RLC电路弹簧耦合系统的级数解

为了研究RLC电路弹簧耦合系统的非线性振动，用统一的能量法考虑机电耦合系统的电场能、磁场能和机械能，应用拉格朗日-麦克斯韦方程建立起一个受到简谐激励的RLC电路弹簧耦合系统的数学模型，该机电耦合系统具有平方非线性。根据线性振动理论对系统运动微分方程组进行分析，得到了一个受简谐激励的Mathieu方程，通过积分变换，得到了Mathieu方程的级数形式解。分别用龙格库塔法和级数法计算了在无外激励的情况下，有阻尼和无阻尼时系统分别对应的时间响应，通过Matlab软件进行模拟分析，发现二者得到的响应曲线吻合，证明了级数法对分析类似系统是个很有效的手段。     

Adams法求解涡激振动压电能量获取问题

研究流-机-电三相耦合圆柱涡激振动能量获取问题,使用矩阵法求解机电耦合频率和机电耦合阻尼,应用Fluent软件求解机电耦合振动方程得到圆柱振动响应,使用Adams法求解机电耦合输出电压和机电耦合输出功率。研究外接载荷对机电耦合输出电压、机电耦合输出功率的影响,以及尾流干涉下,机电耦合输出电压随外接载荷变化的情况。结果表明:Adams法求解机电耦合输出电压的频率范围更加广泛,机电耦合输出电压与外接载荷成正比,机电耦合输出功率在外接负载R=10~6Ω达到了最大值;在约化速度Ur=5时,尾流干涉下的机电耦合阻尼表现出对下游圆柱振幅起明显的抑制作用。     

非线性电磁振动能量采集的辨识研究

提出一种单自由度电磁振动能量采集器的系统辨识方法——电压映射方法,该方法基于恢复力曲面法的辨识思想,在系统恢复力函数、电磁机电耦合函数和等效电感函数的具体形式未知的情况下,能准确辨识出具有强非线性的恢复力函数、电磁机电耦合函数和等效电感函数.利用两个典型的非线性模型算例进行验证:一是含有非线性弹性恢复力的电磁振动能量采...     

横向磁场中对边简支对边固支矩形薄板的分岔与混沌

研究了力磁耦合作用下对边简支对边固支矩形薄板的分岔与混沌问题。在给出横向稳恒磁场和载荷共同作用下的矩形薄板的非线性磁弹性耦合运动学方程的基础上,得到了对边简支对边固支的矩形薄板的磁弹性振动方程。用Melnikov函数法给出该系统发生混沌运动的条件,并用数值方法求解该系统振动方程。通过具体算例,得到了系统的分岔图、Lyapunov指数图,并给出了相应位移波形图、相平面轨迹图、庞伽莱截面图。分析了电磁场参量及外载荷对系统运动状态的影响。     

智能桁架机电耦合动力分析与振动控制

把作为主动杆全部或部分的压电陶瓷作动／检测元件视为多层迭合体，从机电耦合弹性理论出发，利用Ｈａｍｉｌｔｏｎ原理建立了智能桁架结构机电耦合有限元动力分析模型，可用于机械／电载荷共同作用下的结构静／动力分析和振动控制系统设计。同时给出了元件的作动／检测方程，并以压电作动元件输入电压作为控制量，利用结构状态空间方程进行振动系统最优反馈控制律设计。算例表明该分析方法是可行的。     

智能桁架机电偶合动力分析与振动控制

把作为主动杆全部或部分的压电陶瓷作动／检测元件视为多层迭合体，从机电耦合弹性理论出发，利用Ｈａｍｉｌｔｏｎ原理建立了智能桁架机构机电耦合有限元动力分析模型，可用于机械／电载荷共同作用下的结构静／动力分析和振动控制系统设计。同时给出了元件的作动／检测方程，并以压电作动元件输入电压作为控制量，利用结构状态空间方程进行振动系统最优反馈控制律设计。算例表明该分析方法最可行的。     

刚柔耦合系统动力学建模新方法

作高速大范围运动的机械系统，由于运动和变形的耦合将产生动力刚化现象，传统动力学理论难以计及这种影响。通过Kane方程在保证变形广义坐标完全精确到一阶项的前提下建立了系统一阶完备动力学方程。通过与传统动力学方程的对比分析，揭示了传统建模方法不仅遗失了动力刚度项。同时遗失了某些刚柔耦合惯性项。本文提出了一种通过对传统非完备动力学方程的修正以获得一阶完备动力学方程的新方法。     

广义函数论在厚板动力分析中的应用

本文运用广义函数论处理δ函数的导数,对集中力作用下的厚板进行动力分析。基本方程采用由本文作者推演得到的改进的Donnell厚板振动方程。用样条配点法求解广义坐标,对集中力作用下的厚板弹性动力响应给出解的一般表达式。文中以能形板为例给出了数值结果,对按改进理论和经典理论所预示的结果进行了比较。本文方法可以用于厚板物理非线性和几何非线性动力分析和厚板与连续介质共同作用的场合,文中给出了有关表达式。     

基于SOLID5单元压电材料的数学模型研究

压电材料的有限元分析过程中需要根据其特性建立起相应的数学模型,根据出压电体的各种特性,在ANSYS软件平台上将采用SOLID5单元进行分析。在分析SOLID5后通过计算获得个点形函数继而求出单元的位移和电压,从而相应推导出应变以及电场强度。最后基于压电材料的机电耦合本构关系建立有限元分析的方程,可以得出系统的固有频率和模态振型和没有压电机电耦合效应时的一样。     

混合动力挖掘机轴系扭振的主动控制仿真

为研究混合动力挖掘机轴系扭振并尽可能消除其影响,分析动力轴系扭振的原因,提出对轴系主动控制的方法。在三自由度系统Lagrange函数和耗散函数中引入电动机的气隙磁场能,得到动力轴系和异步电机的机电耦合数学模型,建立基于AME Sim-Simulink的多动力源复杂轴系扭振仿真模型;以电机转矩为控制变量,以液压泵负载为干扰量,以扭振最小为控制目标,应用2阶模糊PID控制分别对阶跃负载和6 t混合动力挖掘机实际工况负载进行仿真计算。通过分别对比控制前后轴系转动速度、扭振情况以及扭转角大小,可以看到采用主动控制方式可以使轴系转动速度密切跟踪给定转速曲线,同时显著减小轴系扭转振动,降低扭转角的波动,快速达到稳定状态,结果表明通过模糊PID进行主动控制可以有效地改善混合动力系统轴系扭振情况。     

基于等效线性化方法的非线性振动能量采集器功率分析

输出功率分析是振动能量采集器结构设计、参数选择的重要依据.有鉴于传统功率分析方法比较复杂,以一类电磁式振动能量采集器为对象,提出了一种新的非线性振动能量采集器功率分析方法,其核心是将非线性振动方程进行等效线性化处理,并借助传递函数开展功率优化分析.首先,考虑非线性磁力以及基尔霍夫电流定律,建立了通用化的采集器1.5自由...     

直梁结构光栅光调制器的机电特性分析与实验

介绍了直梁光栅光调制器的结构和原理,建立了器件的机电模型．利用能量法和卡式第二定理分析并得到器件的弹性系数;通过静电力与机械回复力的平衡,得到器件的驱动电压．结合器件的实际参数值,计算得到器件的工作电压为10．71V,吸合电压为11．46V．实验测得器件的实际工作电压为10．5V,吸合电压为12．2V,实验结果与理论分析基本一致．在1kHz脉冲电压的驱动下,器件响应的上升时间和下降时间分别为46．59μs和44．77μs;器件的响应频率约为5kHz．结果表明,加工的直梁光栅光调制器具有较低的驱动电压和较高的响应频率,能够满足微投影显示的要求．     

Probabilistic solution of non-linear vibration energy harvesters driven by Poisson impulses

This paper develops a new solution procedure for obtaining the joint probability density function (PDF) of non-linear energy harvesters under Poisson impulses using the state-space-split method and the exponential-polynomial closure method. In the beginning, a generic electromechanical energy harvester is introduced and its governing equations are transformed into non-dimensional ones. According to the non-dimensional governing equations, a Duffing-type oscillator with piezoelectric conversion mechanism is further considered in this study. The proposed solution procedure includes three steps. First the joint PDF of this system is governed by the generalized Fokker-Plank-Kolmogorov (FPK) equation. The state-space-split method is used to reduce this generalized FPK equation to a low-dimensional one only about displacement and velocity. After that, the exponential-polynomial closure method is further adopted to solve the reduced FPK equation. Finally, the joint PDF of displacement, velocity and voltage can be approximated by the product of the obtained PDF and the conditional Gaussian PDF of voltage. Four cases are investigated considering the effects of non-linearity coefficient, impulse arrival rate and a bistable Duffing oscillator. The PDFs of these state variables and the harvested power are compared with the simulation results, respectively. The good agreement between the obtained PDFs and the simulated results is achieved. Compared with the results of the equivalent linearization method, the strong non-linearity in displacement and lower impulse rate lead the tail PDF of the harvested power to exhibiting hardening and softening behaviors, respectively. For the bistable Duffing oscillator, the PDF of the harvested power differs significantly from the result of the equivalent linearization method in the tail region.     

Calculation and measurement of electromechanical coupling coefficient of capacitive micromachined ultrasonic transducers

The electromechanical coupling coefficient is an important figure of merit of ultrasonic transducers. The transducer bandwidth is determined by the electromechanical coupling efficiency. The coupling coefficient is, by definition, the ratio of delivered mechanical energy to the stored total energy in the transducer. In this paper, we present the calculation and measurement of coupling coefficient for capacitive micromachined ultrasonic transducers (CMUTs). The finite element method (FEM) is used for our calculations, and the FEM results are compared with the analytical results obtained with parallel plate approximation. The effect of series and parallel capacitances in the CMUT also is investigated. The FEM calculations of the CMUT indicate that the electromechanical coupling coefficient is independent of any series capacitance that may exist in the structure. The series capacitance, however, alters the collapse voltage of the membrane. The parallel parasitic capacitance that may exist in a CMUT or is external to the transducer reduces the coupling coefficient at a given bias voltage. At the collapse, regardless of the parasitics, the coupling coefficient reaches unity. Our experimental measurements confirm a coupling coefficient of 0.85 before collapse, and measurements are in agreement with theory.     

Determining the effective fractal dimension of nanodimensional coatings with the aid of magnetic field

Method of the short-range potential that was originally constructed for a three-dimensional space is generalized to Euclidean spaces of arbitrary (including fractional) dimensions. Based on this method, a transcendental equation is derived for the electron binding energy in a superposition of the field of an n-dimensional δ-well and an external magnetic field. The possibility of experimental determination of the fractal dimension of a nanostructured coating using the character of the dependence of its surface work function on the magnetic field strength measured in an atomic force microscope is considered.     

基于改进Ritz法的耗能减震高层建筑结构地震响应分析

用改进Ritz法计算耗能减震高层建筑结构的地震响应。改进Ritz法采用基于外荷载空间分布的Ritz向量和基于外荷载频率的Ritz向量。其中,基于外荷载空间分布的Ritz向量用Lanczos法形成。基于外荷载频率的Ritz向量则用外荷载主频的平方进行特征值平移后再用Lanczos法形成。文中还给出上述两种Ritz向量的截断标准。之后用改进Ritz法的Ritz向量对结构动力方程进行线性变换。由于耗能减震高层建筑结构的阻尼是非比例阻尼,广义阻尼矩阵是非对角矩阵,所以文中采用拟力实模态法对线性变换后的耦联动力方程进行求解。最后的算例说明该方法用于耗能减震高层建筑结构的地震响应分析是有效可行的。     

直线电机驱动的微小型活塞压缩机特性分析

讨论了微小型化的直线电机驱动的活塞压缩机特性.运用电磁场有限元方法对直线电动机电磁场模型进行求解,分析了电动机内部的磁场和磁力线分布情况;建立了电动机动子动力学模型和驱动电路模型,得到系统的运行方程组并对其求解,根据计算结果对压缩机的驱动力、活塞行程、绕组电流和频率特性等进行了分析,同时就余隙容积和泄漏对这种微小型活塞压缩机的影响进行了探讨.结果表明直线电机驱动的微小型活塞压缩机在理论上是可行的,有进一步研究、优化的必要.     

Electric Field Gradient Theory with Surface Effect for Nano-Dielectrics

The electric field gradient effect is very strong for nanoscale dielectrics. In addition, neither the surface effect nor electrostatic force can be ignored. In this paper, the electric Gibbs free energy variational principle for nanosized dielectrics is established with the strain/electric field gradient effects, as well as the effects of surface and electrostatic force. As regards the surface effects both the surface stress and surface polarization are considered. From this variational principle, the governing equations and the generalized electromechanical Young-Laplace equations, which take into account the effects of strain/electric field gradient, surface and electrostatic force, are derived. The generalized bulk and surface electrostatic stress are obtained from the variational principle naturally. The form are different from those derived from the flexoelectric theory. Based on the present theory, the size-dependent electromechanical phenomenon in nano-dielectrics can be predicted.