Solution of an inverse problem for“fixed-fixed”and“fixed-free”spring-mass systems

The tridiagonal coefficient matrix for the ＂fixed-fixed＂ spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring constants from the natural frequencies of the ＂fixed-fixed＂ and ＂fixed-fres＂ spring-mass systems. An example was given to illustrate the results.

Chaotic oscillations in a piecewise linear spring-mass system

Chaotic oscillations are useful in assessing the health of a structure. Hence, simple chaotic systems which can easily be realized mechanically or electro-mechanically are highly desired. We study a new pieeewise linear spring-tnass system. The chaotic behaviour in this system is characterized using bifurcation diagrams and the invariant parameters of the dynamics. We also show that there exists a stochastic analogue of this system, which mimics the dynamical features of its deterministic counterpart. This allows a greater flexibility in practical designs as the chaotic oscillations are obtained either deterministically or stochastically. Also, the oscillations are low dimensional, which reduces the computational resources needed for obtaining the invariant parameters of this system.

Free vibrations of beam-mass-spring systems:analytical analysis with numerical confirmation

Free vibrations of a beam-mass-spring system with different boundary conditions are analyzed both analyt- ically and numerically. In the analytical analysis, the system is divided into three subsystems and the effects of the spring and the point mass are considered as internal boundary con- ditions between any two neighboring subsystems. The par- tial differential equations governing the motion of the sub- systems and internal boundary conditions are then solved us- ing the method of separation of variables. In the numerical analysis, the whole system is considered as a single system and the effects of the spring and point mass are introduced using the Dirac delta function. The Galerkin method is then employed to discretize the equation of motion and the result- ing set of ordinary differential equations are solved via eigen- value analysis. Analytical and numerical results are shown to be in very good agreement.

速度滑冰比赛服个性化样板生成方法

速度滑冰比赛服是重要的运动装备,为解决速滑比赛服定制中样板与个性化体型匹配度较差和制版效率低的问题,提出一种基于质点-弹簧系统的样板生成方法。首先,扫描运动员三维体型,根据体型特征和比赛服分割线提取各主要衣片的三维模型网格;基于三维网格建立质点-弹簧模型;同时,对比赛服弹性面料进行多角度拉伸试验测量面料力学属性,以确定质点-弹簧模型的参数;然后,将衣片三维模型向二维平面投影,给定模型参数和约束条件在二维平面内对质点-弹簧模型进行迭代,在内部能量最小化目标约束下模型收敛后,获得的边界形状即认为是该衣片的样板;最后,经过服装CAD样板调整和裁剪缝纫等加工工艺步骤制作比赛服样衣,经运动员试穿评价后微调得到最终的个性化比赛服样板。试验结果表明,生成样板的测量误差在可接受范围以内,运动员主观试穿反馈样衣合体度良好,本文方法能够有效实现速度滑冰比赛服个性化样板生成,从而为速滑比赛服定制制版提供有效的技术支持和实用工具。

浅埋爆炸下考虑乘员安全的防雷底板设计理论模型

浅埋爆炸载荷下,为更好地开展装甲车防雷底板设计,建立了考虑附加质量-弹簧-阻尼系统的均质梁动态响应理论模型,并采用有限元仿真分析进行验证,理论与仿真结果吻合良好。基于所建立理论模型,分别讨论了炸药质量、均质梁屈服强度、弹簧刚度、阻尼系数和边界条件对均质梁中点和质量块峰值位移、速度、加速度的影响。结果表明:随着TNT质量增大和均质梁屈服强度减小,均质梁中点峰值位移、质量块峰值位移、速度、加速度都增大;当弹簧刚度相同时,随着阻尼系数的增加,均质梁中点峰值位移减小,质量块峰值加速度增大;当阻尼系数一定时,弹簧刚度对均质梁中点的峰值位移和质量块峰值加速度影响较小;针对不同弹簧刚度,选择适当的阻尼系数可以降低质量块峰值速度。

机械网络运动方程与构网型VSG惯量阻尼的比较

随着新能源和电力电子设备的广泛应用,新型电力系统面临着多方面的不稳定性挑战。为了克服这些挑战,采用构网型(grid-forming,GFM)控制技术,可以通过电压支撑和主动惯量调节替代同步机,以确保电力系统的稳定性。但构网型变流器自身的惯量阻尼机理尚不明确,其阻尼系数往往被忽略。该文从机械系统的运动方程出发,首先通过推导质量-弹簧系统的运动方程和构网型虚拟同步机控制方程本质上都是二阶微分方程;然后,通过实验仿真验证了机械网络和电气网络的惯量阻尼机理的一致性;最后,通过Matlab/Simulink仿真在IEEE 39节点系统中验证构网型VSG的阻尼系数在维持稳定同步状态中的关键作用。

基于MATLAB的质量-弹簧-阻尼系统3种仿真方法研究

以常见的二阶质量–弹簧–阻尼系统为研究对象,通过分析该系统的物理过程并建立数学模型,首次采用MATLAB软件提供的.m文件、Simulink和Simscape 3种仿真方法完成对应模型的搭建,并在相同物理参数的条件下仿真、分析和比较,验证了针对该系统的MATLAB 3种仿真方法测试结果的一致性,同时介绍了3种方法的各自优势。按照MATLAB软件提供的元件模块化搭建系统,仿真及测试过程简洁、清晰,便于系统集成和拓展,为技术人员使用MATLAB软件在工程仿真与应用中提供了可靠的参考依据。

Static-deformation based fault diagnosis for damping spring of large vibrating screen

Based on the statics theory, a novel and feasible twice-suspended-mass method(TSMM) was proposed to deal with the seldom-studied issue of fault diagnosis for damping springs of large vibrating screen(LVS). With the static balance characteristic of the screen body/surface as well as the deformation compatibility relation of springs considered, static model of the screen surface under a certain load was established to calculate compression deformation of each spring. Accuracy of the model was validated by both an experiment based on the suspended mass method and the properties of the 3D deformation space in a numerical simulation. Furthermore, by adopting the Taylor formula and the control variate method, quantitative relationship between the change of damping spring deformation and the change of spring stiffness, defined as the deformation sensitive coefficient(DSC), was derived mathematically, from which principle of the TSMM for spring fault diagnosis is clarified. In the end, an experiment was carried out and results show that the TSMM is applicable for diagnosing the fault of single spring in a LVS.

A Virtual Puncture Surgery System Based on Multi-Layer Soft Tissue and Force Mesh

Puncture is a common operation in surgery,which involves all kinds of tissue materials with different geometry and mechanical properties.As a new cross-disciplinary research area,Virtual Surgery(VS)makes simulation of soft tissue in puncture operation possible in virtual environment.In this paper,we introduce a VS-based puncture system composed by three-layer soft tissue,simulated with spherical harmonic function(SHF),which is covered with a force mesh,constructed by mass spring model(MSM).The two models are combined together with a parameter of SHF named surface radius,which provides MSM with real-time deformation data needed in force calculation.Meanwhile,force calculation,divided into the surface spring force and the puncture damping force,makes the force presentation better accord to the corresponding tissue characteristics.Moreover,a deformation resumption algorithm is leveraged to simulate the resumption phenomenon of the broken tissue surface.In evaluation experiment,several residents are invited to grades our model along with other four mainstream soft tissue models in terms of 7 different indicators.After the evaluation,the scores are analyzed by a comprehensive weighted grading method.Experiment results show that the proposed model has better performance during puncture operation than other models,and can well simulate surface resumption phenomenon when tissue surface is broken.

On the Dynamics of Transition of a Classical System to Equilibrium State

In this work we consider a spring with one end is fixed and the other is connected to a block of mass M located on a horizontal rough table. The other side of the block is connected to a massless rope that passes over a frictionless pulley at the end of the table and a second block of mass m is hanged at the rope’s other end. For this system, we analyze and discuss its dynamics of motion as function of time when the second block is released. In particular, the displacement of the system at the end of each half-cycle of motion, the total distance, and the work done against friction are derived. An interesting result is obtained for the case when the table is frictionless. It is found that there is still a work done by friction whose magnitude is exactly the same as the stored energy in the spring.

分裂导线防舞器的设计及其抑舞效果分析

为了减小和抑制分裂导线的舞动幅值,防止舞动灾害的发生,提出了一种对称式双质量弹簧减振结构的防舞器.本文阐述了防舞器基本结构和防舞原理,通过对基本参数进行设计,基于ABAQUS软件进行有限元建模,将该防舞器与摆杆-质量-弹簧防舞器和传统双摆防舞器进行模拟对比,分析其抑舞效果,并优化布置方案.结果表明:该防舞器结构简单、易于安装、适用于任意分裂数导线且防舞性能良好;可弥补摆杆-质量-弹簧防舞器对扭转振动抑制的不足;防舞器的防舞效果稳定,对垂直和扭转方向抑舞效果均优于双摆防舞器,虽然风速增大会导致防舞性能降低,但抑舞效果仍能高达75%以上;同时对防舞器布置方案进行改进能有效提升防舞效果并节约成本.

含不确定参数弹簧质量系统振动反问题的区间分析法

将不确定参数用区间向量进行定量化,基于区间数学理论提出一种可以预测弹簧质量系统的弹簧系数和质量所在范围的非概率区间分析方法.与传统的概率分析方法相比,它只需确定不确定参数所在范围的界限,而不需要其它任何概率统计信息.通过数值算例,以MonteCarlo模拟结果作为基础将区间分析方法与概率分析方法进行了比较,显示了不确定参数在小范围内变化时区间分析方法的有效性和数值稳定性.

基于弹簧-质点系统的薄膜结构曲面展开算法

将用三角形描述的空间膜片映射到初始二维膜片上,并使初始二维膜片与被展空间膜片在参数域与空间域具有相同的拓扑结构.描述空间膜片的三角形与描述平面膜片的三角形的边长存在差异,采用单元节点力代替此差异,节点质量由节点周围的膜单元面积确定,得到了描述系统运动的拉格朗日方程.在求解方程时,每个时间段迭代初始速度置为零,计算过程中节点匀速运动,从而有效地避免了振幅过大和发散问题,收敛速度明显加快.平面膜片的局部精度通过弹簧弹性变形系数予以控制,能够满足膜片边界要求.该曲面展开方法具有精度高、计算速度快和易收敛的特点.

基于集中质量法的普通圆锯片及基体开槽圆锯片振动响应分析

针对普通圆锯片及基体开槽圆锯片的振动响应问题,首次引入集中质量法建立了圆锯片无阻尼多自由度弹簧-质量系统模型。将开槽等效为去除槽分布对应区域内的弯曲弹簧,分别构造了普通圆锯片、基体开径向槽以及周向槽三类圆锯片振动系统模型的质量矩阵与刚度矩阵,并进行了简谐激励响应分析。采用振幅强度因子作为衡量锯片振动强度的指标,通过求解获得了振幅强度因子与频率关系的幅频响应特性曲线,将计算结果同有限元法的结果进行对比分析,结果表明：当峰值对应频率在0～750Hz范围内时,二者的一致性较好;当峰值对应频率大于750Hz时,开始出现较大偏差,验证了集中质量法用于计算圆锯片结构低频固有特性的正确性。本文研究结果对于求解存在几何缺陷的连续体弹性薄板的振动响应具有一定的参考价值。

薄膜型声学超材料的低频吸收性能研究

设计一种能够有效吸收低频声波的镶嵌薄膜结构,镶嵌薄膜结构是由若干个质量-弹簧振子系统和带有硬质边框的硅橡胶薄膜构成。当进入镶嵌薄膜结构中的弹性波与质量-弹簧构成的谐振系统发生共振时,就可实现对低频声波起到理想的吸收效果。研究了镶嵌薄膜结构的声学机理,建立一种局域共振形式的胞元模型,探讨了负有效质量的材料属性。利用有限元仿真模拟,得到了子结构胞元和镶嵌薄膜结构的振动形态,通过谐振单元的理论形式与结构胞元的振动形态进行比较,得到二者吸收机理相同的结论,进一步证明了薄膜对集中质量的牵引力作用与入射声波激励作用的等效关系。同时,对两种不同刚度的薄膜材料进行仿真分析,比较振动形态对声波吸收形式的差异。分别对两种刚度不同的薄膜的声学超材料进行试验研究,同时,研究了结构胞元与周期结构的声学特性关系。结果表明:质量-弹簧系统对低频声波的吸收有很大影响。

充气薄膜结构的SMS展开分析方法

为有效分析充气薄膜结构的展开,提出基于能量原理分析充气薄膜结构展开的SMS方法,即弹簧-质点系统方法.对卷曲折叠充气直管采用SMS方法进行数值模拟,并与实验结果进行对比分析,发现其结果吻合良好,验证了这种方法的正确性.运用SMS方法分析不同充气速率对卷曲折叠充气管展开过程的影响以及充气圆环管和充气膜面的展开过程及动力性能.与传统的有限元方法比较,SMS方法建模简单,思路清晰,数值稳定性好.

应用弹簧-质点模型的双贾卡提花织物形变仿真

为改善双贾卡提花经编织物的结构形变仿真效果,在分析双贾卡织物线圈结构形变影响因素的基础上,建立了成圈型、压纱型和衬纬型线圈几何结构模型;在传统的弹簧质点模型基础上进行改进,取线圈根部作为质点,线圈之间的延展线为弹簧,根据双贾卡提花特点,针对压纱贾卡与衬纬贾卡设定虚拟质点,建立双套弹簧系统;根据牛顿第二定律和显式中点法,计算质点在二维平面的运动形态,从而确定线圈的偏移方向和偏移量;利用建立的弹簧-质点模型与力学分析模型在VC++语言下实现了双贾卡提花经编织物的二维静态仿真,通过实际样例与对应仿真效果对比,验证仿真方法。

双弹簧振子的振动分析

利用分析力学中的拉格朗日方程,推导出了双弹簧振子在小振幅情形下的非线性微分方程,并采用同伦摄动法解出了方程的一阶近似解及一阶近似周期,为工程应用提供了理论基础。

可展开薄膜结构折叠方式和展开过程研究

薄膜材料广泛运用于太空可展开航天器,薄膜的折叠和展开分析是其中的关键技术。从树叶的仿生学出发,提出薄膜结构的几种折叠方式。建立弹簧-质点系统描述薄膜材料,模拟薄膜结构的展开过程。薄膜展开过程中薄膜不可避免地发生自身的接触碰撞,提出了自接触对的判别准则,采用罚函数法有效地解决薄膜自接触问题。分析了三种折叠方式的薄膜的展开过程,并进行比较,叶外折叠方式和Miura折叠法比较适合平面薄膜的折叠。

爆炸冲击震动下双层线性隔震体系的隔震性能

根据振动剂量值 (VDV)隔震标准 ,采用 Runge- Kutta法研究了双层线性隔震系统在核爆炸产生的两类冲击震动作用下的隔震性能。分析结果表明 ,当下层质量弹簧系统的自振频率约为 1Hz时 ,双层隔震系统具有较好隔震效果 ;当下层质量弹簧系统的自振频率为 3Hz时 ,双层隔震系统只在部分参数取值上具有隔震性能。