调制气流声源振动系统有限元分析与实验

用动力有限元方法对调制气流声源振动系统进行了数值模拟,基于电涡流传感器构建了实验系统进行了相关验证,并对产生低频强声和远距离语音广播条件下橡胶弹性元件特性进行了探讨。结果表明,M－R橡胶本构模型描述的振动系统与实验保持了较好的一致性,证明该本构模型描述初始小变形条件下的橡胶振动特性是有效的;理想情况下,动圈－橡胶结构的振动系统为单自由度振动系统,低频振动时,振动位移失真以橡胶等效刚度非线性引起的三次谐波失真为主,随着频率升高至共振频率附近,磁场不均匀等因素引起的二次谐波失真逐渐增大并成为主要失真分量;音圈偏置是导致系统出现多阶振动模态的主要诱因之一。     

Boundary element analysis of 3-D magnetostatic problems usingscalar potentials

A boundary element formulation for 3-D nonlinear magnetostatic field problems using the total scalar potential and its normal derivative as unknowns is described. The boundary integral equation is derived from a differential equation for the total scalar potential where a nonlinear operator term can be separated from a linear term. The nonlinear term leads to a volume integral which can be treated as a known forcing function within an iterative solution process. An additional forcing term results from the magnetic excitation coil system. It is shown that the line integral of the magnetic source field which can be defined outside of the current-carrying regions as a gradient of a scalar potential acts as an excitation term. The proposed method is applied to a test problem where an iron cube immersed in the magnetic field of a cylindrical coil is investigated. The numerical results for different saturation stages are compared with finite element method (FEM) calculations. The comparison with FEM calculations shows a good agreement only in highly saturated iron parts     

新型纳米级微位移致动器的设计

磁致伸缩型微位移致动器通常采用多晶或孪晶结构材料作为驱动单元 ,由于晶界和孪晶界对畴壁的移动具有阻碍作用 ,其低场下的位移输出较小 ,调控精度受到较大影响。采用Tb Dy Fe单晶材料可以有效解决这一问题 ,本文介绍了采用这一单晶材料设计的新型高精度微位移致动器以及致动器的结构和数控电源     

Designing transcranial magnetic stimulation systems

We explain the process of designing optimized transcranial magnetic stimulation systems and outline a method for identifying optimal system parameters such as the number of turns, the capacitor size, the working voltage, and the size of the stimulation coil. The method combines field analysis, linear and nonlinear circuit analysis, and neural strength-duration response parameters. The method uses boundary-element analysis to predict the electric field as a function of depth, frequency, current, and excitation coil size. It then uses the field analysis to determine the inductance as a function of size and, in general, current when a saturable core is used. Circuit analysis allows these electric field computations to be indexed against system parameters, and optimized for total system energy and stimulation coil size. System optimizations depend on desired stimulation depth. A distinguishing feature of the method is that it inherently treats excitation frequency as an unknown to be determined from optimization.     

超磁致伸缩棒磁场强度建模及线圈优化分析

超磁致伸缩棒上的磁场强度对超磁致伸缩致动器(GMA)至关重要,因其幅值和上升、下降时间直接影响致动器的输出力和响应时间.建立电压到磁场强度的模型,并提出较合理的线圈优化方案.将线圈充、放电过程简化为一阶RL线性电路的暂态过程,计算得到线圈电流,并根据线圈电流建立超磁致伸缩棒上的磁场强度模型.由模型可知,致动器尺寸有限制时,棒上磁场强度的优化应主要考虑线圈匝数;通过分析线圈匝数对磁场强度稳态值、上升时间和下降时间的影响确定匝数的取值范围.向线圈施加不同频率和幅值的方波电压信号,得到的模型曲线与测得的实验结果相吻合,从而验证了模型的正确性.     

结构密集模态二分之一阶亚谐共振与线性模型失效问题研究

通过对一个两自由度密频近线性系统１／２阶亚谐共振响应分析,研究了密集模态间弱非线性耦合作用在副共振中的表现形式,如典型的Ｈｏｐｆ分叉导致的概周期响应等,着重考察了线性模型失效途径。     

Combination resonances in the response of the duffing oscillator to a three-frequency excitation

Summary The response of a weakly nonlinear, single-degree-of-freedom system with cubic nonlinearities to multifrequency excitations is studied analytically and numerically. The method of multiple scales is used to obtain uniformly valid, approximate solutions of the governing equation for various combination resonances. The analytical and numerical solutions are in virtually perfect agreement for all cases considered, but difer markedly from the exact solution of the linearized equation of motion. The peak amplitudes in the solutions of the nonlinear equation can be several times those in the solutions of the linearized equation, and they can occur rather more often; moreover, the addition of a static load can affect the natural frequency and, hence, either tune or detune a resonance, producing profound changes in the response. The present results demonstrate that the actual response of a structure can lead to a fatigue life that is much shorter than what is predicted by linear analysis. Hence, the conventional structural engineering practice of considering the structure to be safe from resonant responses when none of the frequencies of the excitation matches the natural frequency is shown to be fraught with danger; a practicing engineer, therefore, cannot afford to be ignorant of nonlinear phenomena.     

桩基非线性轴向振动的多时间尺度分析

假定桩基及桩周土的材料满足非线性弹性和线性粘弹性本构关系，给出了分析桩基轴向振动的非线性偏微分方程。用多时间尺度法推导出一端固定、另一端自由的桩基非线性轴向自由振动的n-阶主频率和位移的近似表达式，给出了数值算例，考察了参数的影响。研究结果表明：非线性系统的n-阶主频率不仅与线性系统的n-阶固有频率有关，而且也与振幅、阻尼系数和材料的非线性特征量有关；系统的响应中除含有主频率的谐波外，还含有2倍、3倍的主频率的高次谐波和二个或三个主频率的和或差的谐波存在。     

The nonlinear resonance magnetoelectric effect in magnetostrictive-piezoelectric structures

We have studied a magnetoelectric (ME) effect that is nonlinear with respect to the alternating magnetic field. It is established that resonance excitation of an alternating electric field takes place in magnetostrictive-piezoelectric bilayer structures under the action of alternating magnetic field at a frequency that is half as small as the electromechanical resonance frequency. The nonlinear ME effect, in contrast to the linear one, does not depend on the constant (magnetizing) bias field and is quadratic with respect to the alternating magnetic field.     

Duffing型隔振的力传递率及跳跃现象的理论分析

摘 要：针对隔振器中普遍存在的非线性特性,以立方非线性恢复力作用的单自由度隔振系统为例,用谐波平衡法求解非线性隔振系统固有频率附近的主共振响应,根据Routh-Hurwitz稳定性判定定理,从理论上说明主共振响应的幅频特性曲线族上垂直切线点的轨迹曲线所包围的区域为不稳定区域。推导出了隔振系统跳跃频率和力传递率的计算公式。计算表明隔振系统力传递率出现跳跃、滞后、以及稳定和不稳定现象,且隔振传递力中的高频谐波分量的影响很小。隔振系统的阻尼、非线性恢复力系数和激励幅值对共振区域的力传递率有影响,对频率低于共振频率区域的力传递率没有影响,其中仅阻尼对频率高于共振频率区域的力传递率有影响。还给出了力传递率小于1的起始频率计算公式。     

Frequency Dependent Strain-Field Hysteresis Model for Ferromagnetic Shape Memory Ni–Mn–Ga

We quantify the relationship between magnetic fields and strains in dynamic Ni-Mn-Ga actuators. As a result of magnetic field diffusion and structural actuator dynamics, the strain-field relationship changes significantly relative to the quasistatic response as the magnetic field frequency increases. We model the magnitude and phase of the magnetic field inside a Ni-Mn-Ga sample as a 1-D magnetic diffusion problem with applied dynamic fields known on the surface of the sample, from which we calculate an averaged or effective field. We use a continuum thermodynamics constitutive model to quantify the hysteretic response of the martensite volume fraction due to this effective magnetic field. We postulate that the evolution of volume fractions with effective field exhibits a zero-order response. To quantify the dynamic strain output, we represent the actuator as a lumped-parameter, single-degree-of-freedom resonator with force input dictated by the twin-variant volume fraction. This results in a second-order, linear ordinary differential equation whose periodic force input is expressed as a summation of Fourier series terms. The total dynamic strain output is obtained by superposition of strain solutions due to each harmonic force input. The model accurately describes experimental measurements at frequencies up to 250 Hz.     

输流管道含有内共振的横向受迫振动研究

利用多元L-P法研究外部周期激励下两端铰支输流管道含有内共振的非线性受迫振动问题。对于外激励作用下的流固耦合系统,当第二阶固有频率约为第一阶值的3倍,并且激励频率接近系统固有频率时,系统会发生含有强烈内部共振的主共振。利用多元L-P法求解这种振动响应,并详细分析振动中前两个模态的运动及外激励幅值对内共振的影响。数值算例揭示了系统由于内共振而发生的更加丰富而复杂的动力学行为,并且表明,随着激励幅值的增大,部分内共振的发生趋势将降低并最终消失。研究结果同时证明了多元L-P法在研究非线性动力学方面是便捷而高效的。     

磁致伸缩层合悬臂梁式作动器的振动分析

为了分析磁致伸缩薄膜型层合悬臂梁式作动器的振动问题,应用磁致伸缩材料的非线性本构关系,由哈密尔顿原理导出了双层悬臂梁的振动微分方程。采用分离变量方法和常微分方程组的解析解法对磁致伸缩薄膜型层合悬臂梁的自由振动和受迫振动进行了理论分析。数值算例表明本文计算结果与有限元结果吻合较好,从而佐证了本文理论模型和求解方法的正确性,并讨论了几何参数、材料参数对层合梁固有频率的影响。还分析了在周期输入磁场激励下悬臂梁的挠度响应,且挠度响应呈现出倍频效应的动态特性。      

基于二次特征值法的矩形薄板的动力稳定性研究

对于面内对边周期荷载作用下携带集中质量的矩形薄板,当周期荷载的激振频率在板的两倍自振频率附近时,板发生面外参数共振失稳。该文基于薄板大挠度理论,运用伽辽金法推导出携带集中质量的矩形薄板非线性动力失稳的Mathieu-Hill方程,进而求解得到板发生面外参数共振失稳时周期荷载的临界激振频率域以及非线性动力失稳曲线。运用有限元软件进行瞬态分析得到不同激振幅值作用下板发生面外参数共振失稳时周期荷载的最小与最大临界激振频率值,通过与解析解进行对比,验证了计算结果的正确性。研究结果表明：随着集中质量的增加,参数共振失稳的临界激振频率及其不稳定域的宽度逐渐减小,不稳定域的位置逐渐向低激振频率的方向移动;随着集中质量的增加,面外参数共振失稳域的临界激励幅值逐渐增加;随着集中质量所处位置的模态位移增加,不稳定域的宽度减小。     

Analysis of solenoid based linear compressor for household refrigerator

This article presents the analytical modeling of an oil-free solenoid actuator based linear compressor used in household refrigerators. The stator coil was excited with the pulse width modulated signal which caused linear oscillations in the armature using helical spring. Dynamic characteristics of the linear compressor were studied analytically considering the nonlinearity of the gas and electromagnetic force. The system dynamic models were validated with the finite element simulation as well as a specially designed experimental setup. Frequency response functions of stroke to current as well as pressure to current ratios were generated to evaluate the effect of excitation frequency on the compressor performance. The higher efficiency of the solenoid actuator was achieved when excited at the natural frequency. The results show that the natural frequency of the designed system is around 19 Hz and the work done in a cycle is approximately 1.3 J. Additionally, 47% isentropic and 87% electrical efficiency were achieved.     

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。     

A dynamics model for nonlinear electrostrictive actuators

This paper examines the nonlinear vibration of an electrostrictive ceramic rod actuator excited by a harmonic voltage source. A frequency-domain model was developed using the nonlinear constitutive law for electrostriction. The results predict harmonic distortion of the device's displacement due to the ceramic's nonlinear behavior. AC voltage signal and DC voltage bias were studied to determine the optimum power source parameters for minimizing distortion. The calculations show that the rod's resonance frequency and amplitude depend on the electromechanical coupling strength and differ greatly for large AC voltages from the equivalent linear piezoelectric results. The nonlinear analysis relates the device's electromechanical coupling coefficient to the computed resonance and antiresonance frequencies. This important result could provide the basis for future measurement of the electrostrictive coupling coefficient using resonance techniques.     

温度场中简谐激励斜梁的1/3次亚谐共振分析

以温度场中简谐激励斜梁的非线性振动方程为研究对象,应用多尺度法,求得非线性振动系统1/3次亚谐共振的一次近似解。对该解进行数值计算,分析温度、激励、几何尺寸等参数对1/3次亚谐共振幅频响应曲线的影响。随着初始温度和激励幅值的增加,1/3次亚谐共振的振幅和共振区增大。随着温度影响系数和长高比的增加,1/3 亚谐共振的振幅和共振区减小。     

温度场中输电线在谐扰力作用下的1/3次亚谐共振研究

研究输电线在温度场中谐扰力作用下的1/3次亚谐共振问题,应用动力学方法建立温度场中受谐扰力作用输电线的非线性振动方程。根据非线性振动的多尺度解法,得到系统满足1/3次亚谐共振情况的近似解,并对其进行数值计算。分析温差变化、外部激励、谐调值、系统阻尼等对系统的影响。得到系统失稳的临界温度。系统随着调谐值和温差的增加,响应曲线的幅值增加;随着阻尼的增加,幅频响应曲线向开口方向移动。     

Numerical Simulation of Nonlinear Dynamic Responses of Beams Laminated with Giant Magnetostrictive Actuators

This paper presents some simulation results of nonlinear dynamic responses for a laminated composite beam embedded by actuators of the giant magnetostrictive material (Terfenol-D) subjected to external magnetic fields, where the giant magnetostrictive materials utilizing the realignment of magnetic moments in response to applied magnetic fields generate nonlinear strains and forces significantly larger than those generated by other smart materials. To utilize the full potential application of the materials in the function and safety designs, e.g., active control of vibrations, the analysis of dynamic responses is requested in the designs as accurately as possible on the basis of those inherent nonlineary constitutive relations among stain, force and applied magnetic field existed in the materials. Here, a numerical code for the nonlinear vibration of laminated beams is proposed on the basis of a nonlinearly coupling constitutive model which fully behaves for the characteristics what are measured in experiments. It is found from this code that the natural frequency of the laminated beams changes with both the bias magnetic field and the pre-stresses, and the dynamic responses excited by an alternating magnetic field of simple harmonic form display strong nonlinear characteristics, for example, the frequency multiplication and the ultraharmonic resonance phenomena.