Abstract: Operational modal analysis (often called output-only or ambient modal analysis) is described in this article. Modal testing is performed on a plate structure with well-defined modes, resonance frequencies and damping values. Frequency Domain Decomposition (FDD) and Enhanced Frequency Domain Decomposition (EFDD) concepts are presented and applied to a plate structure. This article details the signal processing mathematical background and presents alternative curve-fitting processes.

Abstract: Modalanalysishasbeenusedtoidentifynaturalfrequencies,damp-ingcharacteristicsandmodeshapesofwindturbineblades.Differentexperimentalprocedureshavebeenconsideredandthemostappropri-ateofthesehasbeenselected.AlthoughthecomparisonisbasedonmeasurementsonaLM19mblade,therecommendationsgivenarebelievedtobevalidforothertypesofwindturbinebladesaswell.Thereliabilityoftheselectedexperimentalanalysishasbeenquantifiedbyes-timating the unsystematicvariations in the experimental findings. Satisfactoryresults have been obtained for natural frequencies, damping characteristics andforthedominatingdeflectiondirectionoftheinvestigatedmodeshapes.Fornon-dominating deflection directions of the investigated mode shapes, however, theobservedexperimental uncertainty may be considerable – especially for the tor-sionaldeflection.TheexperimentalanalysisoftheLM19mbladehasbeencomparedwithresultsfromaFE-modelingofthesameblade.Forsomeofthehighermodessubstantialdiscrepanciesbetween the naturalfrequencies originatingfrom the FE-modelingandthe modal analysis,respectively, areobserved.Comparing the mode shapes(normalized with respect to the tip deflection in the dominating deflection di-rection) good agreement has been demonstrated for the dominating deflectiondirection. For the non-dominating deflection directions, the qualitative features(i.e.theshape)ofmeasuredandcomputedmodesshapesareingoodagreement,whereastheyquantitativelymaydisplayconsiderabledeviations.Finally,suggestionsofpotentialfutureimprovementsofthe experimentalpro-cedurearediscussed.ISBN87–550–2696–6ISBN87–550–2697–4(Internet)ISSN0106–2840Print:PitneyBowesManagementServicesDenmarkA/S,2002

Abstract: A comprehensive review of vibration damping in vibration and acoustics analysis is presented. The treatment of damping material is an important measure for vibration and acoustics control in engineering. The simulation-based results on vibration and acoustics analysis are very sensitive to the description and input methods of damping properties. In this paper, the consideration of vibration damping using software ANSYS for harmonic and modal analysis is addressed. Several key points are summarized. Introduction When an unacceptable vibration and acoustics problem needs to be controlled, it is firstly desirable and often necessary to understand its whole nature, such as its originating source, the nature and direction of the vibration and acoustics at the problem location, transmission path and frequency content. Then, it must be decided whether the problem would be best solved by passive or active control methods. The passive control involves modification of the stiffness, mass and damping of the vibration system to make the system less responsive to its vibratory environment. This paper is concerned only with the damping modification in passive control methods. If the undesirable vibration and acoustics is dominated by one or more resonance of the structure, it can be often adequately controlled by increasing the damping of the system. Most non-resonant vibration and acoustics problems cannot be solved by the damping treatment. If an added damping system is to be effective, the increased damping must be significantly larger than the initial damping. The most commonly used method of increasing the damping is to include highly damped polymeric material at strategic locations onto the structure. The structure and polymer must interact with one another in such a way as to cause the polymer to dissipate as much energy as possible. In practice, there are two kinds of damping treatments for vibration and acoustics control. The first is called extensional damping treatment. This treatment is also referred to as the unconstrainedor free-layer damping treatment. The treatment is coated on one or both sides of a structure, so that whenever the structure is subjected to flex, the damping material will be subjected to tension-compression deformation. The second one is named as shear type of damping treatment. For a given weight, the shear type of damping treatment is more efficient than the extensional damping treatment. However, this efficiency is balanced by greater complication in analysis and application. The treatment is similar to the unconstrained-layer type, except the viscoelastic material is constrained by another layer. Therefore, whenever the structure is subjected to flex, the extra layer will constrain the viscoelastic material and force it to deform in shear. The maximum shear deformation in the middle layer is a function of the modulus and the thickness of the constraining layer, the thickness and the damping material and the wavelength of vibration in addition to the properties of the damping material. The actual description of the damping force associated with the dissipation of energy is difficult. It may be a function of the displacement, velocity, stress or other factors. Most of the mechanisms which dissipate energy with a vibrating system are non-linear and conform neither to the linear viscous nor to the linear hysteretic damping . However, ideal damping models can be conceived which will often permit a satisfactory approximation. In this paper, the categories of common damping materials in engineering are reviewed. After that, the model for description of structural damping is introduced. Thirdly, it is elaborated how ANSYS considers the damping properties for engineering purpose. Several case studies are carried out to explain the difference of various consideration methods of material damping effects. Finally, some key points are drawn for correct application of damping effects for harmonic and modal analysis in ANAYS. Categories of Damping Materials They are several types of damping. Viscous damping is the form of damping that we are familiar with. It is caused by energy loss that results from fluid flow. An example would be the damping used in vehicle’s shock absorbers. Frictional damping occurs when two objects rub against each other. That is why our hands get warm when we rub them together. Most of damping materials in the market provided by various manufactures belongs to hysteretic damping. Viscous Damping [2,3] When mechanical systems vibrate in a fluid medium such as air, gas, water and oil, the resistance offered by the fluid to the moving body causes energy to be dissipated. The amount of dissipated energy depends on many factors, such as the size and shape of the vibrating body, the viscosity of the fluid, the frequency of vibration, and the velocity of the vibrating body. In viscous damping, the damping force is proportional to the velocity of the vibrating body. Viscous damping force can be expressed by the equation x c F & − = (1) where c is a constant of proportionality and the velocity of the mass shown in Figure 1. x& Figure 1 A forced damped vibration of single DOF [m=0.5 (kg), k=200 (N/m), c=6(N•s/m), F=10 (N)] When the single spring mass system undergoes free vibration, the equation of motion becomes 0 = + + kx x c x m & & & (2) Assuming a solution of the form , we have the eigen or the characteristic equation of the system as st e x = 0 2 = + + k cs ms (3) The solution of equation 3 is         + = −       − −       − t m k m c t m k m c t m c Be Ae e x 2 2

Abstract: Proper orthogonal decomposition (POD) is studied in an effort to increase its applicability as a modal analysis tool. A modification is proposed to make better use of spatial resolution and to accommodate arbitrary spacing in the discretization. The theory for this modification is rooted in the discrete approximation of the integral orthogonality condition for continuous normal modes. The modified POD is applied to a finite element beam and an experimental beam sensed with accelerometers, and the resulting proper orthogonal modes (POMs) are compared to the theoretical modes of the beam. The POMs are used as a basis for decomposing the signal ensemble into proper modal coordinates. The proper modal coordinates are used to evaluate the POMs and to match modes with modal frequencies and damping.

Abstract: A vibration prediction model for the switched reluctance motor is constructed in this paper. Shaker and force hammer tests for vibration measurement are used for measuring crucial parameters like modal frequency and damping ratio for the transfer function. A detailed lookup table of normal force versus phase current and rotor angle is constructed based on finite-element calculations. The model is then verified by experiments, with acceptable accuracy.

Abstract: In this paper on finite element linear quadratic regulator (LQR) vibration control of smart piezoelectric composite plates, we propose the use of the total weighted energy method to select the weighting matrices. By constructing the optimal performance function as a relative measure of the total kinetic energy, strain energy and input energy of the system, only three design variables need to be considered to achieve a balance between the desired higher damping effect and lower input cost. Modal control analysis is used to interpret the effects of three energy weight factors on the damping ratios and modal voltages and it is shown that the modal damping effect will increase with the kinetic energy weight factor, approaching √2/2 as the strain energy weight factor increases and decrease with the input energy weight factor. Numerical results agree well with those from the modal control analysis. Since the control problem is simplified to three design variables only, the computational cost will be greatly reduced and a more accurate structural control analysis becomes more attractive for large systems.

Abstract: Accurate structural models are key to the optimization of the vibro-acoustic behaviour of panel-like structures. However, at the frequencies of relevance to the acoustic problem, the structural modes are very complex, requiring high-spatial-resolution measurements. The present paper discusses a vibration testing system based on pulsed-laser holographic electronic speckle pattern interferometry (ESPI) measurements. It is a characteristic of the method that time-triggered (and not time-averaged) vibration images are obtained. Its integration into a practicable modal testing and analysis procedure is reviewed. The accumulation of results at multiple excitation frequencies allows one to build up frequency response functions. A novel parameter extraction approach using spline-based data reduction and maximum-likelihood parameter estimation was developed. Specific extensions have been added in view of the industrial application of the approach. These include the integration of geometry and response information, the integration of multiple views into one single model, the integration with finite-element model data and the prior identification of the critical panels and critical modes. A global procedure was hence established. The approach has been applied to several industrial case studies, including car panels, the firewall of a monovolume car, a full vehicle, panels of a light truck and a household product. The research was conducted in the context of the EUREKA project HOLOMODAL and the Brite-Euram project SALOME.

Abstract: Measurement of Frequency Response Functions (FRFs) on the Millennium Bridge in London was a key part in the validation of the retrofit solution for excessive sway vibration caused by walking pedestrians during the bridge opening in June 2000. The measured FRFs were employed to verify the analytical response analysis and to estimate and confirm analytical predictions of natural frequencies, modal damping ratios, mode shapes and modal masses corresponding to various configurations of prototype viscous and tuned mass dampers. These results were used to experimentally assess the effectiveness of the proposed retrofit solution. Although FRF measurement technology is fairly standard in many engineering disciplines, its application on the Millennium Bridge was quite problematic and required some unique solutions which are described in this paper. Modal testing of the Millennium Bridge clearly demonstrated that it was possible to measure good quality FRFs around a frequency as low as 0·5 Hz, which was the natural...

Abstract: This paper explores the possibility of using a combination of the empirical mode decomposition (EMD) and the Hilbert transform (HT), termed the Hilbert-Huang transform (HHT) method, to identify the modal damping ratios of the structure with closely spaced modal frequencies. The principle of the HHT method and the procedure of using the HHT method for modal damping ratio identification are briefly introduced first. The dynamic response of a two-degrees-of-freedom (2DOF) system under an impact load is then computed for a wide range of dynamic properties from well-separated modal frequencies to very closely spaced modal frequencies. The natural frequencies and modal damping ratios identified by the HHT method are compared with the theoretical values and those identified using the fast Fourier transform (FFT) method. The results show that the HHT method is superior to the FFT method in the identification of modal damping ratios of the structure with closely spaced modes of vibration. Finally, a 36-storey shear building with a 4-storey light appendage, having closely spaced modal frequencies and subjected to an ambient ground motion, is analyzed. The modal damping ratios identified by the HHT method in conjunction with the random decrement technique (RDT) are much better than those obtained by the FFT method. The HHT method performing in the frequency-time domain seems to be a promising tool for system identification of civil engineering structures.

Abstract: In a room with strong low-frequency modes the control of excessively long decays is problematic or impossible with conventional passive means. In this patent application a systematic methodology is presented for active modal equalization able to correct the modal decay behaviour of a loudspeaker-room system. Two methods of modal equalization are proposed. The first method modifies the primary sound such that modal decays are controlled. The second method uses separate primary and secondary radiators and controls modal decays with sound fed into at least one secondary radiator. Case studies of the first method of implementation are presented.

Abstract: Experimental modal testing of an inflated torus is examined. The principal focus of this investigation is an evaluation of the use of conventional dynamic testing tools in modal testing of a thin-film inflated structure. Because thin-film structures are inherently flexible and lightweight, precautions must be taken in the test procedure. Challenges in testing and identifying natural frequencies and modal damping are detailed. The experimental study shows that whereas localized flexible body dynamics is predominant at higher frequency, the structure behaves in a fashion similar to that of a solid elastic structure for the low-order modes. In addition, natural frequencies and modal damping are shown to be dependent on the level of internal pressurization. Furthermore, viscous (air) damping and structural (strain-rate) damping coefficients are estimated from the experimentally measured modal parameters to provide a more complete assessment of the damping behavior of this structure.

Abstract: This paper proposes a new approach for modal analysis of a large power system that is based on the on-line system identification by using the synchronously measured responses of remote machines. Since the power system is identified as a linear dynamic system, the eigenanalysis can provide the damping constants, modal frequencies and mode shapes of the weakly damped electromechanical modes that appear in the measurer: responses at an operating point. In the paper, it is also discussed how to select a small number of the machines suitable for detecting slow oscillatory modes and estimating the eigenvalues of slow modes. Such machines can be found out by utilizing the slow coherency observed in the global motion between groups of machines. The verification of the new modal analysis and the coherency based machine selection is done by simulation studies of a 3-machine and 9-bus system, and a 25-machine and 66-bus system.

Abstract: This paper presents a dynamic vibration analysis of switched reluctance motor. The main exciting force of the vibration is electromagnetic force in the stator that is calculated using the magnetic charge method. The force densities obtained by the FE magnetic field analysis are applied to the FE mechanical modal analysis. A numerical model of 3-phase 6/4 SRM is tested to obtain the natural frequencies and deformation of the stator. The radial and transverse vibration amplitudes are obtained in time domain. Transient dynamic analysis is also accomplished to compare its results with the ones obtained using the modal method.

Abstract: Modal analysis based damage detection techniques using only first few modes are not sensitive for damage identification. The sensitivity of the modal parameters to damage is greater at the higher modes of vibration. Yet, actuation of structures at high frequencies is very difficult with the conventional modal testing methods. In this paper, a new technique that uses smart piezoelectric (PZT) material to extract the modal frequencies for higher modes of vibration is presented. A PZT transducer possesses simultaneous actuating and sensing capabilities. The electromechanical (e/m) impedance method exploits this feature of the PZT transducer to measure its drive-point impedance characteristics when bonded to a structure. Damage location is identified using the natural frequency shifts obtained from the structural impedance signatures and the corresponding undamaged state modes shapes. This technique is superior to other methods, which rely only on statistical quantification of changes in the measured structural signatures. The damage locations were successfully identified by this method for a finite element simulated beam model. The natural frequencies obtained experimentally for longitudinal and bending modes were fairly consistent with the analytical predictions. However, the modeling of damage as merely a source of stiffness reduction proves insufficient to accurately estimate its location, experimentally.

Abstract: Inflated space-based structures have become popular over the past three decades due to their minimal launch-mass and launch-volume. Once inflated, these space structures are subject to vibrations induced by guidance systems and space debris as well as from variable amounts of direct sunlight. Understanding the dynamic behavior of space-based structures is critical to ensuring their desired performance. Inflated materials, however, pose special problems when testing and trying to control their vibrations because of their lightweight, flexibility, and high damping. Traditional modal testing techniques, based on single-input, single-output (SISO) methods, are limited for a variety of reasons when compared to their multiple counterparts. More specifically, SISO modal testing techniques are unable to reliably distinguish between pairs of modes that are inherent to axi-symmetric structures (such as an inflated torus, a critical component of a gossamer spacecraft). Furthermore, it is questionable as to whether a single actuator could reliably excite the global modes of a true gossamer craft, such as a 25 m diameter torus. In this study, we demonstrate the feasibility of using a multiple-input multiple-output (MIMO) modal testing technique on an inflated torus. In particular, the refined modal testing methodology focuses on using Macro-Fiber Composite (MFC® ) patches (from NASA Langley Research Center) as both actuators and sensors. MFC® patches can be integrated in an unobtrusive way into the skin of the torus, and can be used to find a gossamer structure’s modal parameters. Furthermore, MFC® excitation produces less interference with suspension modes of the free-free torus than excitations from a conventional shaker. The use of multiple actuators is shown to properly excite the global modes of the structure and distinguish between pairs of modes at nearly identical resonant frequencies. Formulation of the MIMO test as well as the required postprocessing techniques are explained and successfully applied to an inflated Kapton® torus.Copyright © 2002 by ASME

Abstract: Sports stadia, like many other civil engineering structures, are being pushed to their limits in terms of slenderness and structural efficiency. This normally has benefits such as increased capacities and improved lines of sight for spectators. However, the increased use of more slender stadium structures is causing concern as they may be susceptible to excitation by the increasingly lively spectators that they accommodate. This paper describes the modal testing of one such structure, a grandstand at a football stadium in the UK. The modal testing, performed using a roving APS113 shaker and 6 reference accelerometers, is described in detail. Due to external considerations, the testing had to be performed in very limited timescales and the entire modal test and preliminary estimation of the modal properties of the structure were completed within a single working day. The results from the modal testing are compared with the results of a pre-test finite element analysis that was performed by an experienced stadium designer. Discrepancies between the FE model and the modal test results are highlighted and some explanations are given.

Abstract: In traditional modal strain energy method, the real eigen-vector of each mode obtained from finite element analysis of the corresponding undamped structure is used to calculate modal strain energy in each material layer, and an iterative approach is used in dealing with the frequency dependency of viscoelastic materials. In this paper, a revised modal strain energy method is presented to significantly improve analysis accuracy of the structural natural frequencies and modal loss factors when the material loss factor is high, and a simplified approach is recommended to replace the iterative analysis to avoid tremendous amount of computational effort.

Abstract: Advanced and innovative materials and structures are increasingly used in civil infrastructure applications. By combining the advantages of composites and smart sensors and actuators, active or smart composite structures can be created and be efficiently adopted in practical structural applications. This paper presents results of active vibration control of a pultruded fiber-reinforced polymer (FRP) composites thin-walled I-beams using smart sensors and actuators. The FRP I-beams are made of E-glass fibers and polyester resins. The FRP I-beam is in a cantilevered configuration. PZT (Lead zirconate titanate) type of piezoelectric ceramic patches are used as smart sensors and actuators. These patches are surface-bonded near the cantilevered end of the I-beam. Utilizing results from modal analyses and experimental modal testing, several active vibration control methods, such as position feedback control, strain rate feedback control and lead compensator, are investigated. Experimental results demonstrate that the proposed methods achieve effective vibration control of FRP I-beams. For instance, the modal damping ratio of the strong direction first bending mode increases by more than 1000 percent with a positive position feedback control.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.