Effects of air damping on quality factors of different probes in tapping mode atomic force microscopy

The AFM probe in tapping mode is a continuous process of energy dissipation,from moving away from to intermittent contact with the sample surfaces.At present,studies regarding the energy dissipation mechanism of this continuous process have only been reported sporadically,and there are no systematic explanations or experimental verifications of the energy dissipation mechanism in each stage of the continuous process.The quality factors can be used to characterize the energy dissipation in TM-AFM systems.In this study,the vibration model of the microcantilever beam was established,coupling the vibration and damping effects of the microcantilever beam.The quality factor of the vibrating microcantilever beam under damping was derived,and the air viscous damping when the probe is away from the sample and the air squeeze film damping when the probe is close to the sample were calculated.In addition,the mechanism of the damping effects of different shapes of probes at different tip–sample distances was analyzed.The accuracy of the theoretical simplified model was verified using both experimental and simulation methods.A clearer understanding of the kinetic characteristics and damping mechanism of the TM-AFM was achieved by examining the air damping dissipation mechanism of AFM probes in the tapping mode,which was very important for improving both the quality factor and the imaging quality of the TM-AFM system.This study’s research findings also provided theoretical references and experimental methods for the future study of the energy dissipation mechanism of micro-nano-electromechanical systems.

Reducing force transmissibility in multiple degrees of freedom structures through anti-symmetric nonlinear viscous damping

In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom （MDOF） structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force trans- missibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.

Loss of energy dissipation capacity from the deadzone in linear and nonlinear viscous damping devices

In a viscous damping device under cyclic loading, after the piston reaches a peak stroke, the reserve movement that follows may sometimes experience a short period of delayed or significantly reduced device force output. A similar delay or reduced device force output may also occur at the damper＇s initial stroke as it moves away from its neutral position. This phenomenon is referred to as the effect of ＂deadzone＂. The deadzone can cause a loss of energy dissipation capacity and less efficient vibration control. It is prominent in small amplitude vibrations. Although there are many potential causes of deadzone such as environmental factors, construction, material aging, and manufacture quality, in this paper, its general effect in linear and nonlinear viscous damping devices is analyzed. Based on classical dynamics and damping theory, a simple model is developed to capture the effect ofdeadzone in terms of the loss of energy dissipation capacity. The model provides several methods to estimate the loss of energy dissipation within the deadzone in linear and sublinear viscous fluid dampers. An empirical equation of loss of energy dissipation capacity versus deadzone size is formulated, and the equivalent reduction of effective damping in SDOF systems has been obtained. A laboratory experimental evaluation is carried out to verify the effect of deadzone and its numerical approximation. Based on the analysis, a modification is suggested to the corresponding formulas in FEMA 3 5 6 for calculation of equivalent damping if a deadzone is to be considered.

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Effects of residual stress and viscous and hysteretic dampings on the stability of a spinning micro-shaft

This study examines the effects of the residual stress and viscous and hysteretic dampings on the vibrational behavior and stability of a spinning Timoshenko micro-shaft.A modified couple stress theory(MCST)is used to elucidate the sizedependency of the micro-shaft spinning stability,and the equations of motion are derived by employing Hamilton’s principle and a spatial beam for spinning micro-shafts.Moreover,a differential quadrature method(DQM)is presented,along with the exact solution for the forward and backward(FW-BW)complex frequencies and normal modes.The effects of the material length scale parameter(MLSP),the spinning speed,the viscous damping coefficient,the hysteretic damping,and the residual stress on the stability of the spinning micro-shafts are investigated.The results indicate that the MLSP,the internal dampings(viscous and hysteretic),and the residual stress have significant effects on the complex frequency and stability of the spinning micro-shafts.Therefore,it is crucial to take these factors into account while these systems are designed and analyzed.The results show that an increase in the MLSP leads to stiffening of the spinning micro-shaft,increases the FW-BW dimensionless complex frequencies of the system,and enhances the stability of the system.Additionally,a rise in the tensile residual stresses causes an increase in the FW-BW dimensionless complex frequencies and stability of the micro-shafts,while the opposite is true for the compressive residual stresses.The results of this research can be employed for designing spinning structures and controlling their vibrations,thus forestalling resonance.

Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.

Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness

A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.

Wind-Induced Vibration Control for Substation Frame on Viscous Damper

In order to study the wind-induced vibration control effect of the viscous damper on the large-scale substation frame,this paper takes the large-scale 1000 kV substation frame of western Inner Mongolia as an example.The time-history sample of pulsating wind load is simulated by harmonic superposition method based on Matlab software.6 kinds of viscous damper arrangement schemes have been designed,and SAP2000 finite element software is used for fine modeling and input wind speed time history load for nonlinear time history analysis.The displacement and acceleration of a typical node are the indicators of wind vibration control.The wind-induced vibration control effects of different schemes under different damping parameters have compared,and the damping parameters are analyzed for the optimal layout scheme.The results show that a viscous damper has installed in the lower layers of the substation;a viscous damper is placed between the ground column and the lattice beam.It is an integrated optimal solution.The wind-induced vibration control effect of the optimal scheme is sensitive to the viscous damper parameters,and the control effect does not increase linearly with the increase of the damping index and the damping coefficient.Corresponding to different damping indexes,the damping coefficient has a better range of values.

Simplified design of nonlinear damper parameters and seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers

Viscous dampers are widely used as passive energy dissipation devices for long-span cable-stayed bridges for mitigation of seismic load-induced vibrations.However,complicated finite element(FE)modeling,together with repetitive and computationally intensive nonlinear time-history analyses(NTHAs)are generally required in conventional design methods.To streamline the preliminary design process,this paper developed a simplified longitudinal double degree of freedom model(DDFM)for single and symmetric twin-tower cable-stayed bridges.Based on the proposed simplified longitudinal DDFM,the analytical equations for the relevant mass-and stiffness-related parameters and longitudinal natural frequencies of the structure were derived by using analytical and energy methods.Modeling of the relationship between the nonlinear viscous damper parameters and the equivalent damping ratio was achieved through the equivalent linearization method.Additionally,the analytical equations of longitudinal seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers were derived.Based on the developed simplified DDFM and suggested analytical equations,this paper proposed a simplified calculation framework to achieve a simplified design method of nonlinear viscous damper parameters.Moreover,the effectiveness and applicability of the developed simplified longitudinal DDFM and the proposed calculation framework were further validated through numerical analysis of a practical cable-stayed bridge.Finally,the results indicated the following.1)For the obtained fundamental period and longitudinal stiffness,the differences between results of the simplified longitudinal DDFM and numerical analysis were only 2.05%and 1.5%,respectively.2)Relative calculation errors of the longitudinal girder-end displacement and bending moment of the bottom tower section of the bridge obtained from the simplified longitudinal DDFM were limited to less than 25%.3)The equivalent damping ratio of nonlinear viscous dampers and the applied loading frequency had significant effects on the longitudinal seismic responses of the bridge.Findings of this study may provide beneficial information for a design office to make a simplified preliminary design scheme to determine the appropriate nonlinear damper parameters and longitudinal seismic responses for long-span cable-stayed bridges.

Moving-Particle Semi-Implicit Method for Vortex Patterns and Roll Damping of 2D Ship Sections

A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 are chosen for the simulation. It shows that the result of MPS is very close to results of experiments or mesh-numerical simulations. In the simulation of MPS, vortices are found periodically in bilges of ship sections. In section S. S. 5.0 and section S. S. 7.0, which are close to the middle ship, two little vortices are found at different bilges of the section, in section S. S. 0.5, which is close to the bow, only one big vortex is found at the bottom of the section, these vortices patterns are consistent with the theory of Ikeda. The distribution of shear stress and pressure on the rolling hull of ship section is calculated. When vortices are in bilges of the section, the sign clmnge of pressure can be found, but in section S. S. 0.5, there is no sign change of pressure because only one vortex in the bottom of the section. With shear stress distribution, it can be found the shear stress in bilges is bigger than that at other part of the ship section. As the free surface is considered, the shear stress of both sides near the free surface is close to zero and even sign changed.

Equivalent damping of SDOF structure with Maxwell damper

To predict the maximum earthquake response of an SDOF structure with a Maxwell fluid damper or supplemental brace-viscous damper system using the seismic design response spectrum technique,a new approach is presented to determine the first-and second-order equivalent viscous damping and stiffness,the peak responses,and the damper force of the above structure.Based on the fact that the dynamic characteristics of a general linear viscoelastically damped structure are fully determined by its free vibration properties and the relaxation time constants of a Maxwell fluid damper and supplemental brace-viscous damper system in engineering practice are all small,the method of improved multiple time scales and the equivalent criterion in which all free vibration properties are the same are used to obtain the first-and second-order equivalent viscous damping and stiffness of the above structure in closed form.The accuracy of the proposed method is higher and significantly better than that of the modal strain energy method.Furthermore,in the parametric range of the requirements of the Chinese ＂Code for Seismic Design of Buildings＂,the error of the proposed second-order equivalent system for the abovementioned engineering structure is not more than 0.5%.

Vortex Patterns and Roll Damping on Various Cross Sections of Ships

A numerical study is presented on roll damping of ships by solving Navier-Stokes equation. Two Dimensional unsteady incompressible viscous flow around the rolling cylinders of various ship-like cross sections are numerically simulated by use of the computational scheme previously developed by the authors. The numerical results show that the location of the vortices is very similar to the existing experimental result. For comparison of vortex patterns and roll damping on various ship-like cross sections, various distributions of shear stress and pressure on the rolling ship hull surface are presented in this paper. It is found that there are two vortices around the midship-like section and there is one vortex around the fore or stern section. Based on these simulation results, the roll damping of a ship including viscous effects is calculated. The contribution of pressure to the roll moment is larger than the contribution of frictional shear stress.

Time-delay damping theory

In this paper,existing damping theories are briefly reviewed.On the basis of the existing damping theories,a new kind of damping theory,i.e.,the time-delay damping theory,is developed.In the time-delay damping theory,the damping force is considered to be directly proportional to the increment of displacement.The response analysis of an SDOF time-delay damping system is carried out,and the methods for obtaining the solution for a time-delay damping system in the time domain as well as the frequency domain are given.The comparison between results from different damping theories shows that the time-delay damping theory is both reasonable and convenient.

Damping Solitary Wave in a Three-Dimensional Rectangular Geometry Plasma

The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper.By introducing a threedimensional rectangular geometry and employing the reductive perturbation theory,a quasi-Kd V equation is derived in the viscous plasma and a damping solitary wave is obtained.It is found that the damping rate increases as the viscosity coefficient increases,or increases as the length and width of the rectangle decrease,for all kinds of boundary condition.Nevertheless,the magnitude of the damping rate is dominated by the types of boundary condition.We thus observe the existence of a damping solitary wave from the fact that its amplitude disappears rapidly for a → 0and b → 0,or ν→ ＋∞.

某高层钢框架结构组合减震设计

某转化医学中心位于高烈度设防地区、地震重点监视防御区,从减震效果和经济性等方面对不同减震方案进行比选后,选用BRB+VFD组合减震方案,同时提出了阻尼器布置原则。采用有限元法进行弹性和弹塑性时程分析,结果表明BRB+VFD组合减震方案可为主体结构提供一定的附加刚度和附加阻尼比,降低地震作用下基底剪力,延缓主体结构破坏,满足主体结构第二道防线设计要求;VFD在多遇地震、设防地震、罕遇地震作用下均发挥耗能作用;BRB在多遇地震作用下仅提供刚度,在设防地震和罕遇地震作用下进入屈服耗能,提高了结构抗震性能;随着地震烈度的增加,结构附加阻尼比随之增大,有效保证了结构抗震性能。

一类带有非线性阻尼项的磁流体动力学方程组的解的整体存在性

本文研究在多孔介质意义下的一类带有非线性阻尼项a|u|^(α-1)u(a> 0)的不可压的磁流体动力学方程组的解的整体存在性问题,通过古典的能量方法和Sobolev紧性嵌入方法获得了解的整体存在性,利用Gagliardo-Nirenberg插值不等式和其它的一些重要不等式得到了解的正则性结果,建立了弱解和强解的整体存在性,这些结果在很大程度改善了之前相关文献的结果,揭示了磁流体运动的物理现象,为磁流体动力学的发展提供了必要的理论基础.

铁路悬索桥车致纵向运动混合阻尼减振研究

针对铁路悬索桥在列车过桥时梁端纵向运动响应控制问题,提出了一种创新的混合阻尼减振方案,采用多种类型的阻尼器控制梁端位移,以满足不同的减振需求.以某在建大跨铁路悬索桥为工程背景,建立了空间桁架精细模型和等效单梁简化模型,系统研究了混合阻尼减振方案不同阻尼器参数对减振效果的影响.该方案将低指数黏滞阻尼器纵向安装于桥塔与加劲梁之间,同时在桥台与加劲梁之间纵向安装电涡流阻尼器.鉴于桥台结构的特殊性,电涡流阻尼器被设计为仅能承受压力的装置,并通过样机试验进行了验证.为了进一步提升减振性能,电涡流阻尼器还配备了摩擦耗能元件.该混合阻尼减振方案能够有效控制列车过桥时梁端的纵向运动响应,显著提高桥梁结构的安全性和耐久性,在类似工程中具有重要的参考价值和借鉴意义.

采用粘滞阻尼器的某超高层建筑消能减震设计与分析

以珠海市某框架–核心筒建筑为例,运用分析程序ETABS建立有限元模型,并设置多组粘滞阻尼器布置方案,采用最大层间位移角与基底剪力双关键指标,对比各方案减震效果并择优选出布置方案。对所得方案进行多遇地震下弹性分析及罕遇地震下动力弹塑性分析。多遇地震分析结果表明,采用粘滞阻尼器的结构双向指标均大幅降低,提供附加阻尼比达4.1%。罕遇地震分析结果表明,结构的层间位移角及整体屈服机制均满足要求。该方案下减震效果与结构抗震性能均良好,可为同类工程提供参考。

调谐惯质阻尼器动力试验和参数识别

研发了一种新型调谐惯质阻尼器(TVMD)装置,该装置分别采用电涡流与金属弹簧作为TVMD的阻尼元件与弹簧元件.首先,对该TVMD装置进行动力试验,研究其动力特性.然后,提出4种基于试验数据识别TVMD参数的方法,即峰值点拟合法、滞回曲线拟合法、时程拟合法和传递函数拟合法.动力试验结果表明:TVMD具有惯性质量放大效应和阻尼增益效应;弹簧元件和惯容元件均表现出理想的线性特性,而阻尼元件由于电涡流阻尼固有属性和TVMD装置中存在的摩擦,表现出非线性特性.参数识别结果表明:4种方法均能合理确定TVMD参数,其中,传递函数拟合法能提供用于调谐设计的等效阻尼系数,而其他3种方法能识别非线性阻尼模型的参数;滞回曲线拟合法和时程拟合法具有更高的参数识别精度,而峰值点拟合法和传递函数拟合法具有更高的计算效率.

空间结构用微振动控制阻尼器动态特性测试

空间桁架是有效载荷的常用支撑结构,由于有效载荷的振动敏感性,为保证有效载荷的在轨性能,保持桁架结构的稳定性,需要对桁架结构的低频振动进行抑制。液体阻尼器具有良好的阻尼性能,常用于卫星结构的振动抑制。对液体阻尼器的动态特性进行了理论分析和试验研究,使用激振器进行激励加载,获取了输入加速度和输出动态力的关系,求解了阻尼器的动刚度及阻尼系数。测试结果表明,该阻尼器可实现较大范围的阻尼系数,阻尼系数较未充液增加10倍以上,具有低频大阻尼、高频小阻尼的特性,可满足空间桁架结构减振需求,对空间结构的振动控制具有较强的工程意义。