J.R.F. Arruda

A Space-Frequency Data Compression Method for Spatially Dense Laser Doppler Vibrometer Measurements

When spatially dense mobility shapes are measured with scanning laser Doppler vibrometers, it is often impractical to use phase-separation modal parameter estimation methods due to the excessive number of highly coupled modes and to the prohibitive computational cost of processing huge amounts of data. To deal with this problem, a data compression method using Chebychev polynomial approximation in the frequency domain and two-dimensional discrete Fourier series approximation in the spatial domain, is proposed in this article. The proposed space-frequency regressive approach was implemented and verified using a numerical simulation of a free-free-free-free suspended rectangular aluminum plate. To make the simulation more realistic, the mobility shapes were synthesized by modal superposition using mode shapes obtained experimentally with a scanning laser Doppler vibrometer. A reduced and smoothed model, which takes advantage of the sinusoidal spatial pattern of structural mobility shapes and the polynomial frequency-domain pattern of the mobility shapes, is obtained. From the reduced model, smoothed curves with any desired frequency and spatial resolution can he produced whenever necessary. The procedure can he used either to generate nonmodal models or to compress the measured data prior to modal parameter extraction.

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.

Design of a reduced–order H∞ controller for smart structure satellite applications

In this paper, the design of a low–order controller for a high–order, smart–structural system is presented. The application considered here is a model of a solar panel dynamically similar to those used on satellites. Smart structure refers here to the use of integrated piezoceramic materials as sensors and actuators in the structural system in order to implement the control. The analytical contribution is made by extending the well–known robust control theory by relating the high–frequency robustness condition to the residual uncertainty, removing a trial–and–error step in the normal robust–control design. The procedure is applied experimentally to a half–metre long frame that is coupled in bending and torsion, verifying that the technique is viable for a reasonably complex structure.

Monopole and Dipole Identification Using Generalized Inverse Beamforming

Aeroacoustic problems pose some challenges to the conventional techniques normally used to source localization and identification. The main difficulties are that sources are normally distributed, with coherent and incoherent regions, and with simultaneous mono and multipole radiation patterns. Among the most recent ones, the Generalized Inverse Beamforming method has the promise to meet these challenges. In this paper, the potential for identification of compact sources in close vicinity, similar to a distributed source, and the potential to identify a dipole center and orientation, induced by two compact sources, are illustrated in two no-flow tests. Results obtained in semi-anechoic room are compared to numerical prediction, and the generalized inverse beamforming performance compared to the conventional beamforming results. This validation is a preparation for the application of the method to aeroacoustic problems.

Comparison of estimation techniques for vibro-acoustic transfer path analysis

Vibro-acoustic Transfer Path Analysis (TPA) is a tool to evaluate the contribution of different energy propagation paths between a source and a receiver, linked to each other by a number of connections. TPA is typically used to quantify and rank the relative importance of these paths in a given frequency band, determining the most significant one to the receiver. Basically, two quantities have to be determined for TPA: the operational forces at each transfer path and the Frequency Response Functions (FRF) of these paths. The FRF are obtained either experimentally or analytically, and the influence of the mechanical impedance of the source can be taken into account or not. The operational forces can be directly obtained from measurements using force transducers or indirectly estimated from auxiliary response measurements. Two methods to obtain the operational forces indirectly - the Complex Stiffness Method (CSM) and the Matrix Inversion Method (MIM) - associated with two possible configurations to determine the FRF - including and excluding the source impedance - are presented and discussed in this paper. The effect of weak and strong coupling among the paths is also commented considering the techniques previously presented. The main conclusion is that, with the source removed, CSM gives more accurate results. On the other hand, with the source present, MIM is preferable. In the latter case, CSM should be used only if there is a high impedance mismatch between the source and the receiver. Both methods are not affected by a higher or lower degree of coupling among the transfer paths.

Predicting and measuring flexural power flow in plates

Structural power flow is an alternative way of analyzing vibrations, where, differently from traditional techniques, the emphasis is put on the active part of the vibration energy instead of the total. The active vibration energy is directly related to the injection and dissipation of energy in the structure and can, therefore, be a valuable tool for solving vibroacoustical problems. However, measuring the active part of the vibration energy in the presence of a highly reverberant field is often impractical. 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, an operational deflection shape measured over the surface of the structure is curve-fitted using a 2D discrete Fourier series approximation. This approximation minimizes the effects of spatial leakage. From the wavenumber-frequency domain data thus obtained, it is straightforward to compute the spatial derivatives that are necessary to determine the structural power flow. An example consisting of a rectangular aluminum plate supported by four rubber mounts and excited by an electrodynamic shakes is used to appraise the proposed method. Both numerically simulated data and experimental data are used.

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 types 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 their contribution to the total structural power flowing through the beam. In this paper, a twisted z-shaped beam is used in order to allow the three types of waves to propagate. The contributions of the structural intensity, due to these waves, are computed from measurements taken over the surface of the beam with a simple homodyne interferometric laser vibrometer. The optical sensor incorporates some polarizing optics, additional 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 nearly all back-scattered light collected from the object to be detect. 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.

Active Control of the Structural Intensity in Beams Using a Frequency-Domain Adaptive Method

This paper presents an active control method which consists of minimizing the active part of the structural intensity aiming at reducing the overall vibration level in beams. The basic idea behind this strategy is that the control forces dissipate the input power due to the perturbing forces, thus preventing the structure from having to vibrate in order to dissipate the incoming energy. A frequency-domain adaptive structural intensity control method (ASIC) is used. The method is investigated using a simple example consisting of an aluminum beam which is fitted at one end with a quasi-anechoic termination (sandbox) and has the other end free. Numerically simulated and experimental results are presented. The numerical simulation uses a state-space model which was identified using experimental data. Results are compared with those obtained minimizing measured vibration directly, and with results using the instantaneous wave amplitudes as error signals in time-domain LMS control schemes. In the preliminary experimental results, the ASIC method and the method that controls the wave amplitudes outperformed one another at different frequencies. At frequencies where the power-flow-based methods performed well, their performance was equivalent to that of the direct control of vibrations. The relative advantages and disadvantages of the different control methods are discussed.

Multisine multiexcitation in frequency response function estimation

Introduction T RUE random single excitation has been widely used in frequency response function (FRF) estimation. It reduces test times when compared to swept or stepped sinusoidal excitation. Transient excitation presents the same advantage, but it has handicaps related to digital signal processing difficulties and difficulties in supplying enough energy in a short period of time without causing nonlinear behavior due to high force amplitudes. When true random excitation is used, averaging is mandatory due to the stochastic character of the signals. Furthermore, some sort of windowing is necessary to reduce leakage in the discrete Fourier transform (DFT). In vibration analysis problems where stochastic phenomena are present, random signal processing techniques are unavoidable. However, this is usually not the case in modal testing, where multifrequency excitation, rather than random excitation, is desired. For this purpose, it is much more reasonable to synthesize an excitation signal by adding sinusoids of arbitrary amplitudes. Synthesized excitation signals may be generated numerically and then sent to a digital-to-analog converter, which produces an analog signal to drive a shaker. This signal may be made periodic with a period equal to the observation window, so that its DFT is leakage-free. It can also be made transient, in which case it is desirable that both the excitation and the response signals vanish within the observation window. Such signals have been called pseudorandom, periodic random, or chirp in the former case, and burst random or burst chirp in the latter. More recently, a generalized approach was given to this problem after the work of Schroeder, which was first used in mechanical system identification by Burrows. True random signals have nonetheless continued to be used in FRF estimation in the case of simultaneous broadband multiexcitation. Otherwise, in modern stepped sine multiexcitation methods, the phase is usually random. It will be shown in this paper that the same results can be obtained using Schroeder-phased multisine excitation signals with linearly independent sets of constant phases.

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.