Mass-spring model for elastic wave propagation in multilayered van der Waals metamaterials

Multilayered van der Waals(vdW)materials have attracted increasing interest because of the manipulability of their superior optical,electrical,thermal,and mechanical properties.A mass-spring model(MSM)for elastic wave propagation in multilayered vdW metamaterials is reported in this paper.Molecular dynamics(MD)simulations are adopted to simulate the propagation of elastic waves in multilayered vdW metamaterials.The results show that the graphene/MoS_(2)metamaterials have an elastic wave bandgap in the terahertz range.The MSM for the multilayered vdW metamaterials is proposed,and the numerical simulation results show that this model can well describe the dispersion and transmission characteristics of the multilayered vdW metamaterials.The MSM can predict elastic wave transmission characteristics in multilayered vdW metamaterials stacked with different two-dimensional(2D)materials.The results presented in this paper offer theoretical help for the vibration reduction of multilayered vdW semiconductors.

Dynamic response of a three-beam system with intermediate elastic connections under a moving load/mass-spring

The objective of this research is to study the dynamic response characteristics of a three-beam system with intermediate elastic connections under a moving load/mass-spring.In this study,the finite Sine-Fourier transform was performed for the dynamic partial differential equations of a simply supported three-beam system(SSTBS)under a moving load and a moving mass-spring,respectively.The dynamic partial differential equations were transformed into dynamic ordinary differential equations relative to the time coordinates,and the equations were solved and the displacement Fourier amplitude spectral expressions were obtained.Finally,based on finite Sine-Fourier inverse transform,the expressions for dynamic response of SSTBS under the moving load and moving mass-spring were obtained.The proposed method,along with ANSYS,was used to calculate the dynamic response of the SSTBS under a moving load/mass-spring at different speeds.The results obtained herein were consistent with the ANSYS numerical calculation results,verifying the accuracy of the proposed method.The influence of the load/mass-spring’s moving speed on the dynamic deflections of SSTBS were analyzed.SSTBS has several critical speeds under a moving load/mass-spring.The vertical acceleration incurred by a change in the vertical speed of SSTBS due to the movement of mass-spring and the centrifugal acceleration produced by the movement of massspring on the vertical curve generated by SSTBS vibration could not be neglected.

Dynamic Behavior and Deformation Analysis of the Fish Cage System Using Mass-Spring Model

Fish cage systems are influenced by various oceanic conditions, and the movements and deformation of the system by the external forces can affect the safety of the system itself, as well as the species of fish being cultivated. Structural durability of the system against environmental factors has been major concern for the marine aquaculture system. In this research, a mathematical model and a simulation method were presented for analyzing the performance of the large-scale fish cage system influenced by current and waves. The cage system consisted of netting, mooring ropes, floats, sinkers and floating collar. All the elements were modeled by use of the mass-spring model. The structures were divided into finite elements and mass points were placed at the mid-point of each element, and mass points were connected by springs without mass. Each mass point was applied to external and internal forces, and total force was calculated in every integration step. The computation method was applied to the dynamic simulation of the actual fish cage systems rigged with synthetic fiber and copper wire simultaneously influenced by current and waves. Here, we also tried to find a relevant ratio between buoyancy and sinking force of the fish cages. The simulation results provide improved understanding of the behavior of the structure and valuable information concerning optimum ratio of the buoyancy to sinking force according to current speeds.

A Three-Stage Cutting Simulation System Based on Mass-Spring Model

The cutting simulation of soft tissue is important in virtual surgery.It includes three major challenges in computation:Soft tissue simulation,collision detection,and handling,as well as soft tissue models.In order to address the earlier challenges,we propose a virtual cutting system based on the mass-spring model.In this system,MSM is utilized to simulate the soft tissue model.Residual stress is introduced to the model for simulating the shrinking effect of soft tissue in cutting.Second,a cylinder-based collision detection method is used to supervise the collision between surgical tools and soft tissue.Third,we simulate the cutting operation with a three-stage cutting method with swept volume,B´ezier curve,and an algorithm named shortest distance nodes matching method.In order to verify the system performance,we carry out three validation experiments on the proposed system:Cutting accuracy experiment,collision detection validation,and practical cutting evaluation.Experiments indicate that our system can well perform the shrinking effect of soft tissue in cutting.The system has fast and accurate collision detection.Moreover,the system can reconstruct smooth incisions vividly.

A Soft Tissue Acupuncture Model Based on Mass-Spring Force Ne

In the simulation of acupuncture manipulation,it is necessary to accurately capture the information of acupuncture points and particles around them.Therefore,a soft tissue modeling method that can accurately track model particles is needed.In this paper,a soft tissue acupuncture model based on the mass-spring force net is designed.MSM is used as the auxiliary model and the SHF model is combined.SHF is used to establish a three-layer soft tissue model of skin,fat,and muscle,and a layer of the MSM based force network is covered on the surface of soft tissue to realize the complementary advantages and disadvantages of spherical harmonic function and MSM.In addition,a springback algorithm is designed to simulate the springback phenomenon of soft tissue skin during acupuncture.The evaluation results show that the soft tissue acupuncture modeling method based on mass-spring force net can effectively simulate the springback phenomenon of soft tissue surface during acupuncture surgery,and has good comprehensive performance in the application of virtual acupuncture surgery simulation.

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.

Mass-Spring-Damper Model with Steady State Parameters for Predicting the Movement of Liquid Column and Temperature Oscillation in Loop Heat Pipe

In order to investigate the mechanism of the temperature oscillation in loop heat pipes,this paper investigated the movement of the phase interface as the changed input power by a mass-spring-damper model.The model was solved with MATLAB and was used to explain the high-frequency and low-amplitude temperature oscillation.Temperature variation with the input power from 20 W to 75 W was investigated based on a LHP prototype in a literature.The model agreed well with the experimental data in the literature.The simulation results suggested that the movement of the liquid column was caused by the fluctuation of pressure difference applied on the liquid column and the stiffness coefficients of the vapor springs increasing with the input power.According to parameter analyses,the temperature oscillation at the outlet of the condenser can be weakened by increasing the mass of the liquid column and keeping the temperature at the outlet of the condenser steady.

纬编双面移圈织物多层弹簧-质点结构模型构建与实现

纬编双面移圈织物工艺结构复杂多变,现有系统在进行设计开发时难以直观地展示出织物的组织结构特点。为实现纬编双面移圈织物的组织结构模拟,本文提出了一种纬编双面移圈织物多层弹簧-质点结构模型。首先建立了成圈、集圈、移圈线圈几何结构模型,接着分析了纬编双面移圈织物结构特征,并在传统弹簧-质点模型的基础上构建了多层弹簧-质点模型,然后采用牛顿第二定律和Velocity-Verlet数值积分法求解了多层弹簧-质点模型的最终位置,最终提出了一种纬编双面移圈织物结构模拟的算法流程。本文建立的多层弹簧-质点结构模型能够反映纬编双面移圈织物的组织结构,具有较好的结构模拟效果。

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

发动机燃油泵附件的管路动力学等效设计及实现

燃油泵附件的管路空间构型复杂,在振动环境试验中直接模拟难以实现。为满足试验要求,采用系统等效缩减/扩展过程(SEREP)方法对管路进行动力学等效设计,选取管路上特定结点为主自由度,并将原管路模型缩减至主自由度模型上,得到缩减质量和刚度矩阵;对子振型矩阵采用SVD分解,使得缩减质量和刚度矩阵进一步简化,得到低阶管路模型的新缩减质量和刚度矩阵参数;提出“质量球—梁弹簧”结构模型,分别用“质量球”和“梁弹簧”来映射缩减的质量和刚度矩阵,进而确定等效设计加工参数;通过实例验证等效设计方法的可行性。结果表明:等效管路与原管路的第一阶频率误差大多在10%以内,满足工程应用要求。

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。

人体分布式动力学模型及其参数识别

建立人体动力学模型获取人体自振频率是土木工程、机械工程、交通工程、航空航天、康复医学等许多领域的共性科学问题,以往研究最常采用的弹簧-质量块-阻尼器集中质量模型,与实际人体质量、刚度沿身高的分布式特性并不相符。本研究提出含有生物自驱力的人体分布参数动力模型,理论上推导了自振频率的表达式,并据此提出了基于步态测试技术的频率识别算法。组织了247名测试者进行步态试验,识别了每位测试者的人体刚度和自振频率,进一步研究了识别参数的概率分布特征,并通过与以往研究结果对比、不同年龄段统计分析等,多角度验证了所提模型的合理性和适用性。

低速冲击下碳纤维面板泡沫夹芯复合材料的损伤分析

主要研究了夹层复合材料受外来载荷作用下的凹痕、横向位移、接触力随时间的变化规律.采用高阶剪切变形理论给出夹层板的广义内力表达式,再由薄板小挠度理论、Hertz接触理论、夹层板平衡方程、Navier法推导出夹层板在外来载荷作用下的动态响应过程.其中,夹层板的接触力和横向位移由两自由度弹簧-质量模型给出.将推导的结果与文献中的理论结果对比,本文计算的误差均不超过6%.并在此基础上比较了不同冲击条件下夹层板的抗冲击性能.

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。

关于魔力弹簧的收缩时间和上端运动问题

针对有关魔力弹簧研究中的几个问题进行探讨和澄清.建立了预收缩力弹簧的模型,推出其形变规律.根据质心运动定理,导出这种弹簧自由下落时,收缩到原长所用的时间、其上端的运动方程和速度公式.研究表明,对于通常演示所用的魔力弹簧,在自由下落时的收缩阶段,其上端不是作匀速直线运动.

基于交织点改进弹簧-质点模型的纬编针织物动态变形模拟

为了对不同线圈单元组成的纬编针织物进行动态变形模拟,从而预设织物结构形态和加速面料设计流程。首先通过建立三维结构模型,获得了线圈中心线型值点和交织点之间的关系,并基于交织点改进传统弹簧-质点模型,得到了与纬编针织物适配度更高的变形模型,然后以交织点为桥梁关联结构模型和变形模型,通过NURBS曲线反算原理绘制线圈中心线路径,采用力学求解方法不断更新织物形态变化,使用计算机工具展现了关联模型的动态模拟过程,并举例展示了不同织物组织的变形模拟效果。模拟效果表明,建立的三维结构模型具有合理性与真实性,改进的弹簧-质点模型具有极高的适配性,基于交织点关联两者为后续模拟提供了支撑,采用NURBS曲线并通过力学求解等方法实现纬编针织物的三维动态模拟具有可行性。

高效展开飞网构型动力学仿真

在空间飞网防护的展开阶段,网面中部质量大导致飞网出现快速回弹现象,严重影响着飞网展开性能。为提升质量非均匀分布的飞网展开率,基于四边形平面飞网,采用弹簧质点法建立飞网展开动力学模型,在不改变飞网总体质量的前提下,通过优化网目结构使飞网质量趋向于均匀化,既不影响展开位移和展开时间,又能够提升飞网展开率。数值仿真对比两种常见不同结构飞网在优化前后的展开性能,结果表明,对于质量非均匀分布的飞网,通过优化拓扑结构和网目结构对其展开率有明显的提升。

圆弧形蜂窝夹芯板在低速冲击下的动力响应研究

为了研究具有负泊松比特性的圆弧形蜂窝夹芯板的动力响应,基于哈密顿原理和一阶剪切变形理论推导了圆弧形蜂窝夹芯板的运动方程,同时建立两自由度的质量-弹簧模型来获得蜂窝夹芯板与冲击器之间的接触力,利用Navier法和Duhamel积分对圆弧形夹芯板的运动方程解析求解。在理论模型有效性验证方面,低速冲击下蜂窝夹芯板中心最大横向位移的理论模型计算结果与ABAQUS有限元仿真结果的最大相对误差为4.9%,同时求得理论模型与已发表文献计算出的接触力最大相对误差为8%,验证了理论模型的有效性。通过理论模型研究了蜂窝胞元参数变化对蜂窝夹芯板动力响应的影响,研究结果表明:随着球形冲击器的冲击速度递增,圆弧形蜂窝夹芯板中心最大横向位移也呈现出递增的规律;圆弧形蜂窝夹芯板的抗冲击特性随着蜂窝胞元半径或角度的增大而减小,当蜂窝胞元半径从5 mm增加至7 mm时,蜂窝夹芯板的抗冲击特性减少40.28%;当蜂窝胞元角度从30°增加至60°时,蜂窝夹芯板的抗冲击特性减少83.64%;蜂窝夹芯板的抗冲击特性随着蜂窝胞元壁厚的增大而增大,当蜂窝胞元壁厚从1 mm增加至3 mm时,蜂窝夹芯板的抗冲击特性提升59.51%。通过减小胞元角度和半径,增加胞元壁厚可以提升圆弧形蜂窝夹芯板的抗冲击特性。

Full Dynamic Model for Liquid Sloshing Simulation in Cylindrical Tank Shape

This study presents a comprehensive full dynamic model designed for simulating liquid sloshing behavior within cylindrical tank structures. The model employs a discretization approach, representing the liquid as a network of interconnected spring-damper-mass systems. Key aspects include the adaptation of liquid discretization techniques to cylindrical lateral cross-sections and the calculation of stiffness and damping coefficients. External forces, simulating various vehicle maneuvers, are also integrated into the model. The resulting system of equations is solved using Maple Software with the Runge-Kutta-Fehlberg method. This model enables accurate prediction of liquid displacement and pressure forces, offering valuable insights for tank design and fluid dynamics applications. Ongoing refinement aims to broaden its applicability across different liquid types and tank geometries.