Efficient modal control strategies for active control of vibrations

Some efficient strategies for the active control of vibrations of a beam structure using piezoelectric materials are described. The control algorithms have been implemented for a cantilever beam model developed using finite element formulation. The vibration response of the beam to an impulse excitation has been calculated numerically for the uncontrolled and the controlled cases. The essence of the method proposed is that a feedback force in different modes be applied according to the vibration amplitude in the respective modes i.e., modes having lesser vibration may receive lesser feedback. This weighting may be done on the basis of either displacement or energy present in different modes. This method is compared with existing methods of modal space control, namely the independent modal space control (IMSC), and modified independent modal space control (MIMSC). The method is in fact an extension of the modified independent space control with the addition that it proposes to use the sum of weighted multiple modal forces for control. The proposed method results in a simpler feedback, which is easy to implement on a controller. The procedure is illustrated for vibration control of a cantilever beam. The analytical results show that the maximum feedback control voltage required in the proposed method is further reduced as compared to existing methods of IMSC and MIMSC for similar vibration control. The limitations of the proposed method are discussed.     

Estimation of interfacial forces in time domain for linear systems

A structural path rank ordering process under transient excitations requires a good knowledge of the interfacial path forces, which are difficult to directly measure. Four time domain methods to estimate the interfacial forces are proposed and comparatively evaluated with application to linear time-invariant, proportionally damped discrete systems. First, the transient response is derived by modal analysis and a direct time domain technique to calculate the interfacial forces is outlined. Next, the frequency domain estimation methods, based on the sub-system concept are reviewed, and an inverse Fourier transform scheme is introduced. An indirect method of estimating interfacial force in transient state is then developed through an inverse procedure of modal analysis. The sub-system approach is employed to obtain the interfacial forces based on the forced vibration response of the original system and modal data of the sub-system. Finally, an approximate time domain scheme is suggested that could be used only if the system properties are known or precisely estimated. Although the proposed indirect methods are designed for eventual experimental applications, this article provides numerical feasibility studies via a simple source-path-receiver system (with parallel vibration paths) that has five translational degrees of freedom. The proposed methods are compared under ideal impulse force excitation input and a periodic sawtooth load (without and with Gaussian noise) to observe the starting transients as well as subsequent motions and interfacial forces. Preliminary comparisons with a laboratory experiment are very promising.     

Passive structural health monitoring of a high-speed naval ship from ambient vibrations

Previous studies have used the cross-correlation of ambient vibrations (CAV) technique to estimate the impulse response (or Green's function) between passive sensors for passive imaging purposes in various engineering applications. The technique (CAV) relies on extracting deterministic coherent time signatures from the noise cross-correlation function computed between passive sensors, without the use of controlled active sources. Provided that the ambient structure-borne noise field remains stable, these resulting coherent waveforms obtained from CAV can then be used for structural monitoring even if they differ from the actual impulse response between the passive sensors. This article presents experimental CAV results using low-frequency random vibration data (<50 Hz) collected on an all-aluminum naval vessel (the HSV-2 Swift) operating at high speed (up to 40 knots) during high sea states. The primary excitation sources were strong wave impact loadings and rotating machinery vibrations. The consistency of the CAV results is established by extracting similar coherent arrivals from ambient vibrations between the pairs of strain gages, symmetrically located across the ship's centerline. The influence of the ship's operating conditions on the stability of the peak coherent arrival time, during the 7 days trial, is also discussed.     

Measurement and analysis of rolling tire vibrations

This paper presents the measurement and analysis of rolling tire vibrations due to road impact excitations, such as from cobbled roads, junctions between concrete road surface plates, railroad crossings. Vibrations of the tire surface due to road impact excitations cause noise radiation in the frequency band typically below 500 Hz. Tire vibration measurements with a laser Doppler vibrometer are performed on a test set-up based on a tire-on-tire principle which allows highly repetitive and controllable impact excitation tests under various realistic operating conditions. The influence on the measured velocity of random noise, cross sensitivity and alignment errors is discussed. An operational modal analysis technique is applied on sequential vibration measurements to characterise the dynamic behaviour of the rolling tire. Comparison between the operational modal parameters of the rolling tire and the modal parameters of the non-rolling tire allows an assessment of the changes in dynamic behaviour due to rolling.     

Modal analysis by free vibration response only for discrete and continuous systems

This work aims to develop the algorithm for modal analysis by free vibration response only (MAFVRO), in particular for the general or non-proportional viscous damping system model. If the structural displacement or acceleration response due to free vibration can be measured, the system response matrices, including the displacement, velocity and acceleration, can be obtained through numerical differential or integration methods. These response matrices can then be applied to the developed MAFVRO method to determine the structural modal parameters. The numerical differential and integration methods are introduced and adopted to establish the modal parameter prediction program for the non-proportional damping model of MAFVRO. This work also shows the applications of MAFVRO to the multiple degree-of-freedom (mdof) systems and the cantilever beam, respectively. Both the discrete and continuous systems are demonstrated for the feasibility of the MAFVRO algorithm. The developed method uses the free vibration output response only and can obtain the structural modal parameters successfully.     

Forced transverse vibrations of an elastically connected complex simply supported double-beam system

The present paper is devoted to analyzing undamped forced transverse vibrations of an elastically connected complex double-beam system. The problem is formulated and solved in the case of simply supported beams. The classical modal expansion method is applied to ascertain dynamic responses of beams due to arbitrarily distributed continuous loads. Several cases of particularly interesting excitation loadings are investigated. The action of stationary harmonic loads and moving forces is considered. In discussing vibrations caused by exciting harmonic forces, conditions of resonance and dynamic vibration absorption are determined. The beam-type dynamic absorber is a new concept of a continuous dynamic vibration absorber (CDVA), which can be applied to suppress excessive vibrations of corresponding beam systems. A numerical example is presented to illustrate the theoretical analysis.     

Vibration testing based on impulse response excited by laser ablation

This paper proposes an innovative vibration testing method based on impulse response excited by laser ablation. In conventional vibration testing using an impulse hammer, high-frequency elements of over tens of kilohertz are barely present in the excitation force. A pulsed high-power YAG laser is used in this study for producing an ideal impulse force on a structural surface. Illuminating a point on a metal with the well-focused YAG laser, laser ablation is caused by generation of plasma on the metal. As a result, an ideal impulse excitation force generated by laser ablation is applied to the point on the structure. Therefore, it is possible to measure high-frequency FRFs due to the laser excitation. A water droplet overlay on the metal is used to adjust the force magnitude of laser excitation. An aluminum block that has nine natural frequencies below 40 kHz is employed as a test piece. The validity of the proposed method is verified by comparing the FRFs of the block obtained by the laser excitation, impulse hammer, and finite element analysis. Furthermore, the relationship between accuracy of FRF measurements and sensitivity of sensors is investigated.     

An investigation into the simultaneous use of a resonator as an energy harvester and a vibration absorber

A mass–spring–damper system is at the core of both a vibration absorber and a harvester of energy from ambient vibrations. If such a device is attached to a structure that has a high impedance, then it will have very little effect on the vibrations of the structure, but it can be used to convert mechanical vibrations into electrical energy (act as an energy harvester). However, if the same device is attached to a structure that has a relatively low impedance, then the device may attenuate the vibrations as it may act as both a vibration absorber and an energy harvester simultaneously. In this paper such a device is discussed. Two situations are considered; the first is when the structure is excited with broadband random excitation and the second is when the structure is excited by a single frequency. The optimum parameters of the device for both energy harvesting and vibration attenuation are discussed for these two cases. For random excitation it is found that if the device is optimized for vibration suppression, then this is also adequate for maximizing the energy absorbed (harvested), and thus a single device can effectively suppress vibration and harvest energy at the same time. For single frequency excitation this is found not to be the case. To maximize the energy harvested, the natural frequency of the system (host structure and absorber) has to coincide with the forcing frequency, but to minimize vibration of the host structure, the natural frequency of the absorber has to coincide with the forcing frequency. In this case, therefore, a single resonator cannot effectively suppress vibration and harvest energy at the same time.     

Experimental investigations of the response of a cracked rotor to periodic axial excitation

In this paper, the coupling of lateral and longitudinal vibrations due to the presence of transverse surface crack in a rotor is explored. A crack in a rotor is known to introduce coupling between lateral and longitudinal vibrations. Steady state unbalance response of a cracked rotor with a single centrally situated crack subjected to periodic axial impulses is investigated experimentally. The cracked rotor is excited axially using an electrodynamic exciter at a frequency equal to its bending natural frequency in both non-rotating and rotating conditions. The resulting time domain and frequency domain signals of the cracked rotor are studied. Spectral response of the cracked rotor with and without axial excitation is found to be distinctively different. When excited axially, it shows prominent presence of rotor bending natural frequency. However for an uncracked rotor, the response is similar with or without axial excitation. It is thus proposed that the response of the rotor to axial impulse excitation could be used for more reliable diagnosis of rotor cracks.     

The mass normalization of the displacement and strain mode shapes in a strain experimental modal analysis using the mass-change strategy

The classic experimental modal analysis (EMA) is a well-known procedure for determining the modal parameters. The less frequently used strain EMA is based on a response measurement using strain sensors. The results of a strain EMA are the modal parameters, where in addition to the displacement mode shapes the strain mode shapes are also identified. The strain EMA can be used for an experimental investigation of a stress–strain distribution without the need to build a dynamical model. It can also be used to determine the modal parameters when, during modal testing, a motion sensor cannot be used and so a strain sensor is used instead. The displacement and strain mode shapes that are determined with the strain EMA are not mass normalized (scaled with respect to the orthogonality properties of the mass-normalized modal matrix), and therefore some dynamical properties of the system cannot be obtained. The mass normalization can be made with the classic EMA, which requires the use of a motion sensor. In this research a new approach to the mass normalization in the strain EMA, without using a motion sensor, is presented. It is based on the recently introduced mass-change structural modification method, which is used for the mass normalization in an operational modal analysis. This method was modified in such a way that it can be used for the mass normalization in the strain EMA. The mass-normalized displacement and strain mode shapes were obtained using a combination of the proposed approach and the strain EMA. The proposed approach was validated on real structures (beam and plate).     

Vibration of branched systems—A displacement excitation approach

Exact solutions for the free and forced torsional vibration of branched systems are obtained in terms of the modal parameters of the branches. The basic technique consists of first isolating the branches by clamping the system at the junction. The conditions necessary for the relaxation of the clamp are then obtained from the response of the system to a displacement excitation at the clamp. The vibration of branched engine installations in which repeated branch natural frequencies sometimes occur are given special attention. It is shown that the technique may be applied to the solution of the vibration problems of certain types of flexural systems.     

周向畸变对跨声速风扇低阶强迫振动的影响研究

边界层抽吸式推进系统(BLI)因具有降低未来商用飞机燃油消耗率的巨大潜力而备受关注.但风扇叶片作为关键组件,需要受到由于边界层吸入而导致的畸变来流的挑战.基于本团队前期在NASA Rotor 67进行的数值模拟,在设计转速附近风扇因受到二阶激励而以一阶弯曲的形式发生低阶模态振动,同时,激发的强度足以引起叶片振动.由于来...     

Effect of bevelling on the thickness vibration of high-frequency Pb(ZrTi)O3 ceramic transducers

The effects of bevelling on the thickness vibration of Pb(ZrTi)O₃ piezoelectric-ceramic disc transducers for generating high-frequency ultrasonic power were studied by measuring electrical characteristics and displacement distributions. A laser heterodyne system was employed for the contact-free measurement of vibration. It was shown for a wide range of diameter-to-thickness ratios that bevelling circular edges was effective in reducing the coupled radial vibrations and enhancing the uniform thickness vibration. The vibration characteristics required for generating high-frequency ultrasound were substantially improved by slight bevelling. These results were accounted for by energy trapping of thickness vibration and by the consequent decrease in the equivalent mass of the transducers.     

Experimental and numerical investigation on structural effects of laser pulses for modal parameter measurement

In this paper it has been described part of the research devoted to the development of a complete non-intrusive experimental modal analysis procedure based on laser techniques both for excitation and for measurement. In particular, attention has been focused on the thermal effects generated by laser pulses on the excited structure. An analytical model of the energy exchange between the light pulse and the target surface is proposed together with a finite element model of thermal and mechanical behaviour of the structure under excitation. Both the models (analytical and numerical) have been experimentally validated by measuring the thermal and the vibration responses induced by the laser pulses. The experimental part of the study has been performed on a cantilever beam excited with laser pulses from an Nd : YAG source (532 nm, 100 mJ/pulse) using an high-speed infrared camera and a scanning laser Doppler vibrometer. Results from this work can be used to improve understanding concerning the features of laser excitation and to establish a mechanical equivalent system of forces and moments, useful in order to increase the accuracy in the measurements of modal parameters when laser pulses are used as excitation sources.     

Pulsed TV-holography recording for vibration analysis applications

TV-holography is a well-known tool for vibration analysis. Using the so-called time-average method, this technique allows to record interferograms showing the mode shapes of a structure submitted to vibration excitation and is currently used for modal identification.Within the frames of a BRITE-EURAM program called vibration intensity processing using full-field multi-pulse laser technique (VIP), a TV-holography equipment has been developed, working with a 25 Hz pulsed laser and allowing easy on-site measurements. A measurement procedure has been defined and a specific data processing has been developed for the determination of structural intensity fields, which give transfer path of the vibration energy within a structure.The measurement of these quantities is possible the using classical means (accelerometers, stress gauges, etc.) but the data processing is complex and require a lot of accurate sensors because it is based on spatial derivatives of high order. The optical techniques (laser vibrometry, holography, etc.) are more suited for that purpose because of the high density of measuring points and because of the well-known advantages of these methods: reduced measurement time and no modification of the mass parameters of the structure as it is the case when using contact sensors.Different kinds of output data are then given: operational deflection shape, amplitude and phase, structural intensity field and its divergence through a further step of data processing. The complete procedure with the associated data processing has been tested (for various configurations of excitation and damping) first on a clamped plate, then on a cylinder and at the end on several industrial components.This paper describes the general measurement procedure and the equipment used. The data processing is also presented and various measurement results are shown. The conclusion gives the main advantages and limitations of the method and evaluates the application possibilities.     

基于PANDA平台的光机部件随机振动响应分析

基于PANDA自主并行计算平台，采用模态叠加法开展了多点基础激励作用下的随机振动响应分析算法设计和并行实现研究，构建了相应的并行求解模块。针对光机装置打靶样机中的六自由度平台结构，基于自主研发的软件模块，分析了该结构的模态特性及结构在地脉动载荷下的微振动响应，并与试验结果及商业软件分析结果进行了比对，在模态频率、振型和位移响应方面，都具有较好的一致性，验证了相关软件模块的正确性和PANDA平台在实际工程结构分析中的可用性。     

The evolution of stiction repair for microelectromechanical system cantilevers using periodic excitation

In some recent experiments, it has been shown that structural vibrations are an efficient means to repair (i.e., unstick) stiction failed microcantilever beams. The analysis that accompanied these experiments identified excitation parameters (amplitude and frequency) that successfully initiated the debonding process between the microcantilever and the substrate. That analysis relied on coupling a static fracture model to a vibration model. However, that analysis could not describe what happened after the debonding process was initiated. For example, the repair could be partial, where the debonding begins but then arrests—or it could be total, where the beam is returned to its free-standing shape. The present paper examines the post-initiation behavior of stiction failed microcantilevers. A new, coupled fracture/vibration model is formulated and used to track the evolution of the repair, in order to determine the extent of the repair under various conditions. Moreover, this model successfully predicts some unusual (but explainable) behavior seen in the previous experiments, regarding partial and complete vibration repair.     

USING THE CROSS-CORRELATION TECHNIQUE TO EXTRACT MODAL PARAMETERS ON RESPONSE-ONLY DATA

Modal parameter identification is used to identify those parameters of the model which describe the dynamic properties of a vibration system. Classical modal parameter extractions usually require measurements of both the input force and the resulting response in laboratory conditions. However, when large-scale operational structures are subjected to random and unmeasured forces such as wind, waves, or aerodynamics, modal parameters estimation must base itself on response-only data. Over the past years, many time-domain modal parameter identification techniques from output-only have been proposed. Among them, the natural excitation technique (NExT) has been a very powerful tool for the modal analysis of structures excited in operating environment. This issue reviews the theoretical development of natural excitation technique (NExT), which uses the cross-correlation functions of measured responses coupling with conventional time-domain parameter extraction under the assumption of white-noise random inputs. Then a frequency-domain poly reference modal identification scheme by coupling the cross-correlation technique with conventional frequency-domain poly reference modal parameter extraction is presented. It uses cross-power spectral density functions instead of frequency response functions and auto- and cross-correlation functions instead of impulse response functions to estimate modal parameters from response-only data. An experiment using an airplane model is performed to investigate the effectiveness of the cross-correlation technique coupled with frequency-domain poly reference modal identification scheme.     

Transient analysis of nonlinear Euler–Bernoulli micro-beam with thermoelastic damping,via nonlinear normal modes

In this paper an Euler–Bernoulli model has been used for vibration analysis of micro-beams with large transverse deflection. Thermoelastic damping is considered to be the dominant damping mechanism and introduced as imaginary stiffness into the equation of motion by evaluating temperature profile as a function of lateral displacement. The obtained equation of motion is analyzed in the case of pure single mode motion by two methods; nonlinear normal mode theory and the Galerkin procedure. In contrast with the Galerkin procedure, nonlinear normal mode analysis introduces a nonconventional nonlinear damping term in modal oscillator which results in strong damping in case of large amplitude vibrations. Evaluated modal oscillators are solved using harmonic balance method and tackling damping terms introduced as an imaginary stiffness is discussed. It has been shown also that nonlinear modal analysis of micro-beam with thermoelastic damping predicts parameters such as inverse quality factor, and frequency shift, to have an extrema point at certain amplitude during transient response due to the mentioned nonlinear damping term; and the effect of system?s characteristics on this critical amplitude has also been discussed.