Martian solar days(Sol)800 to Sol 1,000.This 20-s signal is detected mostly at quiet nighttime—from22:00 to 04:00 LMST(Local Mean Solar Time)—at the InSight landing site.The measurement of the particle motion suggests that this linearly polarized signal focuses on the horizontal plane with an angle of~30°from the north.By examining the temporal variation of the signal’s amplitude and polarization angle and its times of occurrence in relation to the planet’s atmospheric data,we suggest that this20-s signal may be relevant to wind and temperature variations on Mars.Furthermore,we study the possible influence of this 20-s signal on the noise autocorrelation and find that the stacked autocorrelograms can be quite different when the 20-s signal is present.

Pulse-like ground motion observed during the 6 February 2023 M_(W)7.8 Pazarcık Earthquake(Kahramanmaraş,SE Türkiye)

In this study,we analyzed 100 three-component strong ground motion records observed within 200 km of the causative fault of the 6 February 2023 M_(W)7.8 Pazarcık(Kahramanmaraş)Earthquake in SE Türkiye.The wavelet method was utilized to identify and analyze the characteristics of pulse-like ground motions in the near-fault region,while considering the uncertainty of the pulse orientation during the analysis.Our investigation focused on the effects of the focal mechanism and rupture process on the spatial distribution,pulse orientation,and maximum pulse direction of the observed pulse-like ground motion.We also analyzed the amplitude and period of the observed ground pulses and the effect of long-period amplification on the ground motion response spectra.Our results indicated the following:(1)A total of 21 typical ground velocity pulses were observed during this earthquake,exhibiting complex characteristics due to the influence of the strike-slip mechanism and rupture directivity.Most ground pulses(17 out of 21)were recorded within 20 km of the fault,in a wide range of orientations,including normal and parallel to the fault direction.The waveforms exhibited unidirectional features,indicating the effects of left-lateral fault slip.Distinct pulses observed more than 20 km from the fault were mainly oriented normal to the fault.The waveforms were bidirectional with double-or multi-round trips as a result of rupture directivity.(2)The amplitudes of the observed pulses ranged from 30.5 to 220.0 cm/s,with the largest peak velocity of 220.0 cm/s observed at Station 3138.The pulse periods ranged from 2.3 to 14.5 s,with the longest pulse period of 14.5 s observed at Station 3116.The amplitude and period of the pulses observed during this earthquake were comparable to those of similar-magnitude global earthquakes.The amplitude of the pulses decreased significantly with increasing fault distance,whereas the pulse period was not significantly affected by the fault distance.(3)Compared with non-pulse records,the velocity pulse records had a pronounced amplification effect on the acceleration response spectra near the pulse period,with factors ranging from 2.1 to 5.8.The larger velocity pulses also significantly amplified the velocity response spectra,particularly over the long periods.This significant amplification effect of the pulses on the response spectra leads to empirical models underestimating the long-period earthquake ground motion.

海底长周期地震动预测模型:以日本相模湾海域为例

地震动反应谱预测模型是地震危险性分析的基础,基于日本K-NET台网相模湾地区的892组海域地震动数据和4 033组陆域地震动数据,考虑震级、震源距、震源深度以及震源类型和场地,建立了PGA和0.05~15.0 s的海域地震动加速度反应谱预测模型。通过残差分析以及相关性分析检验了模型的合理性,并分析了震源类型以及震源深度对反应谱的影响,对比了海陆地震动预测模型的差异。结果表明:震源类型以及震源深度对模型预测结果影响显著,水平向海域模型以及长周期(T≥1.0 s)竖向海域模型所预测反应谱大于陆域模型所预测的反应谱值,且水平向和长周期竖向模型的场地放大系数均大于1。该模型可为长周期海域地震动模型的建立和概率地震危险性分析提供参考,为长周期海域工程的抗震设防提供依据。

A LARGE-SCALE ESTIMATE OF THE NUMBEROF PERIODIC SMALL OSCILLATIONS OFNONLINEAR SYSTEMS

A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question: How many types of the periodic small oscillation in the whole configuration space of the system are there? Making some hypotheses, it expresses the lower bounds of the number of the types for two cases where critical points of the potential function are nondegenerate and degenerate respectively by the Betti numbers and dimension of the constraint manifold only.

长周期地震动对SRC框架-RC核心筒混合结构协同工作的影响

长周期地震动因含有丰富的低频成分易使(超)高层建筑等长周期结构发生严重震害。SRC(steel reinforced concrete)框架-RC(reinforced concrete)核心筒混合结构作为广泛应用于高烈度区的双重抗侧力结构体系,确保其强震下的协同工作是实现多道抗震防线,形成合理破坏模式的关键。该文通过与普通地震动对比,阐明了远场长周期地震动对SRC框架-RC核心筒混合结构协同工作的影响规律,并基于谐振激励下的结构动力分析模型及经验模态分解初步揭示了其内在机理。算例分析结果表明:受低频特性影响,远场长周期地震动作用下结构框架剪力分担率与底层倾覆力矩占比明显大于普通地震动,最大框架剪力分担率所在楼层与普通地震动相比出现下移,且当峰值加速度增至400 gal时,SRC框架中下部楼层剪力分担率超过40%,底部倾覆力矩占比超过70%,按照现行规范设计的SRC框架将难以保证远场长周期地震动作用下结构的抗震安全;激励频率对于SRC框架-RC核心筒混合结构协同工作的影响与振型参与方式有关,低频激励(周期为0.5倍~2.0倍结构基本周期)下结构响应主要受低阶振型主导;远场长周期地震动的卓越分量是导致框架剪力分担率增大的原因。

基于全耦合模型的海上吊装作业动力响应特征研究

针对现有海上吊装模拟方法不能有效考虑浮吊船舶—系泊系统—吊物系统之间的动态耦合,难以实现基座回转、吊臂变幅连续模拟问题,基于Matlab/Simulink、ADAMS联合仿真平台建立了海上吊装作业全耦合动力分析模型,探究了中长周期波作用下波浪周期、吊缆收放、基座回转、吊臂变幅等参数变化对吊装作业系统动力响应的影响规律。结果表明,波浪周期接近吊物系统固有周期时会引发共振,导致吊物摇摆幅值显著增加。基座回转、吊臂变幅等因改变了吊物的空间位置从而引发了浮吊船舶倾覆力矩的变化,进而对浮吊船舶运动响应产生显著影响。当基座回转90°后,浮吊船舶的横倾角增加约2.74°。

房缩期二尖瓣前向血流速度联合二尖瓣环纵向位移评估左室僵硬度

目的:探索房缩期二尖瓣前向血流速度联合二尖瓣环纵向位移评估左室僵硬度的可行性。方法:募集门诊接受经胸超声心动图检查的志愿者117例。超声心动图测量常规参数,描计组织多普勒a波的速度时间积分记作VTIa′,计算A2/VTIa′。将受试者分为舒张功能正常组(GROUP 1,n=35)、舒张功能障碍I级组(GROUP 2,n=61)、舒张功能障碍Ⅱ级及Ⅲ级组(GROUP 3,n=21),对比三组间A2/VTIa′及其他参数差异;行A2/VTIa′与现有僵硬度参数、僵硬度影响因素的相关性分析;将GROUP 1与GROUP 2归为僵硬度正常组(NS),GROUP 3归为僵硬度异常组(AS),分析A2/VTIa′鉴别两组的诊断效能。结果:舒张功能不同分组间A2/VTIa′差异存在显著统计学意义(P<0.001);A2/VTIa′与LVEDP/LVEDV、KLV分别呈中度、低度正相关(r=0.411、0.222,P<0.05),与年龄、收缩压、E/e′分别呈低度正相关(r=0.364、0.338、0.356,P<0.001),与e′呈低度负相关(r=-0.365,P<0.001);A2/VTIa′鉴别AS与NS的AUC为0.805,诊断敏感度和特异度分别为81.0%和66.7%。结论:A2/VTIa′可用于评估左室僵硬度,且对僵硬度异常的鉴别价值高于目前左室僵硬度评估指标。

Identifying Periodical Activities Independent of Video Content

In this research, a completely new and accurate method has been presented for detecting periodic activities with the help of machine vision. The proposed method is independent of motion tracking complex algorithms unlike the previous strategies and it is fully independent of contents and types of activities by performing low level calculation. Not using of heavy computations while improving the ability of periodicity detection is regarded as the unique feature of this method. The use of general and flexible framework in this method causes to facilitate the machine vision periodic activities identification process.

AVERAGING PRINCIPLE FOR QUASI-GEOSTROPHIC MOTIONUNDER RAPIDLY OSCILLATING FORCING

A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.

The Problem of Quasiperiodic Photonic Structures Solved by Considering the Cut of 2D Periodic Structure

The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.

含双重三要素型吸振器的碰摩转子的振动特性分析

对碰摩故障下安装有抑制共振的最优双重三要素型转子吸振器的转子的振动特性进行了研究。利用转子动力学方法建立了吸振器-转子的动力学方程,通过Newmark-Newton方法对方程进行了求解,借助分岔图分析了吸振器参数、碰摩参数对转子振动特性的影响。结果显示:刚度较小的单体吸振器1的ka1为最优值的1.66~2倍时,吸振器-转子呈现周期二运动,其他参数变动时转子基本处于周期N运动或混沌运动;刚度较大的单体吸振器2的ka2为最优值的1.36~2倍时,吸振器-转子呈周期二运动,其他参数变动时转子基本处于周期N或混动运动。碰摩刚度的变化,会使吸振器-转子的运动由周期四运动转为周期N运动或混沌运动;碰摩摩擦系数除在初始值的0.8~1.18倍、1.48~1.6倍范围内使吸振器-转子呈周期四运动外,其他变动数值时系统呈周期二运动。

长周期地震动作用下某EPR核电站安全壳的隔震性能分析

核电站安全壳是切实有效保证核电站安全的必备设施。研究长周期地震动作用下的安全壳隔震性能,对安全壳具有十分重要的理论意义和工程应用价值。以某EPR核电站安全壳为研究模型,考虑了该安全壳自重和预应力系统,采用软件ANSYS建立复杂的三维数值仿真模型,探讨长周期地震动作用下安全壳的变形、加速度、基底剪力和预应力筋的平均应力,证实在长周期地震动作用下,该安全壳受力性能良好,并在控制范围内。基于此,引入层叠橡胶隔震器和软钢隔震器并联的新型隔震装置,进而研究长周期地震动作用下安全壳的隔震性能。分析结果表明:由于地震动的特性(例如,随机性、不确定性、空间相关性等),核电站安全壳设计必须从多方面重视长周期地震动。短周期地震动作用下新型隔震装置是有效的,长周期地震动作用下隔震失效。研究结果为核电站安全壳隔震设计提供技术指导。

Traveling wave effect on the seismic response of a steel arch bridge subjected to near fault ground motions

In the 1990s, several major earthquakes occurred throughout the world, with a common observation that near fault ground motion （NFGM） characteristics had a distinct impact on causing damage to civil engineering structures that could not be predicted by using far field ground motions. Since then, seismic responses of structures under NFGMs have been extensively examined, with most of the studies focusing on structures with relatively short fundamental periods, where the traveling wave effect does not need to be considered. However, for long span bridges, especially arch bridges, the traveling wave （only time delay considered） effect may be very distinct and is therefore important. In this paper, the results from a case study on the seismic response of a steel arch bridge under selected NFGMs is presented by considering the traveling wave effect with variable apparent velocities. The effects of fling step and long period pulses of NFGMs on the seismic responses of the arch bridge are also discussed.