Active structural acoustics control of beams using active constrained layer damping through loss factor maximization

Vibration and acoustic control of beams with classical boundary conditions using active constrained layer damping is presented. The control input that maximizes the loss factor of the active constrained layer damping is determined through taking the first variation of the loss factor with respect to the control input. Although the loss factor is a positive definite quantity, the first variation yields control input that maximizes the factor. The resulting control input significantly reduces the vibration and acoustic response of the beams at their resonant frequencies.     

Experimental evaluation of a piezoelectric vibration absorber using a simplified fuzzy controller in a cantilever beam

This study presents a novel resonant fuzzy logic controller (FLC) to minimize structural vibration using collocated piezoelectric actuator/sensor pairs. The proposed fuzzy controller increases the damping of the structures to minimize certain resonant responses. The vibration absorber is first experimentally examined by a cantilever beam test bed for impulse and near-resonant excitation cases. Moreover, the effectiveness of the new fuzzy control design to a state-of-the-art control scheme is compared through the experimental studies. The experimental results indicate the proposed controller is highly promising for this application field. Our results further demonstrate that the fuzzy approach is much better than traditional control methods. In summary, a novel vibration absorption scheme using fuzzy logic has been demonstrated to significantly enhance the performance of a flexible structure with resonant response.     

多端输出等幅振动的纵振动变换体

提出了一种一端输入多端输出等幅振动的纵振动方向变换体。变换体由输入杆、半球形过渡体和输出杆组成,通过半球形过渡体将一个输入杆与多个输出杆耦连为一体,并且多个输出杆呈立体分布,可实现一端纵振动输入多个方向上纵振动均匀输出。利用振动变换体端面的自由边界条件,以及各组件连接处的纵向位移、纵向力、横向位移和转角连续条件,推导了纵振动方向变换体的频率方程。解析计算了不同几何尺寸的纵振动变换体的谐振频率,与有限元法的计算值及实验测试值基本吻合。将纵振方向变换体的输入端与谐振频率为19.8 kHz的换能器相连,利用激光测振仪测试了纵振动变换体各输出端振型及各输出端相对于输入端的振幅放大系数,结果显示纵振动经过方向变换体成功地传输到了变换体的各输出杆的端面,且各输出端的振幅基本相等。      

Reduced-order modeling for mistuned centrifugal impellers with crack damages

An efficient method for nonlinear vibration analysis of mistuned centrifugal impellers with crack damages is presented. The main objective is to investigate the effects of mistuning and cracks on the vibration features of centrifugal impellers and to explore effective techniques for crack detection. Firstly, in order to reduce the input information needed for component mode synthesis (CMS), the whole model of an impeller is obtained by rotation transformation based on the finite element model of a sector model. Then, a hybrid-interface method of CMS is employed to generate a reduced-order model (ROM) for the cracked impeller. The degrees of freedom on the crack surfaces are retained in the ROM to simulate the crack breathing effects. A novel approach for computing the inversion of large sparse matrix is proposed to save memory space during model order reduction by partitioning the matrix into many smaller blocks. Moreover, to investigate the effects of mistuning and cracks on the resonant frequencies, the bilinear frequency approximation is used to estimate the resonant frequencies of the mistuned impeller with a crack. Additionally, statistical analysis is performed using the Monte Carlo simulation to study the statistical characteristics of the resonant frequencies versus crack length at different mistuning levels. The results show that the most significant effect of mistuning and cracks on the vibration response is the shift and split of the two resonant frequencies with the same nodal diameters. Finally, potential quantitative indicators for detection of crack of centrifugal impellers are discussed.     

An embedded sensitivity approach for diagnosing system-level vibration problems

In diagnosing a system-level vibration problem, the goals are to identify which component or components(s) are most responsible for the phenomenon and which changes to the system are most likely to mitigate the problem. The use of sensitivity analysis in diagnosing system-level vibration phenomena is examined in this work. It is shown that even if only a small subset of measured system input–output functions is available, an appropriate analytical parameterization of these functions leads to simple relationships between the measured data and the desired embedded sensitivity functions. These functions are then reformulated in terms of transmissibility functions with respect to a single input using a novel modal deflection chain technique in order to accommodate system-level operating response data in the absence of input measurements. The embedded sensitivity approach is used to examine two competing design modifications for reducing a structure-borne noise problem in an exhaust system. The sensitivity analysis shows that although both modifications mitigate the resonant vibration problem of interest, one of the modifications is more effective than the other because it introduces less overall change in the forced response characteristics at other frequencies.     

AN ESTIMATOR-BASED SLIDING-MODE CONTROL FOR MANEUVERING A FLEXIBLE SPACECRAFT

An estimator-based sliding-mode controller (ESMC) is discussed for a linear stochastic system with a known disturbance and is utilized in a flexible spacecraft for the reduction of residual vibration while allowing natural deflection during operation. By converting the tracking problem into a regulator problem, the ESMC minimizes the expected value of the guadratic objective function composed of errors which always remain in the intersection of sliding hypersurfaces. For the numerical evaluation to take place in a flexible with a flexible spacecraft, a large slewing maneuver strategy is devised, with a tracking model for the nominal trajectory. A start-coast-stop strategy for an economical maneuver is employed in conjunction with the input shaping technique. The performance and efficacy of the proposed control scheme are illustrated with a comparison of different maneuvering strategies.     

Resonance in Defect Turbulence under Periodic External Force

The periodically forced spatially extended Brusselator is investigated in the chaotic regime. We explore resonant or non-resonant patterns generated under various forcing frequencies and forcing amplitudes. Resonant spatially uniform oscillation and irregular structures are found. Furthermore two types of regular spatial patterns are generated under appropriate parameters. Our results of numerical simulations demonstrate that periodic force can give rise to resonant patterns in forced systems of spatiotemporal chaos similar to the situation of forced systems of regular oscillations.     

An adaptive pneumatic suspension based on the estimation of the excitation frequency

A pneumatic suspension that can adapt itself to the incoming vibration is presented in this paper. A switching control strategy between two different configurations is proposed and studied. The objective is to avoid undesirable resonant frequencies. The control procedure is based on the pre-knowledge of the incoming vibration frequency, and when this frequency is unknown, a very efficient prediction technique is used. The results show that the adaptable suspension has improved performance as compared to any of its passive counterparts. The transient response when switching typically takes less than three cycles and does not hinder the suspension performance.     

有界大洋对纬向风强迫的响应及共振

为揭示北太平洋主、次要气候模态即太平洋年代际振荡(PDO)和北太平洋流涡振荡(NPGO)的形成机理及其振荡周期与大洋水平尺度之间的联系,采用中纬β通道中的约化重力准平衡线性大洋模型,解析求解了纬向风强迫下的大洋流场响应,讨论了其中的共振问题.1)有界大洋的响应形态分别类似于冬季PDO和NPGO的流场模.2)响应形态分别表现为在大洋西海岸以东,前者有一个椭圆状流涡,后者有南北两个旋转方向相反的流涡并构成流涡偶;在整个大洋,前者有一个洋盆尺度环流,后者在大洋南北分别有两个旋转方向相反的洋盆尺度环流;在中纬度西风急流异常位置偏北和偏南,则能分别强迫出以上的两种情况.3)大洋流场对纬向风场强迫的响应频率(周期)与纬向风强迫频率(周期)相同,但大洋响应要滞后于纬向风的强迫;而响应流场即流函数的强度则与纬向风强迫的大小成正比.当纬向风强迫频率(周期)与该大洋固有频率(周期)相同时,二者会有共振发生,此时大洋响应最为强烈;而二者频率(周期)相差较远时,响应则不大.摩擦越小共振就越强,共振的个数也越多.有界大洋东西向的长度对其固有频率(周期)即共振频率(周期)有明显影响,并起着决定作用;当该长度减小时,相邻两个共振周期的间隔会增大.海洋大气间的两两非线性相互作用,使得随机风场的振荡包含了从极低频到高频的各种成分;通过该共振,可从中挑选出与大洋固有频率相同或相近的共振频率,在该频率上流场对风场的响应最为强烈,从而也就锁定了PDO和NPGO的周期.最终结论为:非线性相互作用、风场对流场的强迫、共振是造成PDO和NPGO的三个关键因子;该解析解的性质为时变的共振Rossby波.     

Nonlinear vibration of micromachined asymmetric resonators

In this paper, the nonlinear dynamics of a beam-type resonant structure due to stretching of the beam is addressed. The resonant beam is excited by attached electrostatic comb-drive actuators. This structure is modeled as a thin beam-lumped mass system, in which an initial axial force is exerted to the beam. This axial force may have different origins, e.g., residual stress due to micro-machining. The governing equations of motion are derived using the mode summation method, generalized orthogonality condition, and multiple scales method for both free and forced vibrations. The effects of the initial axial force, modal damping of the beam, the location, mass, and rotary inertia of the lumped mass on the free and forced vibration of the resonator are investigated. For the case of the forced vibration, the primary resonance of the first mode is investigated. It has been shown that there are certain combinations of the model parameters depicting a remarkable dynamic behavior, in which the second to first resonance frequencies ratio is close to three. These particular cases result in the internal resonance between the first and second modes. This phenomenon is investigated in detail.     

Vibration testing based on impulse response excited by pulsed-laser ablation: Measurement of frequency response function with detection-free input

We have developed a non-contact vibration-measurement system that is based on impulse excitation by laser ablation (i.e. laser excitation) to measure the high-frequency-vibration characteristics of objects. The proposed method makes it possible to analyse the frequency response function just by measuring the output (acceleration response) of a test object excited by pulsed-laser ablation. This technique does not require detection of the input force. Firstly, using a rigid block, the pulsed-laser-ablation force is calibrated via Newton's second law. Secondly, an experiment is conducted in which an object whose natural frequency lies in the high-frequency domain is excited by pulsed-laser ablation. The complex frequency spectrum obtained by Fourier transform of the measured response is then divided by the estimated pulsed-laser-ablation force. Finally, because of the error involved in the trigger position of the response with respect to the impulse arrival time, the phase of the complex Fourier transform is modified by accounting for the response dead time. The result is the frequency response function of the object. The effectiveness of the proposed method is demonstrated by a vibration test of an aluminium block.     

Input shaping and variable structure control for simultaneous precision positioning and vibration reduction of flexible spacecraft with saturation compensation

This paper treats the question of simultaneous robust attitude control and vibration suppression of orbiting spacecraft with flexible appendages. The spacecraft consists of a rigid body and two flexible appendages and the finite dimensional representation of the flexible spacecraft is assumed to be of arbitrary order. Robust nonlinear variable structure control (VSC) strategy integrated with input shaping technique is concerned for the pitch angle control and elastic vibration suppression under actuator saturation limit. More specially, the input shaper is implemented outside of the feedback loop, which is designed for the reference model and achieves the exact elimination of residual vibration; while for the feedback loop, the variable structure controller is designed to make the closed-loop system behave like the reference model with the input shaper in the presence of parametric uncertainty, external disturbances and actuator saturation. To prevent the presence of input saturation from destroying the system performance, a saturation compensator is designed as well for the variable structure attitude control system. For the synthesis of the attitude controller, only the pitch angel and its derivative are used. Simulation results are presented which show that in the closed loop, pitch angel control and elastic mode stabilization are accomplished in spite of uncertainty and external disturbance.     

AN INVERSE METHOD TO COMPUTE EQUIVALENT FORCES ON A STRUCTURE BASED ON SOUND POWER MEASUREMENTS

When modelling the dynamic response of an existing structure to predict the effects of design modifications, many types of forces are difficult to characterize, e.g., those due to unsteady flows or acoustic excitation. To model the forcing function in such cases, a method is presented which solves for an equivalent forcing function based on sound power measurements. The method assumes that the equivalent forcing function may be represented with a superposition of force distributions on a mode-by-mode basis, i.e., there is one force distribution per eigenvalue with the shape of the eigenvector. The method is applied to cases where the structure is lightly damped and has low modal density. Experimental results show that the method accurately predicts the effect of design changes on the structure's radiated sound power. The accuracy of the method is sensitive to small differences between the experimental and theoretical natural frequencies and thus it is important to match the damped natural frequencies of the physical structure as accurately as possible.     

Coupling analysis of a matched piezoelectric sensor and actuator pair for vibration control of a smart beam

This paper presents a theoretical and experimental study of the in-plane and out-of-plane coupling of a matched piezoelectric sensor/actuator pair bonded on a beam. Both the sensor and actuator are triangularly shaped polyvinylidene fluoride (PVDF) transducers and are intended to provide a compact sensor/actuator system for beam vibration control. The measured sensor-actuator frequency response function has shown an unpredicted increase in magnitude with frequency, which was found, to be due to in-plane vibration coupling. An analytical model has been developed to decompose the sensor-actuator response function into an in-plane contribution and an out-of-plane contribution. This in-plane coupling can limit the feedback control gains when a direct velocity feedback control is applied. A method called the j omega s compensation method is proposed to identify the effect of the in-plane vibration coupling at low frequencies. Even after this compensation, however, there was unexpected strong out-of-plane coupling at even modes, which may have been caused by a lack of accuracy in the shaping of the PVDF sensor and actuator. Numerical simulations have confirmed the sensitivity of the matched sensor/actuator pair with shaping errors.     

去耦覆盖层降噪性能评价指标的理论探讨

去耦覆盖层是降低水下结构声辐射的一个重要措施。为了给工程上去耦覆盖层降噪性能评价指标的选择提供理论参考,建立了点激励力作用下敷设去耦覆盖层的四端简支撑矩形板水下振动和声辐射理论模型,定义了可能表征去耦覆盖层降噪性能的五项评价指标。研究结果表明:只有振动传递损失相对独立于基板的长度、宽度和点激励力位置,而且能较好地描述去耦覆盖层隔离基板振动向水层传递的性能;而湿面均方振速插入损失较振动传递损失则能更好地反映辐射声功率插入损失,尤其在低频。作为评价指标,振动传递损失和湿面均方振速插入损失分别有各自的优点和缺点。      

多振子梁弯曲振动中的局域共振带隙

从梁的弯曲振动方程出发,利用传递矩阵法,给出了无限周期结构的一维多振子声子晶体梁的弯曲振动能带结构,并利用有限元方法计算了有限周期结构梁的弯曲振动频率响应.建立了多振子声子晶体梁的简化模型,推导出带隙起始截止频率公式.结果表明:一维多振子声子晶体梁具有比单振子声子晶体梁更宽更丰富的振动带隙,可应用于呈倍频关系的减振降噪中;振动在带隙频率范围内频率响应具有明显的衰减;所建立的简化模型与理论模型结果符合较好.研究工作为梁类结构的减振提供一种新的思路.     

Experimental and numerical investigations of resonant vibration characteristics for piezoceramic plates.

Electronic speckle pattern interferometry (ESPI) is a full field, non-contact technique for measuring the surface displacement of a structure subjected to static loading or, especially, to dynamic vibration. In this article we employ an optical system called the amplitude-fluctuation ESPI with out-of-plane and in-plane measurements to investigate the vibration characteristics of piezoceramic plates. Two different configurations of piezoceramic plates, namely the rectangular and the circular plates, are discussed in detail. As compared with the film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Because the clear fringe patterns will be shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Excellent quality of the interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes is demonstrated. The resonant frequencies of the piezoceramic plates are also measured by the conventional impedance analysis. From experimental results, we find that the out-of-plane vibration modes (type A) with lower resonant frequencies cannot be measured by the impedance analysis and only the in-plane vibration modes (type B) will be shown. However, both the out-of-plane (bending) and in-plane (extensional) vibration modes of piezoceramic plates are obtained by the AF-ESPI method. Finally, the numerical finite element calculations are also performed, and the results are compared with the experimental measurements. It is shown that the numerical calculations and the experimental results agree fairly well for both the resonant frequencies and the mode shapes.     

Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.