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.

Jos&#xe9; Roberto de Fran&#xe7;a Arruda

S&#xe9;rgio Augusto Vianna do Rio

Luiz Antonio Silva Bernardes Santos

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

Different arrangements for double-pulsed holographic and speckle interferometry for vibration analysis will be described. Experimental results obtained with films (classical holographic interferometry) and CCD cameras (digital holographic interferometry) as storage materials are presented. In digital holography, two separate holograms of an object under test are recorded within a few microseconds using a CCD camera and are stored in a frame grabber. The phases of the two reconstructed wave fields are calculated from the complex amplitudes. The deformation is obtained from the phase difference. In the case of electronic speckle pattern interferometry (or image plane hologram), the phase can be calculated by using the sinusoid-fitting method. In the case of digital holographic interferometry, the phase is obtained by digital reconstruction of the complex amplitudes of the wave fronts. Using three directions of illumination and one direction of observation, all the information necessary for the reconstruction of the 3-dimensional deformation vector can be recorded at the same time. Applications of the method for measuring rotating objects are discussed where a derotator needs to be used.

H.J. Tiziani

G. Pedrini

Digital Double-Pulse Holographic Interferometry for Vibration Analysis

Two types of exciters were investigated experimentally One of the exciters uses a small permanent magnet fastened on the object. The force is introduced by the change in the electromagnetic field from a coil via an air gap. The second exciter is an eddy-current electromagnet one. The amplitude of the forces from these exciters are calibrated by using dynamic reciprocity in conjunction with electronic holography. These forces strongly depend upon the distance between the exciter and the object.

Henrik O. Saldner

Calibrated Noncontact Exciters for Optical Modal Analysis

This article discusses computing methods of the equivalent modal damping ratio for a composite tube-type tall building. The equivalent damping ratio of a composite structure under wind-induced vibrations encompasses the combined effects from the different values of damping, mass, and stiffness of the external and internal tubes. A detailed method incorporating Rayleigh damping and the transfer matrix method is proposed for the determination of the equivalent modal damping ratio. A simplified method for engineering applications is also proposed. Results for a 40-story building are presented exemplifying the computation and relationships between the properties of the external and internal tubes.

B.C. Huang

K.M. Lam

A.Y.T. Leung

Y.K. Cheung

Equivalent Modal Damping Ratios of a Composite Tube-Type Tall Building to Dynamic Wind Loading

A detailed solution to the transient interaction of plane acoustic waves with a spherical elastic shell was obtained more than a quarter of a century ago based on the classical separation of variables, series expansion, and Laplace transform techniques. An eight-term summation of the time history series was sufficient for the convergence of the shell deflection and strain, and to a lesser degree, the shell velocity. Since then, the results have been used routinely for validation of solution techniques and computer methods for the evaluation of underwater explosion response of submerged structures. By utilizing modern algorithms and exploiting recent advances of computer capacities and floating point mathematics, sufficient terms of the inverse Laplace transform series solution can now be accurately computed. Together with the application of the Cesaro summation using up to 70 terms of the series, two primary deficiencies of the previous solution are now remedied: meaningful time histories of higher time derivative data such as acceleration and pressure are now generated using a sufficient number of terms in the series; and uniform convergence around the discontinuous step wave front is now obtained, completely eradicating spurious oscillations due to the Gibbs' phenomenon. New results of time histories of response items of interest are presented.

Hanson Huang

Hans U. Mair

Neoclassical Solution of Transient Interaction of Plane Acoustic Waves with a Spherical Elastic Shell

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;

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Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.

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Shock and Vibration - Table of contents 1996

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience. 

Shock and Vibration