Building Spectral Element Dynamic Matrices Using Finite Element Models of Waveguide Slices and Elastodynamic Equations

Structural spectral elements are formulated using the analytical solution of the applicable elastodynamic equations and, therefore, mesh refinement is not needed to analyze high frequency behavior provided the elastodynamic equations used remain valid. However, for modeling complex structures, standard spectral elements require long and cumbersome analytical formulation. In this work, a method to build spectral finite elements from a finite element model of a slice of a structural waveguide (a structure with one dimension much larger than the other two) is proposed. First, the transfer matrix of the structural waveguide is obtained from the finite element model of a thin slice. Then, the wavenumbers and wave propagation modes are obtained from the transfer matrix and used to build the spectral element matrix. These spectral elements can be used to model homogeneous waveguides with constant cross section over long spans without the need of refining the finite element mesh along the waveguide. As an illustrating example, spectral elements are derived for straight uniform rods and beams and used to calculate the forced response in the longitudinal and transverse directions. Results obtained with the spectral element formulation are shown to agree well with results obtained with a finite element model of the whole beam. The proposed approach can be used to generate spectral elements of waveguides of arbitrary cross section and, potentially, of arbitrary order

Localizing Energy Sources and Sinks in Plates Using Power Flow Maps Computed From Laser Vibrometer Measurements

This paper presents an experimental method especially adapted for the computation of structural power flow using spatially dense vibration data measured with scanning laser Doppler vibrometers. In the proposed method, the operational deflection shapes measured over the surface of the structure are curve-fitted using a two-dimensional discrete Fourier series approximation that minimizes the effects of spatial leakage. From the wavenumber-frequency domain data thus obtained, the spatial derivatives that are necessary to determine the structural power flow are easily computed. Divergence plots are then obtained from the computed intensity fields. An example consisting of a rectangular aluminum plate supported by rubber mounts and excited by a point force is used to appraise the proposed method. The proposed method is compared with more traditional finite difference methods. The proposed method was the only to allow the localization of the energy source and sinks from the experimental divergence plots

Estimation of beam material random field properties via sensitivity-based model updating using experimental frequency response functions

Structural parameter estimation is affected not only by measurement noise but also by unknown uncertainties which are present in the system. Deterministic structural model updating methods minimise the difference between experimentally measured data and computational prediction. Sensitivity-based methods are very efficient in solving structural model updating problems. Material and geometrical parameters of the structure such as Poisson’s ratio, Young’s modulus, mass density, modal damping, etc. are usually considered deterministic and homogeneous. In this paper, the distributed and non-homogeneous characteristics of these parameters are considered in the model updating. The parameters are taken as spatially correlated random fields and are expanded in a spectral Karhunen-Loève (KL) decomposition. Using the KL expansion, the spectral dynamic stiffness matrix of the beam is expanded as a series in terms of discretized parameters, which can be estimated using sensitivity-based model updating techniques. Numerical and experimental tests involving a beam with distributed bending rigidity and mass density are used to verify the proposed method. This extension of standard model updating procedures can enhance the dynamic description of structural dynamic models

Analyzing The Total Structural Intensity In Beams Using A Homodyne Laser Doppler Vibrometer

The total structural intensity in beams can be considered as composed of three kinds of waves: Bending, longitudinal, and torsional. In passive and active control applications, it is useful to separate each of these components in order to evaluate its contribution to the total structural intensity flowing through the beam. In this paper, a z-shaped beam is used in order to allow the three kinds of waves to propagate. The contributions of the structural intensity due to the three kinds of waves are computed from measurements made over the surface of the beam with a simple homodyne interferometric laser vibrometer. The optical sensor incorporates some additional polarizing optics to a Michelson type interferometer to generate two optical signals in quadrature, which are processed to display velocities and/or displacements. This optical processing scheme is used to remove the directional ambiguity from the velocity measurement and allows to detect nearly all backscattered light collected from the object. This paper investigates the performance of the laser vibrometer in the estimation of the different wave components. The results are validated by comparing the total structural intensity computed from the laser measurements with the measured input power. Results computed from measurements using PVDF sensors are also shown, and compared with the non-intrusive laser measurements.3411366375Noiseaux, D.U., Measurement of power flow in uniform beams and plates (1970) J. Accost. Soc. America, 47, pp. 238-247Pavic, G., Measurement of structure borne wave intensity, part I: Formulation of methods (1976) J. of Sound and Vibration, 49 (2), pp. 221-230Verheij, J.W., Cross-spectral density methods for measuring structure-borne power flow on beams and pipes (1980) J. of Sound and Vibration, 70, pp. 133-139Bauman, P.D., Measurement of structural intensity: Analytic and experimental evaluation of various techniques for the case of flexural waves in one-dimensional structures (1994) J. of Sound and Vibration, 174 (5), pp. 677-694Halkyard, C.R., Mace, B.R., Wave component approach to structural intensity in beams (1993) Proc. of the 4th Int. Congress on Intensity Techniques, pp. 183-190. , Senlis, France, ABerthelot, Y.H., Yang, M., Jarzinski, J., Recent progress on laser Doppler measurements in structural acoustics (1993) Proc. of the 4th Int. Congress on Intensity Techniques, pp. 199-206. , Senlis, FranceCremer, L., Heckl, M., Ungar, E.E., (1988) Structure-Borne Sound, , Berlin: SpringerBelansky, R.H., Wanser, K.H., Laser Doppler velocimetry using a bulk optic michelson interferometer: A student laboratory experiment (1993) Am. J. Phys., 61 (11), pp. 1014-1019Halliwell, N.A., Laser Doppler measurement of vibrating surfaces: A portable instrument (1979) J. of Sound and Vibration, 62 (2), pp. 312-315Riener, T.A., Goding, A.C., Talke, F.E., Measurement of head/disk spacing modulation using a two channel fiber optic laser Doppler vibrometer (1988) IEEE Transactions on Magnetics, 24 (6), pp. 2745-2747Jackson, D.A., Kersey, A.D., Lewin, A.C., Fibre gyroscope with passive quadrature detection (1984) Electronics Letters, 20 (10), pp. 399-401Goodman, J.W., Some fundamental properties of speckles (1976) J. Opt. Soc. Am., 66 (11), pp. 1145-1150Koo, K.P., Tveten, A.B., Dandridge, A., Passive stabilization scheme for fiber interferometers using (3×3) fiber directional couplers (1982) Appl. Phys. Lett., 41 (7), pp. 616-61

Immunological Balance Is Associated with Clinical Outcome after Autologous Hematopoietic Stem Cell Transplantation in Type 1 Diabetes

Transplantation and autoimmunit

Comparing Oranges And Bananas

[No abstract available]33168Gade, S., Herlufsen, H., Signals and Units (1987) B&K Technical Review, (3), pp. 29-38Papoulis, A., (1977) Signal Analysis, , McGraw-HillBendat, J.S., Piorsol, A.G., (1980) Engineering Applications of Correlation and Spectral Analysis, , J. Wiley & SonsArruda, J.R.F., Godoy, E., A peak classification technique in digital spectral analysis (1989) Proceedings of IMAC, 7, pp. 1582-1586. , Las Vegas, N

Localizing Energy Sources and Sinks in Plates Using Power Flow Maps Computed From Laser Vibrometer Measurements

This paper presents an experimental method especially adapted for the computation of structural power flow using spatially dense vibration data measured with scanning laser Doppler vibrometers. In the proposed method, the operational deflection shapes measured over the surface of the structure are curve-fitted using a two-dimensional discrete Fourier series approximation that minimizes the effects of spatial leakage. From the wavenumber-frequency domain data thus obtained, the spatial derivatives that are necessary to determine the structural power flow are easily computed. Divergence plots are then obtained from the computed intensity fields. An example consisting of a rectangular aluminum plate supported by rubber mounts and excited by a point force is used to appraise the proposed method. The proposed method is compared with more traditional finite difference methods. The proposed method was the only to allow the localization of the energy source and sinks from the experimental divergence plots

Spectral Element-based Prediction Of Active Power Flow In Timoshenko Beams

The analysis of standing waves, which correspond to the reactive part of the power in structures, is not a sufficient tool for studying structural vibration problems. Indeed, the active power component (structural intensity) has shown to be of great importance in studying damped structural vibration problems. One of the most common numerical discretization methods used in structural mechanics is the finite element method. Although this procedure has its advantages in solving dynamic problems, it also has disadvantages mainly when dealing with high frequency problems and large complex spatial structures due to the prohibitive computational cost. On the other hand, the spectral element method has the potential to overcome this kind of problem. In this paper, the formulation of the Timoshenko beam spectral element is reviewed and applied to the prediction of the structural intensity in beams. A structure of two connected beams is used. One of the beams has a higher internal dissipation factor. This factor is used to indicate damping effect and therefore causes structural power to flow through the structure. The total power flow through a cross-section of the beam is calculated and compared to the input power. The spectral element method is shown to be more suitable to model higher frequency propagation problems when compared to the finite element method.38Out/1316691679Arruda, J.R.F., Campos, J.P.R., Piva, J.I., Experimental determination of flexural power flow in beams using a modified Prony method (1996) Journal of Sound and Vibration, 197 (3), pp. 309-328Arruda, J.R.F., Campos, J.P.R., Piva, J.I., Measuring flexural power flow in beams using a spatial-domain regressive discrete Fourier series (1996) Proceedings of the 21st International Conference on Noise and Vibration Engineering, pp. 641-652. , Leuven, BelgiumCraig, R., (1981) Structural Dynamics: An Introduction to Computer Methods, , Wiley, New York, NYDoyle, J.F., (1997) Wave Propagation in Structures, , Springer, New York, NYHalkyard, C.R., Mace, B.R., A wave component approach to structural intensity in beams (1993) Proceedings of the 4th International Congress on Intensity Techniques, , Senlis, FranceHambric, S.A., Taylor, P.D., Comparison of experimental and finite element structure-borne flexural power measurement for a straight beam (1994) Journal of Sound and Vibration, 170 (5), pp. 595-605Noiseux, D.U., Measurement of power flow in uniform beams and plates (1970) Journal of the Acoustical Society of America, 47, pp. 238-247Pavic, G., Measurement of structure borne wave intensity, part I: Formulation of methods (1976) Journal of Sound and Vibration, 49 (2), pp. 221-230Verheij, J.W., Cross-spectral density methods for measuring structure-borne power flow on beams and pipes (1980) Journal of Sound and Vibration, 70, pp. 133-13