Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads

This paper proposes the design and experiment of a vibration isolator capable of isolating a wide range of loads. The isolator consists of two oblique springs and one vertical spring to achieve quasi-zero stiffness at the equilibrium position. The quasi-zero-stiffness characteristic makes the isolator attenuate external disturbance more at low frequencies, when compared with linear isolators. Unlike previous studies, this paper focuses on the analysis of the effect of different loads and the implementation of an adjustment mechanism to handle a wide range of loads. To ensure zero stiffness under imperfect stiffness matching, a lateral adjustment mechanism is also proposed. Instead of using coil springs, special planar springs are designed to realize the isolator in a compact space. Static and dynamic models are developed to evaluate the effect of key design parameters so that the isolator can have a wide isolation range without sacrificing its size. A prototype and its associated experiments are presented to validate the transmissibility curves under three different loads. The results clearly show the advantage of quasi-zero-stiffness isolators against linear isolators.     

Nonlinear vibration isolator with adjustable restoring force

This paper presents a vertical quasi-zero stiffness (QZS) vibration isolator with a mechanism for adjusting restoring force. QZS vibration isolators have high initial stiffness and QZS around the static equilibrium position. This way, excessive deformation due to self-weight can be avoided while having enough vibration reduction capability to dynamic excitations. One of the main issues left for QZS vibration isolators is the difficulty in keeping the vibration reduction capability when the vibration isolated object is replaced. In such a case, adjustment of its restoring force becomes necessary in accordance with the self-weight of the newly placed vibration isolated object. This paper attempts to address this issue by proposing a mechanism that enables quick and easy adjustment of the restoring force of a QZS vibration isolator. The proposed mechanism consists of cranks and a screw jack. With the present mechanism, the restoring force provided by horizontally placed springs can be converted into the vertical restoring force of the vibration isolator. In the conversion, the vertical resisting force can be adjusted simply by applying and removing torque to the screw jack to change and hold the angle of inclined bars placed in the cranks. In this study, a prototype of a class of QZS vibration isolator having the proposed mechanism is produced. Shaking table tests are performed to demonstrate the efficacy of the present mechanism, where the produced prototype is subjected to various sinusoidal and earthquake ground motions. It is demonstrated through the shaking table tests that the produced prototype can reduce the response acceleration within the same tolerance even when the mass of the vibration isolated object is changed.     

Exploring the performance of a nonlinear tuned mass damper

We explore the performance of a nonlinear tuned mass damper (NTMD), which is modeled as a two degree of freedom system with a cubic nonlinearity. This nonlinearity is physically derived from a geometric configuration of two pairs of springs. The springs in one pair rotate as they extend, which results in a hardening spring stiffness. The other pair provides a linear stiffness term. We perform an extensive numerical study of periodic responses of the NTMD using the numerical continuation software AUTO. In our search for optimal design parameters we mainly employ two techniques, the optimization of periodic solutions and parameter sweeps. During our investigation we discovered a family of detached resonance curves for vanishing linear spring stiffness, a feature that was missed in an earlier study. These detached resonance response curves seem to be a weakness of the NTMD when used as a passive device, because they essentially restore a main resonance peak. However, since this family is detached from the low-amplitude responses there is an opportunity for designing a semi-active device.     

一种光电载荷非线性隔振装置的研究

针对光电载荷对隔振性能的需求,提出一种采用菱形连杆机构作为负刚度组件,具有高静、低动刚度特点的非线性隔振器（简称菱形HSLDS隔振器）。采用静力学分析方法,建立了隔振器数学模型,研究了刚度参数设定以及非线性调节方法;利用谐波平衡法（HBM）求解动力学方程,分析了各参数对隔振性能的影响关系;采用动力学仿真软件ADAMS及实物样机对理论模型与结论进行了验证。测试结果表明:菱形HSLDS隔振器具有较方便的参数调整能力,零位刚度及刚度非线性可通过拉簧参数与连杆参数进行设定、优化,隔振的刚度非线性优化程度受主隔振器阻尼以及零位刚度参数影响。相比于传统线性隔振器,菱形HSLDS具有显著的非线性隔振优势,可较好地满足光电载荷隔振需求。     

A tunable high-static-low-dynamic stiffness vibration isolator

In this study, a novel vibration isolator is developed. The developed isolator possesses the characteristics of high-static-low-dynamic stiffness (HSLDS) and can act passively or semi-actively. The HSLDS property of the isolator is obtained by connecting a mechanical spring, in parallel with a magnetic spring that is constructed by a pair of electromagnets and a permanent magnet. The mechanical spring is a structural beam whose stiffness exhibits a hardening behavior. The stiffness of the magnetic spring can be positive or negative, depending on the polarity of the current to the electromagnets. A passive HSLDS isolator is obtained when the electromagnet current is zero. In the stiffness characterization study, the analytical model for each of the springs is established and the tuning parameters are identified. Using the stiffness models, the design optimization issues are investigated. In the experimental study, the effectiveness of the isolator for vibration isolation is tested. The analytical natural frequencies of the isolator are validated experimentally. The relationships between the displacement transmissibility and the exciting frequency are measured both under the passive mode and under the semi-active mode. The on-line tuning capability of the isolator is investigated.     

Critical earthquake load inputs for multi-degree-of-freedom inelastic structures

The problem of modeling earthquake ground motions as design inputs for multi-degree-of-freedom inelastic structures is studied. The earthquake acceleration is expressed as a Fourier series modulated by an envelope function. The coefficients of the series representation are calculated such that the structure inelastic deformation is maximized subjected to predefined constraints. These constraints are taken to reflect known characteristics of recorded earthquakes such as upper bounds on the energy and peak values of the ground acceleration, velocity and displacement and upper and lower limits on the Fourier spectra of the ground acceleration. The material stress-strain behavior is modeled using bilinear and elastic-plastic relations. The resulting nonlinear optimization problem is solved by using the sequential quadratic optimization method. Issues related to various forms of energy dissipated by the inelastic structure are explored. The study also examines the effect of nonlinear damping models and the influence of the strain hardening ratio (ratio of the post-yield stiffness to the pre-yield stiffness) on the derived optimal earthquake and associated inelastic deformation. The formulation is demonstrated for a two-storey inelastic building frame with nonlinear damping.     

A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic

A vibration isolator consisting of a vertical linear spring and two nonlinear pre-stressed oblique springs is considered in this paper. The system has both geometrical and physical nonlinearity. Firstly, a static analysis is carried out. The softening parameter leading to quasi-zero dynamic stiffness at the equilibrium position is obtained as a function of the initial geometry, pre-stress and the stiffness of the springs. The optimal combination of the system parameters is found that maximises the displacement from the equilibrium position when the prescribed stiffness is equal to that of the vertical spring alone. It also satisfies the condition that the dynamic stiffness only changes slightly in the neighbourhood of the static equilibrium position. For these values, a dynamical analysis of the isolator under asymmetric excitation is performed to quantify the undesirable effects of the nonlinearities. It includes considering the possibilities of the appearance of period-doubling bifurcation and its development into chaotic motion. For this purpose, approximate analytical methods and numerical simulations accompanied with qualitative methods including phase plane plots, Poincaré maps and Lyapunov exponents are used. Finally, the frequency at which the first period-doubling bifurcation appears is found and the effect of damping on this frequency determined.     

Crowd-induced random vibration of footbridge and vibration control using multiple tuned mass dampers

This paper investigates vibration characteristics of footbridge induced by crowd random walking, and presents the application of multiple tuned mass dampers (MTMD) in suppressing crowd-induced vibration. A single foot force model for the vertical component of walking-induced force is developed, avoiding the phase angle inaccessibility of the continuous walking force. Based on the single foot force model, the crowd-footbridge random vibration model, in which pedestrians are modeled as a crowd flow characterized with the average time headway, is developed to consider the worst vibration state of footbridge. In this random vibration model, an analytic formulation is developed to calculate the acceleration power spectral density in arbitrary position of footbridge with arbitrary span layout. Resonant effect is observed as the footbridge natural frequencies fall within the frequency bandwidth of crowd excitation. To suppress the excessive acceleration for human normal walking comfort, a MTMD system is used to improve the footbridge dynamic characteristics. According to the random vibration model, an optimization procedure, based on the minimization of maximum root-mean-square (rms) acceleration of footbridge, is introduced to determine the optimal design parameters of MTMD system. Numerical analysis shows that the proposed MTMD designed by random optimization procedure, is more effective than traditional MTMD design methodology in reducing dynamic response during crowd-footbridge resonance, and that the proper frequency spacing enlargement will effectively reduce the off-tuning effect of MTMD.     

Experimental Investigation of Nonlinear Vibration Isolator with Fluidic Actuators (NLVIFA)

This paper elaborates a nonlinear fluidic low frequency vibration isolator designed with the characteristics of quasi-zero stiffness (QZS). The existing model of QZS vibration isolator enhances amplitude of vibration and attenuating vibration frequencies. This concern with displacement plays a vital role in the performance and instability of oblique spring setup reduces the isolator performance in horizontal non-nominal loads, in this accordance; this paper associates double acting hydraulic cylinder (fluidic actuators in short) in oblique and helical coil spring. An approximate expression of unique analytical relationship between the stiffness of vertical spring and bulk modulus of the fluid is derived for Quasi – Zero Stiffness Non-Linear Vibration Isolator with Fluidic Actuators (NLVIFA in short) system and the force transmissibility is formulated and damping ratio are discussed for characteristic analysis. Modal analysis carried out and compared with analytical results and an experimental prototype is developed and investigated. The performance of the NLVIFA reduces the external embarrassment more at low frequencies and the series of experimental studies showing that the soft nonlinearity causes limitation in the resonant frequency thereupon the isolation will be enhanced and NLVIFA greatly outperform some other type of nonlinear isolators.     

多目标粒子群优化算法在交变相位聚焦直线加速器模拟中的应用

现代智能优化算法粒子群算法\,(Particle Swarm Optimization)\,在加速器设计优化上的应用逐渐增多。交变相位聚焦直线加速器\,(Alternative Phase Focused Drift Tube Linac)\,具有节省空间和造价的优点。将交变相位聚焦直线加速器的初步设计方案作为种子,植入粒子群算法中;以加速器的传输效率和束流能量作为目标,得到该方案的Pareto最优解集;在粒子进化过程中,以前沿解集作为粒子的运动方向,以前沿解集的束流径迹作为粒子的参数来源。最终得到了满足能量增益的高传输效率、大接受度的优化方案。The Particle Swarm Optimization(PSO), one of the modern intelligent optimization algorithms,is increasingly employed in the design and optimization of accelerators. Alternative Phase Focused Drift Tube Linac(APF DTL) has an advantage in cost-effecient fabrication and reduced construction space. The preliminary design of APF DTL is involved in the optimization as the anchor; by taking the acceleration efficiency and the beam energy as two fitness functions, the Pareto optimal set is obtained; the evolutionary direction is determined by the Pareto optimal set and the particles’ parameters in the optimization are derived from the simulations of the randomly selected Pareto optimal solutions. A final optimized design with extracted energy of 5.35 MeV/uand acceleration efficiency greater than 83% is acquired.     

Analysis and experimental validation of an HTS linear synchronous propulsion prototype with HTS magnetic suspension

A high temperature superconducting (HTS) linear propulsion system composed of a single-sided HTS linear synchronous motor (HTSLSM) in its middle and HTS magnetic suspension sub-systems on both sides has been developed. The HTSLSM uses an HTS bulk magnet array on the moving secondary, and the field-trapped characteristics of the HTS bulk using different magnetized methods have been measured and compared to identify their magnetization capability. In order to generate a large levitation force for the system, three different types of permanent magnet guideways (PMGs) have been numerically analyzed and experimentally verified to obtain an optimal PMG. Based on comprehensive experimental prototype tests, the results show that the HTS linear propulsion system can run with stable magnetic suspension having a constant air-gap length, and the thrust characteristics versus the exciting current, working frequency and the air-gap length have also been obtained. This work forms the basis for developing a practical HTS linear propulsion system by using HTS bulks both for propulsion and suspension.     

Equation of Motion of an Electric Charge

The appearance of the time derivative of the acceleration in the equation of motion (EOM) of an electric charge is studied. It is shown that when an electric charge is accelerated, a stress force exists in the curved electric field of the accelerated charge, and in the case of a constant linear acceleration, this force is proportional to the acceleration. This stress force acts as a reaction force which is responsible for the creation of the radiation (instead of the radiation reaction force that actually does not exist at low velocities). Thus the initial acceleration should be supplied as an initial condition for the solution of the EOM of an electric charge.     

菱形HSLDS隔振器负刚度机构质量及摩擦力影响分析

以菱形负刚度机构HSLDS（high static low dynamic stiffness）隔振器（简称菱形HSLDS隔振器）为研究目标,采用虚功法建立负刚度机构等效摩擦力模型,并以拉格朗日方法建立包含负刚度机构质量及摩擦力因素的动力学方程;利用谐波平衡法（HBM）求解动力学方程,分析了负刚度机构质量及摩擦力对隔振的影响及其优化措施,并通过实物样机验证了理论模型的合理性。实验结果表明:负刚度机构质量及摩擦力对隔振均产生不利影响,应尽量减小;将负刚度机构连杆较短侧连接于载荷平台端,可以减小负刚度机构质量对较高频段隔振性能的影响;在限定隔振器刚度参数以及铰接副接触参数且同时满足刚度与摩擦力优化条件下,通过增大连杆机构杆长差的方式可以优化低频段隔振性能,并降低负刚度机构摩擦力对高频段隔振的影响。     

On the design of a high-static-low-dynamic stiffness isolator using linear mechanical springs and magnets

The frequency range over which a linear passive vibration isolator is effective is often limited by the mount stiffness required to support a static load. This can be improved upon by incorporating a negative stiffness element in the mount such that the dynamic stiffness is much less than the static stiffness. In this case, it can be referred to as a high-static-low-dynamic stiffness (HSLDS) mount. This paper is concerned with a theoretical and experimental study of one such mount. It comprises two vertical mechanical springs between which an isolated mass is mounted. At the outer edge of each spring, there is a permanent magnet. In the experimental work reported here, the isolated mass is also a magnet arranged so that it is attracted by the other magnets. Thus, the combination of magnets acts as a negative stiffness counteracting the positive stiffness provided by the mechanical springs. Although the HSLDS suspension system will inevitably be nonlinear, it is shown that for small oscillations the mount considered here is linear. The measured transmissibility is compared with a comparable linear mass-spring-damper system to show the advantages offered by the HSLDS mount.     

Energy dissipation of a ring-like metal rubber isolator

Metal rubber （MR） is a kind of homogeneous poroelastic damping material made of metal wire. In this paper, by ana- lyzing the forces on the MR isolator and the MR element, the hysteresis loops of the force and deformation are studied and verified by experiments. The results show that the force and displacement hysteresis loop of the MR isolator is described by the force and deformation hysteresis loops of the MR elements. In addition, the relationship between the energy dissipation coefficient of the MR element and that of the MR isolator is derived. The energy dissipation coefficient is programmed and calculated by MATLAB using experimental data, and the results are compared with the theoretical value. It is the basis for the design and applied research of the MR isolator in a future study.     

Optimal design method for magnetization directions of a permanent magnet array

In many magnetic systems, the permanent magnet (PM) pattern has a great influence on their performance. This study proposes a systematic optimization method for designing discrete magnetization directions. While previous works have been mostly dependent on researchers’ intuition, the developed method is systematic and can be applied to a two-dimensional PM-type eddy current brake model. The effectiveness of the method is confirmed, where the design’s aim is to maximize the braking force on a moving conductor. The sensitivity analysis is accomplished by the adjoint variable method and the sequential linear programming is used as an optimizer. Several optimization results for various conditions through the proposed design method are compared to each other and the optimal magnet configuration for an eddy current brake is suggested.     

太阳能热气流电站系统研究

由于现有模型不足以准确描述太阳能热气流发电系统的物理机制,本文提出一个更完善的数学模型去分析太阳能热气流电站系统的相对压力分布和系统抽力．模型中考虑了太阳辐射和系统尺寸参数对系统相对压力和系统抽力的影响。以西班牙试验电站为例进行数值模拟,探索系统尺寸参数和太阳辐射对系统相对压力和系统抽力的影响。数值计算结果与理论分析具有良好的一致性．     

双级光隔离器理论及装配误差分析

传统双级光隔离器45°装配无法达到隔离度最优化问题。从双级光隔离器的光学结构和工作原理入手,分析了双级光隔离器的插入损耗、反向隔离度,以及偏振相关损耗,使用MATLAB定量分析了双级隔离器装配存在偏转角度误差时的插入损耗和反向隔离度,为双级隔离器装配的最佳化提供了理论上应保证44°装配这一可行的保障方法。     

Vocal Fold Impact Stress Analysis

Vocal fold impact stress (force/area) has been implicated as a factor possibly contributing to the formation of nodules and polyps. The force of impact of a moving body is related to its acceleration. Since the mass of the folds is relatively constant, one expects impact force to be directly proportional to acceleration. A measure that reflects the relative displacement of the vocal folds is photoglottography (PGG). The velocity and acceleration of the folds are easily obtained by calculating the first and second derivatives of the PGG displacement waveform. This study, therefore, compared the second derivative of the PGG signal with simultaneously measured impact stress in an excised canine larynx model. Glottal transillumination (PGG) was measured with a subglottic transducer. A miniature force transducer placed in the midline between the vocal folds measured impact stress at the midglottal position. For nine different larynges, there was a positive and linear relationship between the second derivative of PGG and impact stress. The statistically significant results support the hypothesis that the second derivative of PGG m ay provide a use fulnoninvasive way to estimate relative vocal fold impact stress.     

Design and simulation of magneto-optic Mach-Zehnder isolator

In this paper, we have designed, optimized and simulated the magneto-optic Mach-Zehnder isolator. The waveguide isolator is based on a nonreciprocal phase shift in the magneto-optic branch of the MZ isolator. We have used the finite difference beam propagation method for numerical solution of the scalar wave equation. We have also used the transparent boundary condition. The propagation constant has been achieved by using the effective index method. We have calculated the design parameters to decrease the insertion loss in the forward direction and increase return loss in the backward direction and achieved a 40 dB isolation ratio.