Bessel Function and Damped Simple Harmonic Motion

A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass respectively) have been used as evidence for this observation. It is shown in this paper how Bessel functions can be approximated by the damped sinusoidal function. The numerical method that is introduced works very well in adiabatic condition (slow change) or in small time (independent variable) intervals. The results are also compared with the Lagrange polynomial.

Crystal-Momentum-Resolved Contributions to Harmonics in Laser-Driven Graphene

We investigate the crystal-momentum-resolved contributions to high-order harmonic generation in laser-driven graphene by semi-conductor Bloch equations in the velocity gauge.It is shown that each harmonic is generated by electrons with the specific initial crystal momentum.The higher harmonics are primarily contributed by the electrons of larger initial crystal momentum because they possess larger instantaneous energies during the intraband motion.Particularly,we observe circular interference fringes in the crystal-momentum-resolved harmonics spectrum,which result from the inter-cycle interference of harmonic generation.These circular fringes will disappear if the inter-cycle interference is disrupted by the strong dephasing effect.Our findings can help to better analyze the mechanism of high harmonics in graphene.

Deduction of Market Prices for Futures Derivatives From Projectile Physics With Effects of the Simple Harmonic Oscillations on Equilibrium Price Positions

We investigated the motions associated with prices for futures contracts within financial markets.We aimed to derive the market prices from the physics approach.We used the projectile motion models defined under two distinct conditions(perfect/horizontal and imperfect/drag implication)based on Newton’s and Galileo’s laws of motion.In addition,we applied the simple harmonic oscillatory model to present the movements of prices from the market equilibrium position.Despite that it was more theoretical,we managed to derive the futures price functions and the results showed that futures prices depend largely on market forces of demand and supply and underlying assets price behaviour.Also,we managed to find the terminal prices for the securities given the initial prices,which are a worrying matter to the trading parties.The equilibrium price analysis was done and the simple harmonic model proved to be efficient in such modelling.We managed to identify the price motions to and from the equilibrium point with markets.Results suggested that it is the market frictions(market forces of demand and supply)that propel prices to move.Also,we noted that these forces are responsible for bringing back the prices at equilibrium if the market is left to operate as free.Nevertheless,from the performance comparison of the two models used,results suggested that futures price function from a drag variable is more powerful in modelling the price behaviour for options than the one sorely controlled by market demand and supply forces.And the simple harmonic oscillator model is good at modelling the equilibrium movements of asset prices.Above all,we used the mean absolute deviation(MAD)to validate our futures derivative pricing model.Fortunately,the obtained MAD results supported the efficiency of our model.However,it should not be carelessly taken that the projectile models used are much good at price motions/movements within the market from time to time with a stunted ability to capture in other facts of interest,such as volatility coefficients which pave a research way for other scholars.

Quantization of the 1-D Forced Harmonic Oscillator in the Space (<i>x</i>, <i>v</i>)

The quantization of the forced harmonic oscillator is studied with the quantum variable (x, v∧), with the commutation relation , and using a Schrödinger’s like equation on these variable, and associating a linear operator to a constant of motion K (x, v, t) of the classical system, The comparison with the quantization in the space (x, p) is done with the usual Schrödinger’s equation for the Hamiltonian H(x, p, t), and with the commutation relation . It is found that for the non-resonant case, both forms of quantization bring about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (x, v∧) quantization has fewer oscillations than the (x, p∧) quantization, the average energy of the system is higher in (x, p∧) quantization than on the (x, v∧) quantization, and the Boltzmann-Shannon entropy on the (x, p∧) quantization is higher than on the (x, v∧) quantization.

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.

A STUDY ON THE DYNAMIC RESPONSE OF CAM BEAT-UP MOTIONS FOR RAPIER LOOMS

Based on the requirements of the two-phase rapier loom’s beat-up system characteristics, the dynamic responses of its beat-up system to three different types of cam input motion are studied in this paper. Also, their corresponding analytical comparisons are made. At the end of the paper, the authors put forward a proposal of new type cam beat-up motion for future practice.

Equivalent Response Estimation of Structural Systems Subjected to Long-Period Ground Motion

Long-period ground motion has become an important consideration because of the increasing number of large and long-period structures.Therefore,a thorough investigation on the formation and characteristics of longperiod ground motion is desirable for engineering applications.In this work,an analytical study is performed to examine the effect of several parameters and the combining mode for equivalent harmonic components on the dynamic response of systems.The results of the work show that the harmonic components in equivalent ground motion are evidently influenced by the intensity rise time,duration,phase and combining mode.Moreover,the long-period ground motions are simplified and simulated by separate harmonic components through proper combination.The findings of the work are believed to be useful in the selection of input ground motion in structural seismic analysis.

基于坐标时间序列的地心运动分析与预测

地心运动会影响地球参考框架原点的准确性,是地球参考框架进行非线性维持必须考虑的因素之一,因此提出对地心运动进行多尺度的建模和预测,以实现毫米级地球参考框架的建立和维持。采用网平移法计算的地心运动、全球地球物理流体中心(global geophysical fluids center,GGFC)和国际GNSS服务(international gnss service,IGS)第三次重处理(IGSR03)提供的3组地心运动数据,首先对其一致性和差异进行了分析,然后分别利用谐波模型和Diff-LSTM模型对地心运动进行了长期和短期的建模与预测,结果显示,GGFC地心运动的预测精度优于1.5 mm,而Diff-LSTM模型的地心运动预测结果在短期内优于谐波模型,当预测步长为17时,GGFC和IGSR03的地心运动预测精度均能达到甚至优于1 mm。表明地心运动的预测精度能够满足基于地球质量中心(center of mass of the total earth system,CM)的瞬时地球参考框架的建立与维持。

复合微多普勒信号的时频谐波分析方法

在对复合微动目标的雷达回波进行时频分析时,存在时频曲线能量难以聚焦等问题,影响目标微多普勒特征提取和分析。对此,提出了时频谐波条纹的概念以及相应时频变换方法。基于复合微动包含中心运动分量和高频运动分量的假设,首先利用样条函数拟合中心分量频率曲线,构造时频变换核函数。然后,通过参数化时频变换将时域的复合微多普勒信号转化为时频平面上的谐波条纹。所提方法相比短时傅里叶变换和伪魏格纳分布等经典方法,能够明显改善复合微动目标雷达回波时频变换的能量聚集性与杂散抑制效果,仿真验证了所提方法的有效性和对低信噪比条件的适应性。

基于实时数据采集的摆动力学综合实验

在单摆实验基础上,利用转动传感器设计了摆运动的综合实验。准确测量摆动过程中摆角、摆动角速度随时间变化状态,研究了小角度摆动情况下摆球的实时运动状态,验证了单摆小角度摆动的简谐运动,并通过数据拟合准确测定本地重力加速度为9.77 m/s^(2),百分误差仅为0.22%;同时,研究了大角度摆动时摆球的欠阻尼运动,并测定了摆动过程的空气阻尼系数为0.00224 s^(-1)。该方案通过瞬时量的测量实现了多个动力学知识点的探究,能够有效促进学生对相关知识的理解,激发学生探究运动过程中物理量变化规律的热情。

混合式三稳态压电能量俘获器动力性能分析

为了提高压电能量俘获器在低强度外界激励下的俘能表现,基于三稳态压电悬臂梁能量俘获器模型,在U形框架和基底之间以及压电悬臂梁固定端与U形框架之间分别装置一个弹性放大器,提出一种混合式三稳态压电能量俘获器(TPEH+DEM)模型。基于Hamilton原理建立了TPEH+DEM系统的非线性力电耦合运动方程,并利用谐波平衡法分析了弹性放大器的质量和弹簧刚度、磁铁之间相对距离、负载电阻等对TPEH+DEM系统能量收集水平的影响。结果表明:在一定的外界激励频率范围内,TPEH+DEM系统的响应输出功率存在两个峰值,合理调节弹性放大器的质量和刚度能使系统在较低的外界激励强度下进入阱间运动,产生很高的输出功率。相比于仅带有弹性基底的传统三稳态压电能量俘获器,TPEH+DEM模型在低频外界激励下具有更好的俘能表现。

特殊长周期地震动的参数特征研究

近断层脉冲型地震动和远场软土层场地类谐和地震动是两类特殊的长周期地震动,当前的规范均很少对这两类地震作用进行具体的规定。研究了近断层脉冲型和远场类谐和地震动的幅值、幅值比(V/A,D/V)、傅里叶幅值谱和反应谱的差别,分析了相位角和作用循环周期数对简单脉冲的影响,并用于解释两类特殊地震动的工程特征。以集集地震动为数据基础,分析了两类长周期地震动的傅里叶谱和反应谱特征;将平均加速度和位移规准反应谱分别与规范设计谱进行了比较。建议设计谱在长周期段考虑近断层作用和软土场地面波效应的影响。

有界噪声激励下单摆-谐振子系统的混沌运动

研究了具有同宿轨道和周期轨道的可积单摆-谐振子系统在弱Hamilton摄动(即弱耦合摄动)和弱非Hamilton摄动(即阻尼和有界噪声微扰)下的混沌运动.用Melnikov方程预测Hamilton系统中可能存在混沌运动的参数域,并用Poincare截面验证解析结果.用数值方法计算了有阻尼与有界噪声激励下系统的最大Lyapunov指数和Poincare截面,结果表明有界噪声在频率上的扩散减小了引发系统产生混沌运动的效应.

基于分量分离方法的地震动反应谱

地震动反应谱统计分析中存在的离散性一直是影响设计谱精确估计的重要因素.地震动加速度反应谱离散性偏大的区段主要集中于长周期部分.为了进一步研究地震动反应谱及其长周期段的特征,建立了一个综合强地震动数据库,考虑地震动反应谱的特征将强震记录分为普通型和低频型2类,采用数字滤波方法将低频型地震动中的长周期分量分离,引入了一种2阶段平稳简谐地震动模型用于等效所分离的低频分量.结果表明:滤波后的低频型地震动与普通型地震动反应谱仍有明显差别;低频型地震动与分离后得到的低频分量以及高、中频分量参数间存在一定的相关性;指出普通型地震动与低频型地震动的设计谱须分别单独标定,其中普通型地震动设计谱采用平均谱标定,低频型地震动设计谱可以在普通型地震动设计谱标定方法的基础上对长周期段进行修正得到.该研究为地震动反应谱特征及规律的认识提供了新的方法,为设计谱的精确标定提供了参考和依据.

考虑谐波传动滞后的柔性空间机械臂运动精度

空间机械臂是完成释放、回收卫星以及空间站在轨装配、维修等多种任务的航天器重要维护工具,其末端执行器运动轨迹的精度优劣直接关系到航天工作任务的成败。现有空间机械臂多采用谐波传动作为减速机构,该减速机构会产生运动滞后效应。结合谐波减速器传动滞后模型,基于Rayleigh-Ritz法给出考虑臂杆柔性与谐波传动运动滞后的动力学方程。提出描述输出误差的精度指标,研究臂杆刚度与滞后相位角对输出精度特性的影响,得到了对空间机械臂工程设计有一定参考意义的结果。

凸轮 CAD 中简谐梯形运动规律的研究及应用

简谐梯形运动规律，是凸轮轮廓线设计中常用的运动规律。是将简谐函数与梯形运动规律组合起来形成的一类运动特性优良的运动规律。本文对这一类运动规律在凸轮ＣＡＤ中的应用进行了研究，对原有运动通式中存在的问题进行了改进，用ＶｉｓｕａｌＣ＋＋开发了这一运动规律的通用运算程序，为开发凸轮ＣＡＤ、ＣＡＭ、ＣＡＴ奠定了基础。

内河船舶电力推进系统设计

为研发具有自主知识产权的船舶电力推进产品,根据电力推进系统的特性,在对推进电机运动控制、推进系统运行状态控制和船舶电网谐波治理进行研究的基础上,设计内河船舶电力推进系统.船舶的实际运行验证设计方案的正确性.

科里奥利质量流量计在线连续测量流体密度的理论分析

科里奥利质量流量计是一种直接测量流体质量流量的仪表 ,同时可在线检测流体密度 ,出于对其传感器结构优化设计的目的 ,建立了振动微分方程 ,其解可给出流体密度在线检测的依据 ,并给出密度与温度的对应关系 ,得出双 U型管谐振频率的推导结果 ,并进行具体计算的验证。

简谐波地震动反应谱研究

简谐荷载作用下单自由度体系的动力反应是典型的结构动力学问题,也是地震工程中研究结构地震反应的基础。对简谐地震动反应谱特性的研究有利于认识地震动、尤其是近场地震动的特性以及它对结构地震反应的影响。基于结构动力学的基本理论,推导了简谐地震动作用下,单自由度体系的理论解、瞬态解和稳态解。分析了简谐地震动全解反应谱、稳态解反应谱和瞬态解反应谱的特性并讨论了它们之间的关系。研究结果表明:在简谐地面加速度作用下,高频地震动也可以引起长周期结构产生很大的位移反应,且最大位移反应出现在结构的瞬态自由振动阶段。这不仅揭示了近场地震动对结构反应的重要影响,也从另一个侧面揭示了近场地震动的潜在破坏作用,而且提出了在近场情况下结构抗震不可忽略结构的瞬态自由振动影响的观点。

打纬共轭凸轮机构的设计

提出一种适合打纬共轭凸轮机构的新型运动规律 ,建立打纬共轭凸轮廓线的坐标方程 .利用三角函数运动规律的组合和主、回凸轮廓线的共轭特性 ,探讨打纬共轭凸轮机构的设计 .推导出适合打纬共轭凸轮机构的双简谐运动规律和共轭凸轮廓线的坐标方程 .研究表明 ,双简谐运动规律可用于设计打纬共轭凸轮机构 。