Radiation efficiency of a baffled circular plate in flexural vibration

The radiation efficiency of an edge-clamped circular plate, which is vibrating flexurally in one of its natural modes and is mounted in an infinite baffle, is theoretically determined from the total power radiated to the far field. The vibrations of the plate are investigated both by the classical plate theory and by the improved plate theory (Mindlin plate theory). Approximation formulae for the low frequency region are derived, and curves covering the entire frequency range for the first fifteen modes are obtained through numerical calculation. Except for frequencies much higher than the critical frequency, there exist some differences in the radiation efficiencies between the results obtainedby the two theories. The difference increases with the thickness of the plate and with the mode numbers, especially for modes having many nodal diameters.     

Radiation characteristics of multiple and single sound hole vihuelas and a classical guitar

Two recently built vihuelas, quasi-replicas of the Spanish Renaissance guitar, one with a small body and one sound hole and one with a large body with five sound holes, together with a classical guitar are investigated. Frequency dependent radiation strengths are measured using a 128 microphone array, back-propagating the frequency dependent sound field upon the body surface. All three instruments have a strong sound hole radiation within the low frequency range. Here the five tone holes vihuela has a much wider frequency region of strong sound hole radiation up to about 500 Hz, whereas the single hole instruments only have strong sound hole radiations up to about 300 Hz due to the enlarged radiation area of the sound holes. The strong broadband radiation of the five sound hole vihuela up to about 500 Hz is also caused by the sound hole phases, showing very consistent in-phase relations up to this frequency range. Also the radiation strength of the sound holes placed nearer to the center of the sound box are much stronger than those near the ribs, pointing to a strong position dependency of sound hole to radiation strength. The Helmholtz resonance frequency of the five sound hole vihuela is influenced by this difference in radiation strength but not by the rosettas, which only have a slight effect on the Helmholtz frequency.     

The effect of the coupling between the top plate and the fingerboard on the acoustic power radiated by a classical guitar (L)

An experimental investigation on the coupling between the fingerboard and the top plate of a classical guitar at low frequencies is presented. The study was carried out using a finished top plate under fixed boundary conditions and a commercial guitar. Radiated sound power was determined in one-third octave bands up to the band of 1 kHz based on measurements of sound intensity. The results provide evidence that the way in which the fingerboard and top plate are coupled is not a relevant factor in the radiated acoustic power of the classical guitar in the studied frequency range.     

Radiation modes of a five-layer symmetric slab waveguide

The radiation modes of a five-layered symmetric slab waveguide are treated in detail. Since the slab is assumed to be infinitely extended in the yz plane, all field quantities are considered to be independent of y. The analysis is based on modal expansion formulation and the modes can be classified as TE and TM as well as even and odd ones. Applying the boundary conditions at interfaces, the expansion coefficients of the field components are easily calculated. In addition, the normalization factors and the orthogonality properties are determined by deriving appropriate integrals over the cross section of the waveguide. Finally, the validity of the orthogonality relations between the radiation modes and the guided ones, which propagate in such a waveguide, is proved explicitly.     

A note on transverse vibrations of a rectangular plate with a free,rectangular, corner cut-out

An approximate solution to the title problem is presented, obtained by using the Rayleigh-Ritz method. The analysis is presented for the case of simply supported and clamped plates. For the case of a rigidly clamped plate results are presented of numerical experiments on minimizing the calculated value of the fundamental frequency coefficient by using Schmidt's approach. An experimental investigation is described on a clamped square plate with a free square, corner cut-out, which has led to the conclusion that the fundamental frequency coeficient remains practically invariant with respect to size when compared with the frequency coefficient of the fully clamped plate. A similar conclusion is arrived at by means of the mathematical model. The problem under consideration is important from a practical viewpoint since cut-outs of the type considered here are quite common in engineering practice.     

Radiation of cylindrical duct acoustic modes with flow mismatch

An analysis is presented for the radiation of spinning acoustic modes from a round duct. The model, based on a plug flow exhaust jet, allows for a flow temperature and velocity mismatch. Solutions to the convected wave equations within and outside the jet are devised, the continuity of acoustic pressure and particle displacement match at the jet interface being used. Formal solution is obtained by applying Fourier transforms, inversion being accomplished by using the Wiener-Hopf technique coupled with the Carrier-Koiter approximations. The analysis also is extended formally to include the inlet problem, but with a plug type inlet flow.The calculations suggest that the influence of the Mach number discontinuity is to offer a conflict between the effects of convection and refraction, the former becoming increasingly more significant at high subsonic Mach numbers by the presence of a strong lobe in the shadow zone. Effects of flight conditions are to weaken such conflicts so that in the limit of uniform Mach number, one recovers Carrier's well-known solution.The effect of a temperature mismatch is rather more dramatic, resulting in a sharp beaming of sound off to the side. This is consistent with the kinematic picture of a plane wave impinging on a temperature discontinuity.     

Lamb wave reflection at the free edge of a plate

This study concentrates on the reflection of Lamb waves at the free end of a plate. The conversion phenomena are examined in detail over a large frequency range and the energy conversion coefficients are obtained by three different ways: theoretically, numerically (finite element method) and experimentally. The experimental energy determination is obtained from the measurement of the plate normal displacements, by mean of a laser interferometer. All results are in relatively good agreement and the energy balance between incident and reflected waves is discussed in each case.     

A multi-technique chemical characterization of a Stradivari decorated violin top plate

This paper focuses on the characterization of the materials of a violin top plate made by Antonio Stradivari (17th century), with different diagnostic techniques and with an integrated and non-destructive analytical methodology to study surface coatings and decorations. The UV-induced visible fluorescence, optical digital microscopy, ED-XRF associated with micro-FTIR spectroscopy analysis, and dendrochronology were performed. The investigations were aimed to identify the presence of original varnish layers and to characterize the composition of the decorations, either the inlaid purflings or the composite false-inlay strip between them. Several results were achieved: (i) evidence of the absence of varnish layers on the surface as a result of extended and inappropriate restoring; (ii) identification of the dye used for the black layers of the purflings; (iii) characterization of the black matrix and the white elements of the decoration. Furthermore, a dendrochronological dating was performed. A copy of the top plate was realized with materials similar to those identified on the Stradivari original; the same analyses performed on the original model were carried out on the same areas of the copy.     

The binaural performance of a cross-talk cancellation system with matched or mismatched setup and playback acoustics

Cross-talk cancellation is a method for synthesizing virtual auditory space using loudspeakers. One implementation is the "Optimal Source Distribution" technique [T. Takeuchi and P. Nelson, J. Acoust. Soc. Am. 112, 2786-2797 (2002)], in which the audio bandwidth is split across three pairs of loudspeakers, placed at azimuths of +/-90 degrees, +/-15 degrees, and +/-3 degrees, conveying low, mid, and high frequencies, respectively. A computational simulation of this system was developed and verified against measurements made on an acoustic system using a manikin. Both the acoustic system and the simulation gave a wideband average cancellation of almost 25 dB. The simulation showed that when there was a mismatch between the head-related transfer functions used to set up the system and those of the final listener, the cancellation was reduced to an average of 13 dB. Moreover, in this case the binaural interaural time differences and interaural level differences delivered by the simulation of the optimal source distribution (OSD) system often differed from the target values. It is concluded that only when the OSD system is set up with "matched" head-related transfer functions can it deliver accurate binaural cues.     

Thickness-shear modes and magnetoelastic waves in a longitudinally magnetized ferromagnetic plate

Magnetoelastic (ME) waves and thickness-shear modes in the ferromagnetic plate are studied. Coupled vibrations of magnetization and shear elastic deformations excited simultaneously by a variable magnetic field propagate in two mutually perpendicular directions: parallel and normal to a surface. For parameters characteristic of isotropic ferromagnet with the sample magnetization and Zeeman field parallel to the surface, resonant frequencies of shear modes are computed and their dispersion law is examined. It is shown that the dependence of dimensional resonances frequencies on wave number k_z of ME wave propagating along saturating field direction occurs. The possibility of excitation of ME waves with different k_z explains multimode character of thickness ME resonances.     

Vibrating rectangular plate with a free edge: The effect of a concentrated mass and an internal support

It is shown that use of a polynomial coordinate function and the Rayleigh-Schmidt method constitute a convenient approach for determining the fundamental frequency of vibration of the title system. Experimental results are presented for the case where three edges are rigidly clamped; and it is shown that the values are in good engineering agreement with the analytical predictions.     

Exact solutions of in-plane natural vibration of a circular plate with outer edge restrained elastically

We solve exactly the equations of in-plane natural vibration for a circular plate whose outer edge is restrained elastically. The mode shapes are represented by trigonometric functions with a number of nodal diameters in the circumferential direction and mode functions in the radial direction. We present the exact frequency equations and mode functions and tabulate the frequency parameters satisfying the frequency equations. The corresponding mode functions and two-dimensional mode shapes are illustrated when both radial and tangential stiffness are zero (free edge), infinity (clamped edge), or medium. Comparisons with previous reported results confirm the accuracy of the present work.     

Radiation from modes of a rectangular panel into a coupled fluid layer

Modal radiation efficiencies are evaluation for a rectangular panel which is simply supported in an infinite baffle and coupled to a fluid layer. The analysis is based on the calculation of the acoustic power radiated into the layer by the panel vibrating in one of its in vacuo natural modes. At low frequencies, the efficiency is inversely proportional to the layer depth; at high frequencies, it exhibits a complex, multiple peak characteristic, associated with the acoustic field of the layer. Comparison with the modal radiation efficiencies of a panel coupled to a fluid half-space shows a similar dependence on mode order and panel dimensions.