VIBRATION SUPPRESSION OF A BEAM STRUCTURE BY INTERMEDIATE MASSES AND SPRINGS

A method based on the dynamic Green function has been proposed to determine the optimum values of masses and/or springs and their locations on a beam structure in order to confine the vibration at an arbitrary location. In the analysis, the beam is driven by a harmonic external excitation. The added masses on the beam and the springs attached are modelled as simple reactions that provide transverse forces to the beam. These forces act as secondary forces that reduce the response caused by the external force. Numerical simulation shows that the vibration of the beam can be confined in a certain region by the presence of masses and springs in best arrangement. This method is demonstrated for both a simply supported and a cantilever beam. An experimental set-up was designed in which a simply supported beam is excited by an electrodynamic shaker and the response of the beam is measured using an He-Ne laser system. This assures very accurate measurements and avoids any additional loading effects as in the case of accelerometers. Comparisons of the theoretical and the experimental results show good agreement.     

原子力显微镜探针悬臂几何结构变化对高次谐波信息增强的研究

轻敲模式原子力显微镜高次谐波信号包含待测样品表面纳米力学特性等方面的信息, 但是传统原子力显微镜的高次谐波信号非常微弱. 里兹法证明在探针悬臂的特定位置打孔可以实现探针的内共振从而增强高次谐波信号强度. 本文通过有限元仿真计算获得探针第一共振频、第二共振频及其比值随着孔的尺寸和位置变化的规律. 在实验上通过聚焦离子束在探针悬臂上打孔使其第二共振频约为第一共振频的6倍, 提高了第6次谐波信号的信噪比, 并在实验室研制的高次谐波成像实验装置上获得了6次谐波图像. 关键词： 轻敲模式原子力显微镜 探针悬臂几何结构 高次谐波 聚焦离子束加工     

Modal Control of Cantilever Beam Using a Gyrostabilizer

In this paper, an experimental model of a horizontal cantilever beam with a rotating/oscillating attached to the shaker for harmonic excitation at the one end and a gyrostabilizer at the other end is built to verify the equations of the Lagrangian model. The primary focus of the study was to investigate the parameters of excitation amplitude, natural frequency, rotating mass (disk mass), and disk speed of gyro that would minimize the amplitude of the beam to identify these effects. Numerical and experimental results indicate that the angular momentum of the gyrostabilizer is the most effective parameter in the reduction of beam displacement.     

Autoparametric vibration absorber effect to reduce the first symmetric mode vibration of a curved beam/panel

This paper presents the implementation of autoparametric phenomena to reduce the symmetrical vibration of a curved beam/panel under external harmonic excitation. The internal energy transfer of a first symmetric mode into first anti-symmetric mode in a curved panel is one example of autoparametric vibration absorber effect. This is similar to the vibration energy transfer from the resonance of a primary structure to the resonance of a secondary spring–mass (tuned mass damper). The nonlinear response of a curved beam is analyzed using an equation with two modes, and a shaker test. The effect of different configurations of the curve beam/panel, including damping ratios and excitation levels, on the energy transfer of the first symmetric mode to the first anti-symmetric mode was studied.The conventional tuned mass damper (TMD) can reduce the resonance response by energy transfer using damping dissipation, whereas an autoparametric vibration absorber (AVA) can reduce the resonance response by energy transfer using parametric interaction. The results indicate that there is a non-absorption region in which vibration is amplified. For the AVA, the non-absorption region can be minimized by tuning the resonance frequency of the first anti-symmetric mode to half of the first symmetric mode resonance frequency using additional mass. No additional damping material is required for achieving sufficient vibration reduction. The AVA can maintain reliable performance in hot and corrosive environments where damping material cannot perform effectively. This paper presents the first successful experimental results of an autoparametric vibration absorption mechanism in a curved beam.     

In-plane vibration characterization of microelectromechanical systems using acousto-optic modulated partially incoherent stroboscopic imaging

A technique using acousto-optic modulated partially incoherent stroboscopic imaging for measurement of in-plane motion of microelectromechanical systems (MEMS) is presented. Vibration measurement is allowed by using flashes of the partially incoherent light source to freeze the positions of the microstructure at 12 equally spaced phases of the vibration period. The first-order diffracted beam taken out by an acousto-optic modulator (AOM) from the light beam of a laser is made partially incoherent by a rotating diffuser and then serves as the stroboscopic light source. Both the MEMS excitation signal and the flash control signal are provided by a dual-channel function generator. The main advantage of this measurement method is the absence of a stroboscopic generator and a high speed digital camera. Microscale prototypes are fabricated and tested. Quantitative estimates of the harmonic responses of the prototypes are obtained from the recorded images. The results agree with those obtained with a commercial MEMS motion analyzer^TM with relative errors less than 2%.     

The use of an acoustic signal in diagnosing a cross crack in a cantilever beam

The results of experimental investigations are described on the basis of which a method of diagnosing the formation and growth of a cross crack in a cantilever beam is developed. The diagnostic criterion is the nonlinear distortion factor calculated as the ratio of the rms value of the higher harmonic amplitudes to the rms value of the amplitude of the investigated acoustic signal. It is established that, by using this factor, it is possible to detect the initiation of a cross crack in a cantilever beam, observe the change in the beam structure within the period before its fracture, and monitor the crack’s development.     

基于悬臂梁调谐技术的光纤光栅无源振动监测

采用匹配光纤光栅设计了一种结构简单的振动信号无源监测装置.该装置利用悬臂梁调谐技术能够将微小振动信号转化为光电探测器可探测的光强信号,利用示波器实现实时监测.实验中对振幅为3mm的简谐振动信号进行了监测,测量结果与振动频率一致,可测量7～20Hz的振动,信噪比不低于14.9dB.监测频率受限是因为悬臂梁的性质,如采用金属材料或者采用齿轮组对转子进行减速,该装置可探测更高的频率.     

Theoretical and experimental study on the transverse vibration properties of an axially moving nested cantilever beam

An axially moving nested cantilever beam is a type of time-varying nonlinear system that can be regarded as a cantilever stepped beam. The transverse vibration equation for the axially moving nested cantilever beam with a tip mass is derived by D’Alembert?s principle, and the modified Galerkin?s method is used to solve the partial differential equation. The theoretical model is modified by adjusting the theoretical beam length with the measured results of its first-order vibration frequencies under various beam lengths. It is determined that the length correction value of the second segment of the nested beam increases as the structural length increases, but the corresponding increase in the amplitude becomes smaller. The first-order decay coefficients are identified by the logarithmic decrement method, and the decay coefficient of the beam decreases with an increase in the cantilever length. The calculated responses of the modified model agree well with the experimental results, which verifies the correctness of the proposed calculation model and indicates the effectiveness of the methods of length correction and damping determination. Further studies on non-damping free vibration properties of the axially moving nested cantilever beam during extension and retraction are investigated in the present paper. Furthermore, the extension movement of the beam leads the vibration displacement to increase gradually, and the instantaneous vibration frequency and the vibration speed decrease constantly. Moreover, as the total mechanical energy becomes smaller, the extension movement of the nested beam remains stable. The characteristics for the retraction movement of the beam are the reverse.     

The effects of large vibration amplitudes on the dynamic strain response of a clamped-clamped beam with consideration of fatigue life

The effects of large vibration amplitudes on the dynamic strain response, near to the fundamental resonance, of a clamped-clamped, thin beam is examined. Complementary theoretical and experimental studies showed that the harmonic distortion of the induced total strain, due to sinusoidal excitation at mid-span, is mainly due to the axial strain component. A limited set of fatigue experiments showed the considerable decrease in fatigue life, which occurs due to non-linear vibration, compared to that of a cantilevered beam of the same material. The statistical approach to the analysis of non-linear vibration induced by random loading is examined theoretically and experimentally, good correlation being achieved between predicted and measured fatigue lives.     

The effects of large vibration amplitudes on the fundamental mode shape of a clamped-clamped uniform beam

The non-linear vibration of a clamped-clamped beam at large displacement amplitudes is examined in this work. Complementary theoretical and experimental studies have been carried out to examine the amplitude dependence of the fundamental mode shape and its derivatives and the spatially-dependent harmonic distortion of the transverse displacement which occurs at large deflections.     

非线性磁式压电振动能量采集系统建模与分析

为便于评价、优化磁式压电振动能量采集系统的性能,系统研究了该类系统的建模与分析方法,建立了非线性的分布参数模型用于描述系统的非线性动力学行为,并采用谐波平衡法给出了谐波响应的解析解.随后利用仿真模型分析了磁铁间距、加速度幅值、负载阻抗对输出功率的影响,比较了不同激励频率和加速度幅值下的最优阻抗.结果表明:双稳态特性适用于低强度的振动环境,且愈接近临界区域,输出功率愈高,而单稳态渐硬特性适用于高强度振动环境,其最优间距并不靠近临界区域;阱间大幅运动和阱内小幅运动均存在高低能量态共存的现象,愈接近临界区域,现象愈明显;激振频率是影响最优负载阻抗的决定性因素.     

High Performance Open Loop Control of Scanning with a Small Cylindrical Cantilever Beam

The steady-state response motion of a base excited cantilever beam with circular cross-section excited by a unidirectional displacement will fall along a straight line. However, achieving straight-line motion with a real cantilever beam of circular cross-section is difficult to accomplish. This is due to the fact that nonlinear effects, small deviations from circularity, asymmetric boundary conditions, and actuator cross coupling can induce whirling. The vast majority of previous work on cantilever beam whirling has focused on the effects of system nonlinearities. We show that whirling is a much broader problem in the design of resonant beam scanners in that the onset of whirling does not depend on large amplitude of motion. Rather, whirling is the norm in real systems due to small system asymmetries and actuator cross coupling. It is therefore necessary to control the growth of the whirling motion when a unidirectional beam motion is desired. We have developed a novel technique to identify the two eigen directions of the beam. Base excitation generated by virtual electrodes along these orthogonal eigen axes of the cantilever beam system generates tip vibration without whirl. This leads to accurate open loop control of the motion of the beam through the combined actuation of two pairs of orthogonally placed actuator electrodes.     

Transient response optimization of vibrating structures by Liapunov's second method

Liapunov's second method is applied to minimize an integrated square performance measure for damped vibrating structures subjected to initial excitation. The method reduces the calculation of the performance measure and its derivatives with respect to design parameters to the solution of a set of linear algebraic equations. The computational effectiveness of the method is illustrated by applying it to the classical vibration absorber and to a cantilever beam carrying an absorber at its midpoint.     

Performance of a cantilever piezoelectric energy harvester impacting a bump stop

Piezoelectric cantilever beam energy harvesters are commonly used to convert ambient vibration into electrical energy. In practical applications, energy harvesters are subjected to large shocks which can shorten the service life by causing mechanical failure. In this work, a bump stop is introduced into the design of a piezoelectric cantilever beam energy harvester to limit the maximum displacement of the cantilever and prevent excessively high bending stresses developing as a result of shocks. In addition to limiting the maximum displacement of the beam, it is inevitable that the deflected shape of the beam and the electrical output are modified. A theoretical model for a piezoelectric cantilever beam harvester impacting against a stop is derived, which aims to develop an understanding of the vibration characteristics of the cantilever and quantify how the electrical output of the harvester is affected by the stop. An experiment is set up to measure the dynamics and the electrical output of a bimorph energy harvester and to validate the theoretical model. Numerical simulation results are presented for energy harvesters with different initial gaps and different stop locations, and it is found that the reduction in maximum bending stress is at the expense of the electrical power of the harvester.     

Compact FBG diaphragm accelerometer based on L-shaped rigid cantilever beam

A compact fiber Bragg grating(FBG) diaphragm accelerometer based on L-shaped rigid cantilever beam is proposed and experimentally demonstrated.The sensing system is based on the integration of a flat diaphragm and an L-shaped rigid cantilever beam.The FBG is pre-tensioned and the two side points are fixed,efficiently avoiding the unwanted chirp effect of grating.Dynamic vibration measurement shows that the proposed FBG diaphragm accelerometer provides a wide frequency response range(0-110 Hz) and an extremely high sensitivity(106.5 pm/g),indentifying it as a good candidate for embedding structural health monitoring and seismic wave measurement.     

充液管路系统流体声与结构声的复合有源控制

采用基于谐频自适应控制算法的有源消声与消振系统对充液管路系统突出的低频线谱噪声进行有源控制实验研究.建立了泵水循环管路实验系统,在管路中安装有源消声器对流体声进行控制,在管路出口障板上采用8×8通道有源消振系统控制结构声辐射。开展的低频线谱噪声与振动有源控制实验结果表明,在50~200 Hz频带内,通过结合有源噪声与振动控制可在多数频点取得10 dB以上的降噪效果。针对该实验系统,通过分别控制流体声和结构声分析了两者的贡献.实验结果验证了有源消声与消振系统具有较好的降噪性能,各频点处流体声与结构声占比情况不同,需要综合控制流体声与结构声才可以取得显著的降噪效果。      

基于单幅数字散斑投影及图像相关的离面振动测量

采用单幅数字散斑图投影及高速数字图像采集技术,研究了动态离面位移的测量。采用商用液晶投影仪将计算机产生的模拟散斑图投影到待测动态变形物体表面,由高速数字图像采集设备摄取并保存变形散斑图,采用时间序列数字图像相关软件计算出物体表面各点随时间变化的离面位移。这种方法用于振动分析时不仅可以获得振型分布,而且还可以获得各点的振幅值。与现有的激光频闪照相测振及激光多普勒测振等方法相比,具有光学系统简单,可全场定量测量。悬臂梁振动实验结果证实了该方法的有效性。     

Experimental identification of viscous damping in linear vibration

This paper is concerned with the experimental evaluation of the performance of viscous damping identification methods in linear vibration theory. Both existing and some new methods proposed by the present authors [A.S. Phani, J. Woodhouse, Viscous damping identification in linear vibration, Journal of Sound and Vibration 303 (3–5) (2007) 475–500] are applied to experimental data measured on two test structures: a coupled three cantilever beam with moderate modal overlap and a free–free beam with low modal overlap. The performance of each method is quantified and compared based on three norms and the best methods are identified. The role of complex modes in damping identification from vibration measurements is critically assessed.     

On utilizing delayed feedback for active-multimode vibration control of cantilever beams

We present a single-input single-output multimode delayed-feedback control methodology to mitigate the free vibrations of a flexible cantilever beam. For the purpose of controller design and stability analysis, we consider a reduced-order model consisting of the first n vibration modes. The temporal variation of these modes is represented by a set of nonlinearly coupled ordinary-differential equations that capture the evolving dynamics of the beam. Considering a linearized version of these equations, we derive a set of analytical conditions that are solved numerically to assess the stability of the closed-loop system. To verify these conditions, we characterize the stability boundaries using the first two vibration modes and compare them to damping contours obtained by long-time integration of the full nonlinear equations of motion. Simulations show excellent agreement between both approaches. We analyze the effect of the size and location of the piezoelectric patch and the location of the sensor on the stability of the response. We show that the stability boundaries are highly dependent on these parameters. Finally, we implement the controller on a cantilever beam for different controller gain-delay combinations and assess the performance using time histories of the beam response. Numerical simulations clearly demonstrate the controller ability to mitigate vibrations emanating from multiple modes simultaneously.