Time-domain analysis of the energy exchange between structural vibrations and acoustic radiation using near-field acoustical holography measurements

Abstract

The vibrational energy in a structure and the radiated acoustic energy are analyzed in the time domain using data from near-field acoustical holography measurements. A signal processing method is described that uses data from a single broadband acoustical holography measurement to determine the structural and acoustic responses for synthetic forces different from the original measurement force. The processing is based on the assumption that the measured acoustic pressure and particle velocity are related to the drive force by a linear shift invariant transfer function. Finite time length synthetic forces are examined for measurements from a fluid-loaded, point-driven, finite cylindrical shell. Comparisons of the amount of energy input to the structure by the driver, the energy injected into the fluid near field, and the energy radiated to the fluid far field show large amounts of energy that enter the fluid near field while the drive force is on, but then re-enter the structure where it is damped once the drive force is turned off. We are also able to see the rate that energy radiates to the acoustic far field and the areas of the structure which contribute most significantly to the far-field radiation. Results show that approximately 50% of the far-field energy is radiated during the active time of a transient driving force.

Structural wave propagation and sound radiation study through time and spatial processing

“…The field quantity y{t, x, xg) (acoustic pressure or particle velocity at position x in the fluid due to the force at ZQ on the structure) can be related to the drive force by the transfer function h{T,x,XQ), which is also referred to as the impulse response function. Note that h{T,x,XQ) only relates the drive force at xq to a particular field point x; thus /i(t, X, sq) is needed for every spatial location of interest [13].…”

“…It can be concluded that analyzing wave propagation and sound radiation in the time domain provides a powerful means to identify and understand phenomena. For example, the speed at which waves propagate in a structure can be determined [14], and the sound radiation resulting from a particular incident wave on a discontinuity can be seen and quantified [13]. Also the influence of different forcing functions on the response of a structure can be studied [13].…”

“…Due to the nature of practical data acquisition, some measures need to be taken in order to prevent errors resulting from improper data processing. The measures that are taken are explained in detail by Mann et al [13] and Kruger [15], so they will only be summarized here.…”

“…Zero-padding extends the aperture of the original signal by adding zeros to the time history. In this study, zero-padding was applied to the time signal to double its original length [13]. The impulse response and synthetic force spectra were first inverse Fourier transformed to time where zeros were added.…”

Forward projection of transient sound pressure fields radiated by impacted plates using numerical Laplace transform

“…This can be attributed to the use of direct and inverse time domain discrete Fourier transforms ͑DFTs͒ involved in the standard NAH formulation, leading to time aliasing errors in the propagated signals if the initial data are not properly padded with zeros. 7 Aliasing errors are negligible for sound pressure signals much shorter than the observation time window. The sound pressure radiated by the loudspeakers or the transducer mentioned above are examples of very short signals.…”