Measurement of vibrational energy flow in a plate with high energy flow boundary crossing using electronic speckle pattern interferometry

Abstract

Citation: ECK, T. and WALSH, S.J., 2012. Measurement of vibrational energy flow in a plate with high energy flow boundary crossing using electronic speckle pattern interferometry. Applied Acoustics, 73 (9), pp. [936][937][938][939][940][941][942][943][944][945][946][947][948][949][950][951] Additional Information:• This article has been published in the journal, Applied Acous- ABSTRACTThe measurement of vibrational energy flow is an important tool in understanding the vibrational behaviour of structures. In the past, because of transducer constraints, the measurement of vibrational energy flow was mostly restricted to single point measurements. However, recent developments in advanced laser measurement techniques, such as electronic speckle pattern interferometry (ESPI), have gained interest in applying two-dimensional, multi-point measurement techniques to the estimation of vibrational energy flow. This paper addresses the measurement of vibrational energy flow in a plate by using an ESPI based vibrational energy flow measurement technique. A radially symmetric bending wave plate vibration model is introduced and theoretical expressions for energybased quantities are derived. To assess the accuracy of the measurement method, these theoretical quantities are compared to synthetic results derived from the ESPI energy flow measurement technique. The ESPI measurement technique is also applied to an experimental 'infinite' plate. Thus, a specially designed experimental apparatus was constructed so as to minimise undesired wave reflections in the plate and, thus, achieve a high energy flow boundary crossing at the edges of the plate. To reduce the effect of optical noise contamination on the ESPI measured out-of-plane plate displacement data, optimal filters were applied prior to the vibrational energy flow computation. To appraise the accuracy of the experimental method, measured vibrational power on the plate is compared with measured vibrational input power. A difference of less than 1 dB between both quantities indicates that vibrational energy flow within a rectangular plate that contains radially symmetric wave propagation can be measured to a good degree of accuracy if appropriate filtering is applied.

Structural intensity analysis of flat plates based on digital stroboscopic holography measurements

“…A low-pass filter is applied to the data in the wavenumber domain to attenuate the amplification of measurement noise. The combination of this spatial derivation with filtering was shown to be less susceptible to corrupted data, when compared to its finite-difference concept counterpart [3][4][5]8,26,27]. The low-pass filter developed by Li et al [28] is used in the present work.…”

“…The Eqs. (2)(3)(4)(5)(6)(7)(8)(9)(10)(11) were implemented as if the plate was homogeneous with respect to the thickness and stiffness, i.e., = 69 GPa and ℎ = 5 mm. The displacement fields' derivatives were carried out with a cut-off wavenumber equal to the ones used on the experimental data ( =315 rad/m) and the energy paths were estimated ( Figure A.3).…”

“…The main limitation of such an approach is that it alters the system's behavior due to the added mass of the transducer. Later, non-contact methods which do not add mass to the measured structure were used to detect surface motions, i.e., the Laser Doppler Vibrometry (LDV) [3][4][5][6], acoustic-holography [7], electronic speckle interferometry [8] or holographic interferometry [9]. These techniques are not only non-contact but also allow the measured displacement or velocity fields to be recorded with higher spatial resolution than the mentioned pioneering studies.…”

“…These techniques are not only non-contact but also allow the measured displacement or velocity fields to be recorded with higher spatial resolution than the mentioned pioneering studies. Moreover, the grid sizes from non-contact measurements found in literature vary from 165 (15 x 11) [10] to 15876 (126 x 126) [8] measurement points.…”

Structural intensity analysis of stepped thickness rectangular plates utilizing the finite element method

“…In this context it is also worthy to mention frequency response technique introduced by Linjama and Lahti [12], near-field acoustical holography presented by Saijyou and Yoshikawa [13], and scanning laser vibrometer presented by Pascal et al [14]. Eck and Walsh [15] used electronic speckle pattern interferometry to measure vibrational energy flow in a plate with high energy flow boundary crossing, while Mandal et al [16] performed experimental investigation of power flow in thin technical orthotropic plates in frequency domain by the twotransducer method, using the cross-spectra of acceleration signals. In the context of numerical models, application of the finite element (FE) method using the normal mode approach to SI analysis of structures is illustrated for a simply supported plate by Gavric and Pavic [17].…”