Vibrations of a cylindrical shell with partially constrained layer damping (CLD) treatment

This paper presents a mathematical model for a cylindrical shell with a partially constrained layer damping (CLD) treatment. A thin shell theory in conjunction with the Donnell–Mushtari–Vlasov assumptions is employed to yield the model. Employing the assumed-mode method, the discretized equations of motion in terms of shell’s transverse modal coordinates are derived. The effects of treatment length, of constraining layer (CL) thickness and stiffness, and of viscoelastic material core (VEM) thickness are then discussed. Numerical results show that thicker or stiffer CL warrants better damping. Thicker VEM does not always give better damping than thinner ones when CL exceeds a certain thickness.     

被动约束层阻尼梁动力学优化研究

研究被动约束层阻尼(passive constrained layer damping,PCLD)梁的动力学优化问题,优化变量为PCLD的起始位置、覆盖长度、阻尼层厚度和约束层厚度。在局部覆盖PCLD梁动力学特性的传递函数解的基础上,建立PCLD梁的单目标和多目标优化模型。单目标优化中以结构模态损耗因子最大为优化目标,讨论约束条件中PCLD附加结构质量系数对优化结果的影响。多目标优化中以各阶模态损耗因子最大、各阶固有频率改变量最小和PCLD附加的结构质量最小为优化目标,增加约束层纵振频率的约束条件,讨论优化目标函数中各权重系数对优化结果的影响。此外,还在有限元软件MSC.Patran/Nastran中二次开发出PCLD梁动力学优化模块。两种方法的优化结果一致,验证本文计算结果的正确性。     

Vibration of a three-layered viscoelastic sandwich circular plate

The equations of motion for a three-layer sandwich circular plate with viscoelastic core are derived. The Donnell–Mushtari–Vlasov assumptions follow to simplify. For the case of iso-symmetric annular plate, five equations are further reduced to three equations. The assumed-mode method then yields the free and the forced solutions being characterized by six generalized coordinates for each circumferential wave number n. Due to the splitting of transversal and in-plane terms the study of vibration response can be reduced to the consideration of the SDOF linear oscillator with hysteretic damping. Numerical results first illustrated the frequency response function (FRF) for two different visco models and slight difference is observed. The effects of frequencies changes and damping due to viscoelastic material (VEM) core for several core-to-face thickness ratios are studied. The results, via the FRF's, show that a relatively thin visco (VEM) core can reduce vibration effectively, but as the core thickness exceeds it the damping gradually reduces. The embedded VEM core decreases the frequencies as expected. The damping effects upon individual modes are looked into as well. The results show that the n=0 mode is affected the most by VEM core.     

约束层阻尼板的有限元建模研究

粘弹性材料（VEM）的本构关系随频率和温度的变化而变化，对粘弹结构难以进行动特性分析及控制研究。基于Hamilton原理，给出了一种建立约束层阻尼（CLD）板动力学方程的新建模方法，建模时，考虑到VEM的纵向位移影响，并引入虚拟自由度，导出了标准二阶定常线性系统模型，从而避免因粘弹性材料导致的高阶非线性方程。采用GHM方法描述VEM的本构关系，它能直接与有限元法融合。算例分析了夹芯层为ZN—1型粘弹性材料的CLD悬臂板的动态特性，并与相关文献中的计算及试验结果进行比较，计算结果更加准确，表明新建模方法是准确的。     

Dynamic response analysis of rotating composite-VEM thin-walled beams incorporating viscoelastic materials in the time domain

This paper addresses the analytical modeling and dynamic response of the advanced composite rotating blade modeled as thin-walled beams and incorporating viscoelastic material. The blade model incorporates non-classical features such as anisotropy, transverse shear, rotary inertia and includes the centrifugal and coriolis force fields. The dual technology including structural tailoring and passive damping technology is implemented in order to enhance the vibrational characteristics of the blade. Whereas structural tailoring methodology uses the directionality properties of advanced composite materials, the passive material technology exploits the damping capabilities of viscoelastic material (VEM) embedded into the host structure. The VEM layer damping treatment is modeled by using the Golla-Hughes-McTavish (GHM) method, which is employed to account for the frequency-dependent characteristics of the VEM. The case of VEM spread over the entire span of the structure is considered. The displayed numerical results provide a comprehensive picture of the synergistic implications of both techniques, namely, the tailoring and damping technology on the dynamic response of a rotating thin-walled beam exposed to external time-dependent excitations.     

带气膜阻尼悬臂平板的振动特性研究

针对航空发动机叶片振动疲劳损伤问题,建立了带振动能量耗散机制的气膜阻尼理论模型.将气膜内气体的流动分别等效为牛顿流体的流动和泊肃叶流体的流动,推导出气膜阻尼结构的阻尼比方程,研究了带气膜阻尼悬臂平板的振动特性.目的是为航空发动机风扇叶片气膜阻尼的结构设计提供理论依据和技术支撑.结果表明:泊肃叶流体能够考虑更多的振动能量...     

主被动约束层阻尼在结构振动控制中的应用与设计

导出了自感知主被动阻尼控制梁结构的振动控制方程。引入速度负反馈形成闭环控制,对被动控制和主被动控制的控制效果进行了分析比较。分析了粘弹层、压电层厚度和压电片位置等结构参数变化以及材料参数变化对控制效果及结构频率的影响。并分析了主被动阻尼控制结构的特点和设计中应注意的问题。     

Passive vibration damping enhancement of piezoelectric shunt damping system using optimization approach

Piezoelectric materials can be used for structural damping because of their ability to efficiently transform mechanical energy to electrical energy and vice versa. The electrical energy may be dissipated through a connected load resistance. In this paper, a new optimization technique for the optimal piezoelectric shunt damping system is investigated in order to search for the optimal shunt electrical components of the shunt damping circuit connected to the piezoelectric patch on a vibrating structure for the structural vibration suppression of several modes. The vibration suppression optimization technique is based on the idea of using the piezoelectric shunt damping system, the integrated p-version finite element method (p-version FEM), and the particle swarm optimization algorithm (PSOA). The optimal shunt electrical components for the piezoelectric shunt damping system are then determined by wholly minimizing the objective function, which is defined as the sum of the average vibration velocity over a frequency range of interest. Moreover, the optimization technique is performed by also taking into account the inherent mechanical damping of the controlled structure with the piezoelectric patch. To numerically evaluate the multiple-mode damping capability by the optimal shunting damper, an integrated p-version FEM for the beam with the shunt damping system is modeled and developed by MATLAB. Finally, the structural damping performance of the optimal shunt damping system is demonstrated numerically and experimentally with respect to the beam. The simulated result shows a good agreement with that of the experimental result. This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin Jin-Young Jeon received his Ph.D. degree in Mechanical and Aerospace Engineering from Tokyo Institute of Technology in 2005. Dr. Jeon is currently a senior engineer at Digital Printing Division, Digital Media & Communications Business at Samsung Electronics Co., Ltd., Korea. His research interests are the areas of structural-acoustic optimization, sound quality, motion quality, and vibration control.     

主动约束层阻尼板的振动控制研究

研究局部附加主动约束层阻尼（active constrained layer damping,ACLD）结构板的振动控制问题。基于Hamilton原理，提出一种新的建立主动约束导板动力学模型的方法，同时给出一种用于确定粘弹材料GHM（Golla-Hughes-Mctavish）模型参数的优化问题。采用GHM方法描述弹性材料的本构关系，将粘弹性材料的动力特性描述与工程上最常用的有限元分析结合起来，推导得到ACLD结构的动力学方程为标准二阶定常线性系统方程。应用LQR控制理论进行结构振动控制仿真，结果表明，本文给出的新建模方法是准确可靠的，ACLD结构能够有效抑制结构振动。     

DYNAMIC BOUNDARY CONTROL OF BEAMS USING ACTIVE CONSTRAINED LAYER DAMPING

A globally stable boundary control strategy is developed to damp the vibration of beams fully treated with active constrained layer damping (ACLD) treatments. The devised boundary controller is compatible with the operating nature of the ACLD treatments where the strain induced generates a control force and moment acting at the boundary of the treated beam. The development of the boundary control strategy is based on a distributed-parameter model of the beam/ACLD system in order to avoid the classical spillover problems resulting from using ‘truncated’ finite element models. Such an approach makes the boundary controller capable of controlling all the modes of vibration of the ACLD-treated beams and guarantees that the total energy norm of the system is decreasing continuously with time. The control strategy is provided also with a dynamic compensator to shape the vibration damping characteristics of the ACLD in the frequency domain. The effectiveness of the ACLD in damping out the vibration of cantilevered beams is determined for different control gains and compared with the performance of conventional passive constrained layer damping (PCLD). The results obtained demonstrate the high damping characteristics of the boundary controller particularly over broad frequency bands.     

基于渐进法的约束阻尼结构拓扑多目标动力学优化

为实现阻尼结构减振优化,从阻尼材料的力学本构出发,基于虚功原理建立了约束阻尼板动力学平衡方程,从阻尼耗能角度推导出模态损耗因子解析计算式。构建了以模态损耗因子最大且模态频率变动最小为目标、以阻尼材料用量为约束的阻尼板多目标优化数学模型。在对模态损耗因子及模态频率灵敏度进行推导的基础上,构建了归一化复合灵敏度算式,并引入拓扑渐进法求解优化模型。编制出阻尼板渐近法优化程序,并对阻尼板进行了优化仿真。结果显示,采用多目标拓扑渐进优化,既能大幅提高阻尼材料的减振效能,又能保证阻尼板频率特性的稳定,且可较大幅度地降低阻尼材料用量。对阻尼板进行了谐响应分析,验证了优化结果的有效性。该优化法在对结构动力学特性有严格要求的减振设计中存在应用前景。     

Modeling and analysis of rotating plates by using self-sensing active constrained layer damping

This paper proposes a new finite element model for active constrained layer damped (CLD) rotating plate with self-sensing technique. Constrained layer damping can effectively reduce the vibration in rotating structures. Unfortunately, most existing research models the rotating structures as beams that are not the case many times. It is meaningful to model the rotating part as plates because of improvements on both the accuracy and the versatility. At the same time, existing research shows that the active constrained layer damping provides a more effective vibration control approach than the passive constrained layer damping. Thus, in this work, a single layer finite element is adopted to model a three-layer active constrained layer damped rotating plate. Unlike previous ones, this finite element model treats all three layers as having the both shear and extension strains, so all types of damping are taken into account. Also, the constraining layer is made of piezoelectric material to work as both the self-sensing sensor and actuator. Then, a proportional control strategy is implemented to effectively control the displacement of the tip end of the rotating plate. Additionally, a parametric study is conducted to explore the impact of some design parameters on structure??s modal characteristics.     

Concrete-based constrained layer damping

This paper describes a novel structural damping method that allows a fabricated (welded) machine tool structure to be designed for minimum cost and maximum dynamic stiffness comparable to polymer concrete structures. The damping method is a constrained layer damping (CLD) design where the layers are replicated in place using expanding concrete inside of viscoelastic damping inserts. The novel design is highly flexible and economical while providing excellent damping for a wide range of structural shapes.     

约束阻尼板双线性材料插值法拓扑动力学优化

为减小阻尼板质量并提高减振性能,研究了结构动力学优化技术。构建了以移动常数与模态损耗因子差值为目标、阻尼层单元密度为拓扑变量、阻尼层体积用量及振动模态频率为约束的阻尼板优化模型。利用序列凸规划法构造目标函数的凸性逼近式,采用拉格朗日乘子法解算逼近函数,以获取全局优化的阻尼层布局。利用模态损耗因子与模态应变能的本构关系推导目标函数关于拓扑设计变量的灵敏度,基于K-T条件构造拓扑变量迭代式。引入双线性插值函数惩罚拓扑变量并使其值聚集于0或1,编写并实现了悬臂阻尼板优化程序。当阻尼层体积用量控制在50%时,1阶模态损耗因子增大52.29%,灰度单元占比1.78%。阻尼板谐响应分析表明优化构形具良好减振特性。双线性插值优化既能充分发挥阻尼层的耗能效力又可大幅减少灰度阻尼单元数。     

具有主、被动约束层阻尼的拉压型结构研究

粘弹性材料已广泛用于阻尼结构的弯曲振动。具有主动与被动相结合的约束层 阻尼技术研究目前也多集中于梁、板等结构的弯曲振动,而主、被动约束层阻尼拉压 型结构则很少研究。本文给出了一种主、被动约束层阻尼拉压型结构模型,推导了一 些数学表达式,给出了优化设计方法及分析结果。     

局部粘弹性被动约束阻尼梁的振动分析

针对夹层约束阻尼梁结构的减振特性进行深入研究.应用粘弹性材料的耗能原理结合模态应变能法对局部粘弹性被动约束阻尼简支梁的振动特性进行数值分析,对梁铺设阻尼层前后的时域和频域特性分别进行比较,可以得出约束阻尼梁的振动得到有效抑制,同时看到模态应变能法对板梁结构的分析更便捷.     

Vibration suppression of atomic-force microscopy cantilevers covered by a piezoelectric layer with tensile force

In this paper, vibration suppression of a micro-beam covered by a piezoelectric layer is studied. The micro-beam is modeled with the specific attention to its application in AFM. The AFM micro-beam is a cantilever one which is stimulated close to its natural frequency by applying a harmonic voltage to the piezoelectric layer. The beam is an Euler-Bernoulli beam which abbeys Kelvin-Voigt model. Using such model supplies the comparison between elastic and viscoelastic beams; and one of the most important properties of viscoelastic materials, damping effect can readily be investigated. The pump provides an axial load with the result that it suppresses the vibrations. First, the vibration equations are extracted using Lagrangian and extended Hamiltonian method in vertical, longitudinal, as well as torsional directions and are discretized by exploiting the Galerkin mode summation approach. The discretized time-domain equations are solved by the aid of the Runge-Kutta method. The viscoelastic beam is compared with the elastic one, and the effects of damping ratio on vibration responses are presented. Additionally, the effects of micro-pump load, excitation voltage, and initial twist angle are investigated on the amplitude of vibration and natural frequency of system. It is observed that viscoelasticity of beam and axial load of the pump reduce vibrations and provide uniform time-domain responses without beatings.     

剪切型阻尼U型柔性铰链设计与实验分析

根据柔性铰链的无阻尼结构特点,并利用黏弹性阻尼材料的剪切损耗特性,提出一种剪切型阻尼U型柔性铰链的结构模型,并结合GHM(Goulla-Hughes-MacTavish,简称GHM)黏弹性理论模型建立带阻尼铰链动力学方程。该铰链通过提高外加黏弹性阻尼层材料的剪切效应,达到增强结构阻尼目的。为了测试剪切型阻尼结构对该U型铰链的振动抑制效果,对其进行自由振动信号测试和动态力学分析(dynamic mechanical analysis,简称DMA)实验。结果显示,该阻尼结构能使铰链结构在120~150Hz的共振频段内因振幅增大,阻尼层剪切效应加剧,出现明显的阻尼损耗峰值,有效增强了铰链的结构阻尼。     

Physical nature and properties of dynamic surface layers in friction

Simulations of the dynamic processes in micro contacts with the Method of Movable Cellular Automata (MCA) show that their common feature is formation of a boundary layer where intensive plastic deformation and mixing processes occur. The boundary layer is well localized and does not spread to deeper layers. We call this layer a ‘quasi-fluid layer’. The thickness of the boundary layer is roughly proportional to the viscosity of solid. This parameter thus should play an important role in determining the wear rate of materials in friction.To better understand the physical nature of the dynamic surface layers, we consider a simplified model of a solid consisting of many thin sheets, interacting with each other according to a ‘friction law’ of Coulomb type. A quasi-fluid layer is always developing if the ‘friction law’ does allow a bi-stability in some range of stresses with one static and one dynamic state at the same stress.The existence of the boundary layer motivates us to change the existing approach to calculating wear in frictional contacts. The wear should be understood not as ‘fracture’ but as ‘mass transport out of friction zone’. The process of stochastic transport of wear particles in the closed friction zone is at the same time the main mechanism of development of surface topography.A very important fact is that the conditions for appearance of a quasi-fluid layer depend on the minimal size of structural elements of the medium, which means that this effect cannot be principally described in the frame of a continuum model.     

Vibration control efficiency of piezoelectric shunt damping system

The piezoelectric shunt damping technique based on the direct piezoelectric effect has been known as a simple, low-lost, lightweight, and easy to implement method for passive damping control of structural vibration. In this technique, a piezoelectric material is used to transform mechanical energy to electrical energy. When applying the piezoelectric shunt damping technique to passively control structural vibration, the piezoelectric materials must be bonded on or embedded in host structure where large strain is induced during vibration, thus to ensure vibrational mechanical energy to be transformed into electrical energy as much as possible. In this paper, the concept of vibration control efficiency of a piezoelectric shunt damping system is proposed and studied theoretically and experimentally. In the study, PZT patches are used as energy converter, and the vibration control efficiency is expressed by the vibration reduction rate per area of the PZT patches. Emphasis is laid on the effect of the generalized electromechanical coupling coefficient K₃₁ on the vibration control efficiency. Four PZT patches with different sizes are bonded on the geometrical central area of four similar clamped aluminum plates, respectively, and vibration control experiments are conducted for these plates using the R-L shunt circuit. The results indicate that the bigger the coupling coefficient K₃₁, the larger the rate of vibration reduction, and hence, the higher the vibration control efficiency. It also shows that the vibration responses of the first mode of the plates bonded with different PZT patches can be reduced by about 30.5%，48.58%，85.47%, and 89.91%, respectively. It comes to a conclusion that the vibration control efficiency of the piezoelectric shunt damping system decreases with the increase of the area of the PZT patch, whereas the vibration reduction of the plate increases with the area of the PZT patch. Therefore, it is necessary to make topology optimization for the PZT patch in the vibration control utilizing the piezoelectric shunt damping technique.