THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0.The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions satisfy.Furthermore,the exact bound of a special case is given using the Chebyshev system.At the end,some numerical simulations are given to illustrate the existence of limit cycles.

Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

Convergence Phenomenon with Fourier Series of tg(x2)and Alike

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

Mechanism of Pendulum-type wave phenomenon in deep block rock mass

Pendulum-type ( μ wave) wave is a new type of elastic wave propagated with low frequency and low velocity in deep block rock masses. The μ wave is sharply different from the traditional longitudinal and transverse waves propagated in continuum media and is also a phenomenon of the sign-variable reaction of deep block rock masses to dynamic actions, besides the Anomalous Low Friction (ALF) phenomenon. In order to confirm the existence of the μ wave and study the rule of variation of this μ wave experimentally and theoretically, we first carried out one-dimensional low-speed impact experiments on granite and cement mortar blocks and continuum block models with different characteristic dimensions, based on the multipurpose testing system developed by us independently. The effects of model material and dimensions of models on the propagation properties of 1D stress wave in blocks medium are discussed. Based on a comparison and analysis of the propagation properties (acceleration amplitudes and Fourier spectra) of stress wave in these models, we conclude that the fractures in rock mass have considerable effect on the attenuation of the stress wave and retardarce of high frequency waves. We compared our model test data with the data of in-situ measurements from deep mines in Russia and their conclusions. The low-frequency waves occurring in blocks models were validated as Pendulum-type wave. The frequencies corresponding to local maxima of spectral density curves of three-directional acceleration satisfied several canonical sequences with the multiple of 2～(1/2), most of those frequencies satisfied the quantitative expression (2～(1/2))i V p/2△ .

Asymmetric Environmental Regulation:Mechanism and a Yardstick Phenomenon

In discussing the policy effects of environmental regulation,we should focus not only on whether environmental regulation helps improve the environmental and economic performance of firms,but also on how such improvement is materialized,i.e.whether the obsolete mode of production is reversed.After matching the database of China’s industrial enterprises with that of pollution emissions from these industrial enterprises,this paper identifies the asymmetric scope of clean production standards to test the effect of environmental regulation on the total factor productivity(TFP)of the industrial enterprises.Our empirical research finds that the implementation of clean production standards may induce TFP improvement.However,such improvement only occurs for polluters who cannot or who barely meet clean production standards and does little to improve the production standards of polluters with low pollution emission,reflecting the yardstick phenomenon of the asymmetric environmental regulation policy effect:While polluters are forced to improve,clean enterprises that pollute less are more likely to take no action.Further research finds that such TFP improvement is materialized primarily by means of overall firm optimization;the compensation effect is insignificant and does not reverse the backward mode of production.Polluters cope with the implementation of clean production standards by purchasing more equipment and expanding capacity,which adds to the tension between the expansion of capacity and the abatement of pollution emission.

Measurement of remanent magnetic moment using a torsion pendulum with single frequency modulation method

In Tian Qin spaceborne gravitational-wave detectors, the stringent requirements on the magnetic cleanliness of the test masses demand the high resolution ground-based characterization measurement of their magnetic properties. Here we present a single frequency modulation method based on a torsion pendulum to measure the remanent magnetic moment mr of 1.1 kg dummy copper test mass, and the measurement result is(6.45 ± 0.04(stat) ± 0.07(syst)) × 10^(-8)A · m^(2). The measurement precision of the mr is about 0.9 n A · m^(2), well below the present measurement requirement of Tian Qin. The method is particularly useful for measuring extremely low magnetic properties of the materials for use in the construction of space-borne gravitational wave detection and other precision scientific apparatus.

Inexplicable Multi-Annual Astral Action on the Precession of Allais Pendulum: An Influence of the Solar System (and Especially of Jupiter?)

Between 1954 and 1961, Allais conducted 6 one-month observations of the azimuth of the plane of oscillation of a pendulum installed in his laboratory. That of 1958 also implemented a second pendulum, identical to the first, located 6 km away in an underground quarry. Although, over these 6 years, the average azimuth of each observation, the amplitude of the 24 h 50 min and 24 h waves, as well as certain other quantities, have evolved considerably, in 1958 their values were very close to those of the second pendulum. The analysis shows that these evolutions could only result from an action external to the pendulum, that no classical phenomenon seems to be able to explain, and which appears, at least mainly, to be an astral action. The evolution of the average azimuth of the pendulum and of the amplitudes of the 24 h and 24 h 50 min components can be decomposed into a component associated with the annual revolution of the Earth around the Sun, and a multi-annual component, whose harmonic 1 has a period which was estimated to 5.74 years. An action of Jupiter is an excellent candidate to explain a large part of the multi-annual action: everything happens as if there were an important action of the modulus of its declination on the multi-annual component, and an important daily action of its hour angle on the azimuth of the pendulum. We cannot exclude an action of the solar cycle, whose period was then about 11 years. The main results were obtained by Allais himself, but this was only published in his book “The Anisotropy of Space”, and remained very little known. Starting from the raw data of Allais, the author of this article found them again, and completed them on certain points.

Correction of dynamic Brazilian disc tensile strength of rocks under preloading conditions considering the overload phenomenon and invoking the Griffith criterion

Dynamic tensile failure is a common phenomenon in deep rock practices,and thus accurately evaluating the dynamic tensile responses of rocks under triaxial pressures is of great significance.The Brazilian disc(BD)test is the suggested method by the International Society for Rock Mechanics and Rock Engineering(ISRM)for measuring both the static and dynamic tensile strengths of rock-like materials.However,due to the overload phenomenon and the complex preloading conditions,the dynamic tensile strengths of rocks measured by the BD tests tend to be overestimated.To address this issue,the dynamic BD tensile strength(BTS)of Fangshan marble(FM)under different preloading conditions were measured through a triaxial split Hopkinson pressure bar(SHPB).The fracture onset in BD specimen was captured through a strain gage around the disc center.The discrepancy between the traditional tensile strength(TTS,determined by the peak load P_(f) of the BD specimen)and the nominal tensile strength(NTS,obtained from the load P_(i) when the diametral fracture commences in the tested BD specimen)was applied to quantitatively evaluating the overload phenomenon.The Griffith criterion was used to rectify the calculation of the tensile stress at the disc center under triaxial stress states.The results demonstrate that the overload ratio(s)increases with the loading rate(σ)and decreases with the hydrostatic pressure(σ_(s)).The TTS corrected by the Griffith criterion is independent of theσ_(s)due to the overload phenomenon,while the NTS corrected by the Griffith criterion is sensitive to both the andσ.Therefore,it is essential to modify the tensile stress in dynamic confined BD tests using both the overload correction and the Griffith criterion rectification to obtain the accurate dynamic BTS of rocks.

Medical and interventional therapy of Kasabach-Merritt phenomenon associated with Kaposiform hemangioendothelioma:A case report

An infant with Kasabach-Merritt Phenomenon(KMP)presented with a giant subcutaneous mass in the right lower limb,severe hypofibrinogenemia,and thrombocytopenia.Glucocorticoids,along with supportive treatments including transfusion of blood products and clotting factors,were administered to reverse fatal disseminated intravascular coagulation and acute hemolysis.The glucocorticoid dose was tapered slowly,and sirolimus was added to treat the hemangiomas.The patient subsequently underwent interventional therapy.After 6 months of medical and interventional therapy,the patient was doing well with a normal platelet count,the tumor volume was markedly reduced,and the primary cutaneous lesion became pale pink.Currently,the patient remains on sirolimus,and no recurrence of thrombocytopenia or further growth of the mass was observed after six months of follow-up.

The Extended Non-Elementary Amplitude Functions as Solutions to the Damped Pendulum Equation, the Van der Pol Equation, the Damped Duffing Equation, the Lienard Equation and the Lorenz Equations

In this paper, we define some non-elementary amplitude functions that are giving solutions to some well-known second-order nonlinear ODEs and the Lorenz equations, but not the chaos case. We are giving the solutions a name, a symbol and putting them into a group of functions and into the context of other functions. These solutions are equal to the amplitude, or upper limit of integration in a non-elementary integral that can be arbitrary. In order to define solutions to some short second-order nonlinear ODEs, we will make an extension to the general amplitude function. The only disadvantage is that the first derivative to these solutions contains an integral that disappear at the second derivation. We will also do a second extension: the two-integral amplitude function. With this extension we have the solution to a system of ODEs having a very strange behavior. Using the extended amplitude functions, we can define solutions to many short second-order nonlinear ODEs.

Anesthetic management of a patient with preoperative R-on-T phenomenon undergoing laparoscopic-assisted sigmoid colon resection:A case report

BACKGROUND The R-on-T phenomenon is a malignant arrhythmia associated with potentially catastrophic consequences.It may initiate ventricular tachycardia or ventricular fibrillation,which can result in syncope or sudden cardiac death.This manifestation poses a great challenge for anesthesiologists.However,it is rarely encountered in the perioperative setting.CASE SUMMARY We herein present a case in which the R-on-T phenomenon was incidentally revealed by 24-h Holter monitoring in a patient diagnosed with sigmoid colon cancer.Careful evaluation and treatment with mexiletine were carried out preoperatively under consultation with a cardiovascular specialist,and surgery was uneventfully performed under general anesthesia after thorough preparation.CONCLUSION Physicians should be vigilant about this infrequent but potentially fatal arrhythmia.Our experience suggests that the anesthetic process can be greatly optimized with careful preparation.

Project-Based Teaching in Control Theory Education Based on V-REP: A Cart Inverted Pendulum Case

This paper provides a teaching concept for control theory education based on Virtual Robot Experimentation Platform(V-REP).A cart inverted pendulum virtual physical model is developed on V-REP.Students must analyze,design,and implement a suitable controller for the cart inverted pendulum system using their knowledge of the control theory.Different from traditional experiment and numerical simulation,virtual experiment is safe and less constrained.Moreover,the experiment results are more intuitive and obvious.This study can improve students’interest in learning the control theory and help students understand the relevant content better.

一种摆式谐振加速度计的微杠杆结构设计与分析

为提升摆式谐振式加速度计性能,设计了一种将质量块与微杠杆结构一体化的摆式微杠杆结构,实现惯性力的敏感与放大,提升结构的鲁棒性。首先建立了微杠杆结构力学模型,并进行了关键参数计算。其次,根据微杠杆结构放大倍数影响机理,分析了质量块、支撑梁及微杠杆结构尺寸参数对放大倍数的影响;理论分析与有限元仿真结果均表明,支点梁与输出梁的宽度应作为该类微杠杆的关键优化参数。最后,根据上述结论对现有结构尺寸进行优化,优化后的微杠杆放大倍数为15.68,系统放大倍数为12.88,标度因数为70.52 Hz/g,较优化前分别提升了36.94%、36.87%和36.88%,验证了优化方法的有效性。

基于LQR对直线倒立摆的稳摆控制研究及实现

针对倒立摆的稳摆控制问题,研究设计了一个LQR控制器。首先,考虑摆杆摆动的阻力矩,采用牛顿力学分析方法推导出直线倒立摆的数学模型,建立了其线性状态空间模型,并分析了系统的稳定性、能控性与能观性。通过采用仿真试凑确定加权矩阵Q、R,得到状态反馈增益矩阵K,完成LQR控制器的设计。之后,搭建了以开放式运动控制器为核心的倒立摆实验平台,在计算机上开发了实时人机交互程序,在运动控制器里编写了倒立摆控制算法。最后,进行了仿真与实测实验,验证了所设计的LQR控制器的有效性和可行性。

新型万向球摆式隔震装置的设计与应用

针对浮放物体防震保护的迫切需求,研发了一款基于万向球的摆式隔震装置。首先介绍了它的构造特征与运行原理,并以某陈列佛塔为对象进行方案设计,利用有限元软件模拟万向球与圆盘间的接触关系,评估该装置的承载能力;然后通过试验验证了内部阻尼机构力学模型的准确性,采用时程分析法检验了该装置在8度极罕遇地震作用下的隔震效果,并与传统滑动摩擦摆的减震性能进行了对比。结果表明,该隔震装置不仅结构简单、性能可靠,而且具有摩擦系数低,起滑加速度阈值小,阻尼灵活可调的特点。装置中的点面接触具有一定的承载能力,能够满足设计需求。端部设置黏滞阻尼器的阻尼机构表现出明显的速度相关性,阻尼力会随速度的增大而增大。该装置隔震性能良好,在满足位移限值的情况下达到了设定的隔震目标,而且相比于传统型,在位移和加速度响应均需兼顾的情况下,通过合理调整阻尼机构的性能参数,该装置在各地震工况中能够取得更优的综合隔震效果。

基于遗传模糊PID算法的倒立摆稳摆抑噪抗扰实验与分析

倒立摆稳摆控制原理应用的实际工程需求牵引,使倒立摆成为检验各类控制算法的理想替代实验研究平台。因此,将倒立摆摆杆的姿态稳定控制和抑噪抗扰作为研究内容,以理论分析、编程实现、仿真实验和实物实验验证作为研究手段,聚焦控制器设计的优化。首先,引入模糊控制对PID参数调节进行优化,改固定参数调节为在线参数调节,旨在提高系统的鲁棒性与抗扰性;然后,运用遗传算法的量化因子和比例因子完成调节参数的在线寻优,通过设计适应度函数和选择算子,经过选择、交叉、变异不断演化迭代,最终获取最佳适应度个体、找到最优解,通过仿真验证遗传模糊PID算法突出的抑噪抗扰优势;最后,基于该控制策略进行倒立摆实物实验,验证了其指令跟踪有效性的结论。该研究表明:遗传模糊PID算法具有良好的指令跟踪和抑噪抗扰性能,具有一定的工程应用价值。

水平偏心摆波能装置运动获能特性研究

以水平偏心摆波能装置为对象,通过物理模型试验和数值模拟,对装置在单自由度和多自由度下的运动和获能规律进行研究。不同波周期下,摆体出现小幅振荡、旋转和振荡旋转三种运动状态。研究表明,装置在单自由度下出现对获能不利的“锁停”现象,而多自由度的获能相对较好,平均功率随波浪周期出现两次峰值。第一次峰值对应波周期与能量输出(PTO)阻尼和摆臂长度正相关,峰值与PTO阻尼正相关;第二次峰值及对应波周期与外浮体轴比正相关。

基于负刚度装置的超长联大跨连续梁桥地震反应控制研究

为完善超长联大跨连续梁桥的减、隔震技术,将负刚度装置引入到超长联大跨隔震连续梁桥中组成新型减、隔震系统,并与黏滞阻尼器-摩擦摆支座组合减震系统进行比较。基于CSiBridge软件建立全桥有限元模型,负刚度装置采用弹性多段线模拟,摩擦摆支座采用双线性恢复力模型,黏滞阻尼器采用Maxwell模型,输入3条地震波进行非线性时程分析,考查两种新型减、隔震系统下桥梁结构的地震反应,探究负刚度系统及黏滞阻尼器系统对超长联大跨连续梁桥地震反应的控制效果。研究结果表明:负刚度装置与黏滞阻尼器均可以有效地减小超长联大跨隔震连续梁桥的支座位移。负刚度装置对桥墩内力反应及梁体加速度反应的控制优于黏滞阻尼器。负刚度装置在超长联大跨连续梁桥地震反应控制中有较好的应用前景。

直角凸壁面附近非对称位置的空泡动力学行为实验研究

空化破坏现象在核电厂中广泛存在。为了更深入地揭示空化破坏的机理,本文借助高速摄影实验系统,研究了直角凸壁面附近非对称位置空泡的动力学行为。具体分析了空泡的轮廓变形,形心的移动距离和方向,以及空泡射流的方向随着空泡与壁面相对位置d、h的变化规律。本文主要结论如下:(1)空泡的变形与空泡和固体壁面的相对位置d、h有关。随着空泡与右壁面的距离d的增大,空泡的非对称性越来越弱。随着空泡与上壁面的距离h的增大,在整个空泡的动力学过程中空泡的非球形特征逐渐减弱。(2)在空泡的溃灭和再生长过程中,空泡形心会持续地向左下方移动,且形心向左移动的距离随着d和h的增大而明显减小。(3)当空泡与上壁面的距离h适当时,会产生明显的斜向左下方的射流现象,且射流方向角θ随着d的增大而增大。

circRNA CCND1对人肝癌HepG2细胞增殖、凋亡、侵袭和迁移的影响

目的 探讨circRNA CCND1对人肝癌HepG2细胞增殖、凋亡、侵袭和迁移的影响。方法 采用荧光原位杂交(FISH)实验及实时荧光定量聚合酶链反应(qRT-PCR)检测circRNA CCND1在HepG2细胞及L02细胞中的表达情况;进一步干扰及过表达circRNA CCND1后,通过qRT-PCR检测circRNA CCND1在HepG2细胞中的表达情况,CCK-8法和EDU法检测HepG2细胞增殖情况,流式细胞术检测细胞凋亡、细胞周期,Transwell实验检测细胞侵袭情况,划痕实验检测细胞迁移情况。结果 HepG2细胞circRNA CCND1相对表达量较LO2细胞高(P <0.05)。Si-circRNA CCND1组circRNA CCND1相对表达量较Control组和Si-NC组下降(P <0.05),Oe-circRNA CCND1组较Control组和Oe-NC组升高(P <0.05)。各组细胞培养0、24、48、72和96 h后细胞增殖活性比较,经重复测量设计的方差分析,结果:(1)不同时间点细胞增殖活性比较,差异有统计学意义(P <0.05);(2)各组细胞增殖活性比较,差异有统计学意义(P <0.05);(3)各组细胞增殖活性变化趋势比较,差异有统计学意义(P <0.05)。与Control组及Si-NC组比较,Si-circRNA CCND1组细胞凋亡率升高(P <0.05),G_(0)/G_(1)期比值升高(P <0.05),S及G_(2)/M期比值下降(P <0.05);与Control组及Oe-NC组比较,OecircRNA CCND1组细胞凋亡率下降(P <0.05),G_(0)/G_(1)期比值下降(P <0.05),S及G_(2)/M期比值升高(P <0.05)。Si-circRNA CCND1组细胞侵袭数、细胞迁移数较Control组、Si-NC组少(P <0.05),Oe-circRNA CCND1组较Control组及Oe-NC组多(P <0.05)。结论 circRNA CCND1能够促进人肝癌细胞HepG2细胞增殖、侵袭和迁移,抑制细胞凋亡。